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Produced by the NASA Center for Aerospace Information (CASI) https://ntrs.nasa.gov/search.jsp?R=19750021913 2020-03-22T20:54:56+00:00Z 0 EE•M C-; bL H WW Final Report ML CALCULATIONS FOR !N!TERPRETATICIN OF SOLAR 'VECTOR ACNETOCRAPH DATA U) U CU I Ln I—z U) w ^ N rn w •o M u, 101 1.4 CU I- V V U)V(f) W Z >. w w C^ b 4 va I r— U) w ^ U ^ HVv` .^ D •rl p w +^ Q^ V ra: V W rl ►-I U G Peu V V I/1 • ^ +r ^ w w+ w ^. V U Ui w q CL) z w x w V try U J H N c V N •-1 W H C 4lw.tl V 1r w >. I L14 b I1 134 RC r' a: r+ r+ v zZ4E•+ M BROWN ENGINEERING Cummings Research Park • Huntsville, Alabama 35807 4qj fFINAL REPORT j EE -MSFC -1900 1^ J, i a j CALCULATIONS FOR INTERPRETATION OF SOLAR VECTOR MAGNETOGRAPH DATA a x^ I , By Ll 3 k ; A. R. Dunn, Ph. D. x ni r F, rIlk- Ll1 r May 1975 tiS i E Prepared For f ,:k ELECTROMAGNETIC AND'SOLID STATE_ DIVISION SPACE SCIENCES LABORATORY GEORGE C. MARSHALL SPACE FLIGHT CENTER R HUNTSVILLE, ALABAMA Contract No. NAS8 -2 6376 s Prepared By - RESEARCH DEPARTMENT ELECTRONICS AND ENGINEERING TELEDYNE BROWN ENGINEERING HUNTSVILLE, ALABAMA t !1 tP ABSTRACT This report ,describes the work which has been done on Contract No. NAS8-26376 between October 1,970 and May 1975. The report is divided into three self-contained sections, each dealing with ;a separate portion of the performance period. In Section_ 1, the work done between October 1970 and October 1971 is discussed. Section 2 covers the period from October 1971 to June 1973. Section 3 covers the period from June 1973 to May 1975 APPROVED I ^ lain r Ian i ti s i .a f SECTION 1 ANALYSIS OF SUNSPOT 3a.. S PECTRAL DATA ft^ i iaTABLE OF CONTENTS x: F F page C INTRODUCTION . . . . . . . . . . . - 5 ? SUNSPOT SPECTRUM OBSERVATIONS . . . . . . . 6 REDUCTION OF THORIUM CALIBRATION WAVELENGTHS TO STANDARD CONDITIONS . . . . . . . . . . . . . 12 t LINE PROFILE DATA REDUCTION PROGRAM . . . . . . . 1.6 MAGNETIC FIELD STRENGTH DETERMINATIONS FROM THE 5, 2 50'. 216 LINE . . . . . . . . . . . . . . . . 28 ,ra The Iron Line at 5, 2 50.216 A . . . . . 29 ^^r) Preliminary Determination of Sunspot Magnetic Field 31 1 Detailed Magnetic Field Determination . . . . . 34 REFERENCES - SECTION 1 . . . . 3 F ; 4 a i 2 9 Y I^ h i LIST OF ILLUSTRATIONS I ^ . Figure Title Page 1 Microdensitometry Pattern for Sunspot Observations . . . . . . . . . . . . . . . 10 2 Edlen Correction to Measured Wavelengths 14 3 Listing of Line Profile Reduction Program 17 4 Field Strength Program . . . . . . . . . . 32 5 Line-of-Sight Field Strengths in Gauss,g g Ll Observations of 14 July 1969 . . . . . 33 6 Summary of Magnetic Field Calculation . . . . 35 I 4 r i 1 4 Ll _ r ti r s a - 3 fill. ! INTRODUCTION a Observations of the profile of the neutral iron line at 0. 5250216 o micrometer (5, 250. 216 ) are described in this section. The reduction of the observations to obtain residual intensities, line widths, and the lu locations of the Zeeman components is discussed. The components of magnetic field strength along the line of sight are determined and plotted ..-> in the form of a sunspot map. Finally, the steps to be followed in a s more complete analysis of the data are outlined. t L LI t f t 5 ISUNSPOT SPECTRUM OBSERVATIONS This section describes the analysis of sunspot spectral observa- tions made during July 1969 by Dr. M. J. Hagyard with the spectrograph of the McMath solar telescope at the Kitt Peak National Observatory. (The spectrograph and telescope are described in Reference 1). Although both photographic and photoelectric observations were made, the photo- graphic data are of primary interest here. Because the spectra were intended for Zeeman effect studies, the polarization form of the observed intensity had to be known. A partial linear polarization is introduced within the telescope in the reflection at the primary mirror; this was compensated in the observations by placing a glass flat in the light path. The only remaining instrumental effect is then a possible phase shift introduced at the primary. Such a phase shift would not be detectable in the results before a more advanced stage in the analysis- is reached. In order to check for residual instrumental polarization, photoelectric and photographic observations were made of the photosphere, which should be intrinsically unpolarized. Photospheric - d intensities were measured in right and left circularly polarized light and in light linearly polarized at 0, 45, and 90 degrees to the entrance slit. 3: x No dependence of intensity upon polarization form was observed for any of the photospheric observations; residual instrumental polarization is, therefore, negligible. Control over the polarization form of the observed light was achieved by placing polarizers_in front of the spectrograph slit. The s slit was always parallel to the east-west direction on the Sun. Immedi;- ately preceding the slit was a calcite analyzer oriented to pass only those light components which were linearly polarized parallel to the slit. The calcite analyzer was preceded by a soleil compensator, which can be adjusted to form a quarter-wave or a half-wave plate. The form of j1 t l^r 6 Fa polarization transmitted is defined by specifying the angle a between the compensator's axis and the transmission direction of the calcite analyzer. Y The polarization forms transmitted by the compensator-analyzer com- bination are summarized in Table 1; the sequence numbers 1 through 5 were used to identify the combinations throughout the observations. 3 amR Bit A predisperser was used to eliminate overlapping orders. The slit width was 0. 1 millimeter for all observations; the effective slit length was determined by the soleil compensator setting. The exposure times were either 6 or 12 seconds, and stepwedge calibrations were made for both these exposure times. All the spectra discussed in this w. report were photographed on 14 July 1969 between 2:40 and 3:15 p, m. C blended in those two references were investigated further. In Table 3, "t "UA" signifies Utrecht Atlas; "KPNO", the Kitt Peak photographic f spectra; and "MMH", the Moore, Minnaert, and Houtgast solar wave- length table (Ref. 2). The spectral line identifications in this 'last reference are useful for detecting and identifying, blends. 1 It must be emphasized that probably no strong line can be found to be entirely frt. a of blends in sunspots because of the large number of molecular lines which can form under these conditions. The presence Eof weak blended lines therefore cannot disqualify a spectral line for magnetograph use. Li Spectral lines at greater distances from X5250 also might be ^`) y considered. Some interest now exists in the polarization of lines in the near infrared (Ref. 19), but these would not be suitable for use in { a magnetograph located near sea level because of the strong telluric absorption by water vapor at long wavelengths. Harvey (Ref. 20) has ? published a list of lines with large Zeeman splittings, which could be .r 57 dTABLE 3. PRELIMINARY SURVEY OF SPECTRAL LINES NEAR 5200 ANGSTROMS- WAYELENGTH (A) RESULT Of BLEND STUDY CONCLUSION 5082.351 KPNO and UA spectra suggest blends are not serious; according to MMH, Probably best avoided because of (Nil, multiplet number 130) it may be blended in the wings with lines of C 2 -and-KV small splitting and weakness in sunspots e g12 = 39 x 10- 30 cm2 ,( von Kluber)- • Transition; z 3 P° - e 3P1 Excitation potential of lower level = 3.642 electron volts • According to von Kluber, line is weakened in ,sunspots 5145.104 Both KPNO,and UA spectra show serious blends Not usable 5202.351 KPNO spectrum shows serious blend-, confirmed by MMH Not usable 5215.190 UA spectrum shows blend in red wing; continuum is depressed in this Not usable (FeI, multiplet number 553) region. • Transition: z SDi - e 5D3 • Excitation potential of lower level = 3.26 electron volts 5217,398 Profile looks fairly clean in UA and KPNO spectra; MNH suggests Probably could be used but is not (FeI, multiplet number 553) possible blend _ a good choice because of small splitting (see entry for x5263) • 912 = 41 x 10-10 cm2 _ • Transition: z 5D04 - e SD, • Excitation potential of lower level = 3.197 electron volts 5229.862 Profile looks clean in UA but KPNO spectrum shows possible blend Probably could be used but is not (FeI, multiplet numbers 553, 1090) in red wing a good choice because of small splitting (see entry for X5263) • gX2 = 41 X 10-10 cm2 • Transition: z sDi - e 'De • Excitation potential of lower level = 3.269 electron volts 5247.576 • gat = 69 x 10' 30 cm2 This line has no advantages over (CrI, multiplet number 18) 15250 • Transition: a 5D - z sPi @ Excitation potential of lower level = 0.957 electron volts This line, like 15250, would be an excellent magnetograph line if it had a higher excitation potential. Attempts to calculate absorption profiles for sunspot models have shown that a profile cannot be defined for the same reasons that profiles are not defined for 15250. r ^ .,.......o- r.^ .w:...,..., p U'l .p WAVELENGTH (A°) RESULT OF BLEND STUDY CONCLUSION 5253.470 Appearance of profile is good in UA and KPNO spectra; MMH shows blends Splitting may be too small for(Fe1, multiplet number 553 ) with two faint lines line to be a good choice. It is probably usable. 9X2 = 41 x 10-30 cm' • Transition: z 5Di - e 5D, e Excitation potential of lower level = 3.27 electron volts Zeeman splitting is not detectable in the KPNO spectrum, For a field of 2000 gauss, the value of oa H lshould be about 38 milliangstroms, compared to about 90 milliangstrom for X6173 for about the same field 1 strength. If a AX H as small as 2.5 milliangstroms could be resolved, the lower limit on measurable field strength would be about 130 gauss. 5263.316 Appears badly blended in UA and KPNO spectra Not usable 5273.172 Appears badly blended in UA and KPNO spectra Not usable 5283.631 Appears badly blended in UA and KPNO spectra Not usable 5302.309 Profile looks clean in UA but KPNO spectrum appears blended Not usable because of conspicuous (FeI, multiplet number 553) blend in sunspots and smallgX 2 = 42 x 10' io '^m2 splitting • Transition: z 5D01 - e SD2 • Excitation potential of lower level = 3.269 electron volts 5324.193 Profile looks clean in UA but appears to be blended with a weak line, Probably usable. (This is the line (FeI, multiplet number 553) possibly Cr 1, in KPNO used by the Aerospace Corporation magnetograph.) • nX2 = 42.5 x 10'10 cm2 r Transition: z 5D40 - e 504 • Excitation potential of lower level = 3.20 electron volts For a field of 2000 gauss, AX H = 39.6 milliangstroms 5339.939 Profile looks blended in both UA and KPNO spectra Not usable 5393.178 Profile looks blended in both UA and KPNO spectra, confirmed by MMH Not usable (FeI, multiplet number 553) rIt examined. Zwaan and Buurman have compiled a list of sunspot lines which are very weak in the photosphere and which therefore should not be distorted in shape by the effects of stray light. This list does not appear to have been published. One of the lines listed, according to Reference 21, is 16064.626 of neutral titanium. Another relevant 1reference is Reference 22, in which Wittmann reports the results of examining a number of red lines for the presence of blends. This material would form a starting point for a more extensive search of the I solar spectrum. a f G! 31 1 f, xl Y^i s^+ I f iR } I r 4 -60 SOURCES OF ERROR FOR SOLAR MAGNETOGRAPH E EFFECTS WHICH DEPEND SOLELY ON POSITION ON THE SOLAR DISK i r! As is well known, the radiation observed at the center of the solar disk characterizes a greater range in depth than that observed i. at the limb. A crude numerical estimate of this effect can be made by using the Eddington-Barbier relation, k Te = cos 8 = µ , LI where Te represents the maximum optical depth in the solar atmosphere Fi ± which can be observed at solar position angle A . ` Y ( Since the geometrical depth, d, in the atmosphere is approxi- I L mately proportional to the log of the optical depth, 3 a; dph _ Kph log -rph dpe - Kpe log Tpe _du = Ku log Tu where ph - photosphere Y pe - penumbra IJ u - umbra.r # tf C x i 61 Kph * Kpe 0 Ku In general, _Ph * dp e 0 du - The approximate form of the relation between d and µ across the solar disk can be shown by letting K = 1. The zero point in the geo- metrical depth scale is arbitrary; here it has been chosen so that d 1 at p 1, which is the deepest level observed. d 1.00 1.00 0.90 0.955 0.80 0.903 0.70 0.846 0.60 0.779 Increasing 0.50 0 . 700 depth 0.40 0.603 0.31 0 - 0.'478 0.20 0.301 0.10 0.000 Thus, for a given solar feature the depth observed at 0. 5 will be about 0. 7 of that observed at µ = 1. This property can be very. useful, since it allows a partial determination of the variation of observ- able quantities with depth in the Sun. Foreshortening toward the limb will tend- to decrease the spatial resolution of the observations. The magnetograph aperture has a pro- jected size of about 5 minutes of arc square, at the distance of the Sun from the Earth. The aperture will accept a distance on the Sun at the VIE VT 62 ^1^ H L j a i'. T I n 5 d .. ff'. t^ L ff center of the disk of 2. 17 X 10 5 kilometers. If the aperture is placed so that its outer edge is just at the limb, the linear distance it subtends on the Sun becomes 5. 84 X 10 5 kilometers, or more than two and one- half times as large as at the disk center. Finally, any observation using line profiles will be affected to some extent by the tendency of profiles to broaden and flatten toward the solar limb. This tendency should not be reflected in the degree of polarization in the profile, so the effect for a polarization magnetograph will be mostly that of reducing the signal level somewhat, since both the brightness of the Sun and the depth of the line profile, which provides contrast, are reduced. The "limb darkening" is observed to be smaller in the umbrae of sunspots than in the photosphere; the photospheric and penumbral limb darkening are approximately the same. EFFECTS CAUSED BY CHANGES IN STRENGTH AND SHAPE OF LINE PROFILE One assumption which is implicit in the entire magnetograph design and operation is that the line absorption coefficient in each ofg P rP 3 a the Stokes parameters is identical to the line absorption coefficient in i the absence of a magnetic field, although it may be shifted in wavelength by an amount which corresponds to the Zeeman splitting. Knowledge of the form of the line absorption coefficient is,, in principle, sufficient to determine the shape and strength of the line profile corresponding to a transition between known levels in a model atmosphere of known proper- ties; therefore, the interpretation of the magnetograph results can be derived from the properties of the line profile thus determined. It ,! follows that anything which alters the shape cz strength of the line pro- file on the Sun will affect the interpretation of the magnetograph; measurements. 1 63 'f ..r The profile of X5250.216 is particularly susceptible to altera- tion by varying local conditions on the Sun. Since determining and using a separate magnetograph calibration for each of these local areas is difficult, an average calibration usually is used. The local variations will then result in errors when the average calibration is used to inter- pret results in the variant regions. The local variations can be dependent on time and on position of the solar disk. They also vary in magnitude. A quantitative estimate of their effects is almost impossible to achieve, but qualitative descrip- tions can be given. The effect ors line profiles of motion of the solar gas is well known. If the scale of the motion is small compared to the range of s depths over which the lines are formed (microturbulence), the line profile is broadened and its equivalent width is increased. If the scale of the motion is large compared to the range of line-formation depths (macroturbulence), the profile is broadened but its equivalent width is unchanged. Large-scale motions may also shift the entire profile in wavelength or cause it to become asymmetrical. The turbulence p _.., Aeffects depend upon posit-.on on the solar disk: the profiles tend to broaden and flatten toward the limb. The normal variation toward the limb can be determined and compensated for in the reduction and analysis. (If it is not compen- sated, errors of residual intensity of 0. 10 or more -- 10 percent of the continuum value -- can result.) In a system which uses a filter to isolate the line, and does not have an entrance -slit, shifts of the entire_ }! profile must be compensated in that way also. Most of the uncompensable " ` s error will come from undetected asymmetries and from unresolved random motions in umbrae, penumbrae, and active regions. The 'i y w uncompensable errors in residual intensity in each Stokes parameter probably will be less than 0.05; the relative error in each measurement, of course, will depend upon the part of the profile in which the measure- ment is made. Since the average degree of circular polarization, Pvt is found by combining signals measured in two different polarization states, and since both signals may contain errors which are comparable in absolute value and partially interdependent, the resulting error in Pv cannot be estimated for a general case. Wiehr (Ref. 23) discusses errors caused by miscentering of the line profile in the original polarim- eter designs used at the Crimea observatory and at the Locarno station of the G5ttingen observatory; these errors can be very large. Of the spectral lines used for magnetic field determinations, X5250. 2 shows some of the largest natural variations in strength. The line has moderate strength in the photosphere; it is stronger in sunspots and weaker in photospheric magnetic regions. C."hapman and Sheeley (Ref. 24) give the photospheric equivalent width as 62 milliangstroms; the equivalent width they measured in photospheric magnetic regions is 27 percent smaller. The equivalent width in sunspots is difficult to deter-mine because the spot spectra are usually contaminated by stray light, and no reliable estimate has been found. The strength variations are thought to be caused partly by temperature effects and partly by magnetic saturation (Refs. 24, 25, and 26); the temperature effects appear to be confined to the line cores. Whatever the cause, the variations in profile strength have been responsible for discrepancies between magnetograph results obtained with X5250 and with other lines. Usually, the calibration for X5250 is based on an "average" profile for the solar disk and thus cannot t--Ilz 11 found that the fields they measured using X5250 appeared to underesti- mate the true field strength by a factor of about 2 in the linear portion of the profile and about 5 near the line core; Chapman and Sheeley (Ref. 24) have estimated that a calibration using an average disk profile of X5250 will yield magnetic field strengths which are too low by a factor of 1.5 to 2; and measurements made with molecular lines also differ consistently from the X5250 values (Ref. 28). Therefore, calibrations based only on disk-average profiles of X5250 generally appear to yield estimates of magnetic field strength which are much too low. Some supplementary information is needed. Indeed, Harvey et al (Ref. 25) now use data from X5233 to establish the average field strength in the areas they observe, and use the X5250 observations to provide finer detail. ERRORS WHICH ORIGINATE WITHIN THE TELESCOPE AND THE MAGNETOGRAPH The magnitudes of errors arising within the magnetograph and the telescope will be determined by making measurements of auxiliary sources or solar regions whose characteristics are known. Although a complete description of the errors cannot be made until that has been done, a general review of some of the possible sources of error can be given here. The magnetograph contains a flat glass plate to be used to com- pensate for residual polarization introduced by the telescope. Even after this compensation has been made, a careful check should be made for residual polarization in all modes to be measured, because residual polarization is very difficult to remove completely. Furthermore, if any residual polarization can be measured, it may be possible to remove its effect in the data analysis. Residual polarization studies should be made for a number of different source intensities and telescope orientations. 66 e^ One of the chronic difficulties experienced with umbral and pen- umbral observations is contamination of the fainter solar intensities by stray light from brighter regions. The scattering processes which k redistribute the light occur in the Earth's atmosphere and within the Ai telescope. The net polarization produced by the atmospheric scattering should be e negligible, but the redistribution of light at the telescopeg P optical surfaces may introduce a net polarization. Thus, a small polarized component of stray light may exist which would tend to dis- tort the relative intensities measured in different polarization states. i This component, if present, would probably be essentially linear and therefore less serious for the circular polarization measurements. Nevertheless, it is a possibility that should be examined, since such " polarized stray light might cause an appreciable distortion if the signal level is very low.x A more serious possibility is that of intercommunication or u-. - "crosstalk" between signals. If, for example, some fraction of unpolar- ized intensity is mixed with a circularly polarized component, a sizable error can result. Instruments which use electrically switched polarizing subject this leakage, the jcrystals are to type of signal so possibility of its existence should be examined (see, for example, Reference 25). "a " ERRORS CAUSED BY LIMITED RESOLUTION The Cassegrain telescope to which the magnetograph is attached has a diameter of about 30. 5 centimeters. The corresponding Rayleigh criterion value at X = 5250 angstroms is, 0. 43 second of arc; this will be assumed to be the diffraction-limited spatial resolution of the tele- scope. The design goal for the magnetograph optics is a spatial resolu- tion of 2. 5 seconds of arc for the 5-by-5 minute of arc field size, and " 67 a t ^ _ j^ } 1 second of arc for the 2-by-2 minute field size obtained with the magnification system (Ref. 29, p. 2-1 1 ). The r^ solution values 1 ori - 2. 5 seconds thus represent the best possible performance of the system; the resolution may be further limited by atmospheric seeing. a The typical daylight seeing values at the telescope tower have not yet been completely determined; in most locations, however, 1 second of arc is considered excellent, and 2 seconds or more are more =°°1 usual ( Ref. 12, p. 19). Moreover, the seeing usually varies rapidly with time, even on the best days, so an observation of more than a few 1 , seconds in length probably will show distortion. A reasonable predic- s tion would be that on average days, observations made with the 5-minute } field size should not be severely seeing-limited; the full resolution of i the 2 -minute field will be attained only at times of exceptionally good seeing. Good spatial resolution is required for precise mapping of magnetic fields on the Sun. (A really fine discrimination of position a 4 is not possible from the Earth, since here an angle of 1 second of arc a corresponds to a linear distance of about 725 kilometers at the center of the solar disk.) Spatial resolution is also important because the Sun. shows many surface inhomogeneities of sizes near the limit of res- w olution or smaller. At maximum resolution, the smearing- of these inhomogeneities will be smallest, and the resulting distortions of the i- }} observations will be minimized. Several of these inhomogeneities are t briefly t.escribed below: • Umbral dots are small, bright transient regions which appear in sunspot umbrae. The mean diam- eter of the dots measured by Beckers and Schroter (Ref. 30) was 420 kilometers (about 0. 6 second of .. arc); the mean lifetime was 1500 seconds. (The life- time was defined as the time between the occurrence t 68 _- ( n^i ^i ^I. 1 of half-maximum brightness in the increase and decrease of the dot"s intensity.) Umbral dots may be associated with inhomogeneities. in the umbral magnetic field. • Penumbral filaments (Ref. 12, p. 75) are irregular, elongated bright regions in the penumbra. The lengths of the filaments vary a good deal; a representative value for large &pots is about 10 seconds of arc. Their lifetimes are of the order of a few hours, so a promi- nent penumbral filament in an observed region probably would be noticed. • Magnetic knots are small regions in the photosphere which are characterized by unusually strong magnetic fields (Ref. 31). The strengths of many spectral lines, including X5250, decrease in these regions. A typical field strength is 1000 gauss; diameters are about 1000 kilometers. Lifetimes of knots are g-realer than 30 minute s. • Pores are small sunspots with no penumbrae (Ref. 31). Their diameters are 2 to 5 seconds of arc, so at times, of very poor seeing they may not be resolved. They typically have brightnesses of about half that of the Bur- rounding photosphere and field strengths greater than 1500 gauss. • Nonmagnetic gaps (Ref. 31) are regions in the photo- sphere where the strength of certain spectral lines decreases and the continuum brightness increases, but there is no strong local magnetic field. The diam- eters of these regions are about 1100 kilometers, and lifetimes are about 40 minutes. Any of these inhomogeneities is capable of producing some distortion of the magnetograph record, especially at times of poor seeing. The amounts of such distortion will be determined largely by ^. the magnitudes of the effects of errors arising within the telescope and magnetograph. tt 69 3t It is apposite to quote here a statement made by Deubner and Liedler in their discussion of the magnetograph at the Fraunhofer Institut (Ref. 32): "In attempting to calibrate the vectormagnetograph, it has been shown here that due to our limited knowledge of the nature of these inhomogeneities (on the solar surface), which doubtless exists, the construction of a universal calibration curve is more or less impossi- j`ble or even meaningless. Such a calibration would be valid only for the single spot from which it was derived during a particular state of develop- ment, and only for the prevailing spot field. " ERRORS ASSOCIATED WITH UNCERTAINTIES IN THEORY Calibration curves relating magnetograph signal levels to magnetic field strengths on the Sun must be based, ultimately, on some theory of line formation in magnetic fields. As will be shown later, theory does not yet permit a precise prediction of signal levels for, all conditions on the Sun. Approximate calibration curves have already been calculated. While they are not exactly applicable, they should serve to show the general behavior of signal as a function of field strength. The rela- tions tllus obtained consist of a series of nested curves, lone for each value of the field orientation angle. These curves are fairly closely spaced; since in some cases the spacing may be of the order of the uncertainty of the signal, the interpretation could be ambiguous even supposing that the calibration curves were precisely known. More- over, the curves are not monotonic; the signal increases with increas- ing field strength until a field of the order of 1000 gauss is reached; as the field increases beyond that value, the signal drops abruptly. There- fore, an additional ambiguity exists in the region around the peak unless i{ ii independent information is available to show on which branch of the curve the signal lies. To make matters worse, at present there is no way to determine an absolute calibration curve for x,5250, so given signal values cannot be attributed to specific field strengths. This comes about partly through the inherent difficulties of calculating the polarized intensities in a solar magnetic field, and partly through the properties of the transition producing x,5250.216. Only one or two transitions can be treated in detail in solar magnetic fields, and the calculations for these cases are so cumber- some as to be impractical for the large number of repetitions needed to define a calibration curve. House and Cohen (Ref. 33) described the calculations necessary to define the scattering in a magnetic field (with simplifying approximations) for a resonance line which gives rise in a magnetic field to a normal Zeeman triplet. The field must be weak. The transition considered is 1 So -+ 1 P1 , which for the solar astro- physical case would be found only in the resonance lines of neutral calcium and magnesium, in the visible wavelengths. f The 5250. 216 angstrom line comes from the transition 5 D 7 D 1 (Ref. 3.4) • the lower excitation potential is 0. 12 electron volt, the upper ` _J ' 2.47 electron volt. The line is therefore one of low excitation but not a resonance line. One would expect it to have a strong scattering component, and this expectation is reinforced by its behavior on the Sun, where the variation in line strength from center to limb is less than would be _ expec•ced for a line formed in pure absorption, (Ref. 4). Nevertheless, k the line also has a strong absorption component. It cannot be correctly treated by either 'a pure scattering or a pure absorption approximation, r; and these are the only computational methods which are practical for the large number of calculations required. The two most often used pro- cedures for calculations in a magnetic field, described in References 10 and 35, require that pure absorption or pure scattering be assumed. 71 , __ TV t 1 µ ences between the regions, calibration curves established for the photosphere should not be used in interpreting sunspot observations. The calculation of expected signal values in sunspots is even more i difficult than in the photosphere. All the difficulties of the photospheric calculation remain, and in addition the existing sunspot models do not permit a self-consistent profile calculation under any set of assump- tions (Ref. 36). The interpretation of the observations is even more uncertain because of several magneto-optic effects which can alter the plane of polarization after it is produced in the spectral line transition on the Sun. The Hanle effect usually is mentioned in this connection; others may enter as well (see Ref. 37, for example). The effects are much more severe for linear than for circular polarization. Indeed, Beckers has stated, "There is no simple relationship between the amount and direction of linear polarization and the strength and direc- tion of the magnetic field. Only with very large approximation can one say that the degree of polarization is related to the total field strength and the direction to the longitudinal magnetic field strength. " (See Ref. 38, p. 13. Many magnetograph calibrations_ take advantage of the fact that, for small fields, the measured signal is (approximately) directly pro- portional to the field strength. This relation can be used if it is under- stood that it applies to small fields only and that the proportionality ^ Y f ` "constant" depends explicitly on position on the solar disk, so that the value used must be correct for the solar coordinates of the sunspot p 1(see Ref. 12 194, and Ref. 29, p. 1-17). Adjustment of the "constant" according to disk position will be discussed in a later sec- tion of this report. a fi 72 3 i v" PROBABLE ERRORS IN FIELD STRENGTHS DETERMINED FROM ZEEMAN SPLITTING I The results of a determination of magnetic fields in sunspots from the Zeeman splitting of X 5250 illustrates the error which can • _ enter a well-documented field strength determination. The observations and method of deriving field strengths awe described in Section 1. The ,calculated field strengths were reviewed to estimate the error in the final values. Most of the field strengths areaverages of several values obtained from separate spectra made of the same location in j the sunspot, so the deviations of the separate values from the average form a. part of the error estimate. When the calculated field strength_ M values were. reviewed, the identification of the separate Zeeman com- i Xj ponents was also reviewed. In some cases, the identifications were A revised, causing changes in the average field value for the location. These changes generally were small. A value which departed greatly from the average of the other values was discarded in one location `I ° (square XI -g of the 'magnetic field map). The final map is shown in f (`: Figure 4; it does not differ appreciably from the one given in Reference 39. The deviations from the mean values shown in the map are tabulated -. for each location in the sunspot in Table 4. i The average deviation for all the values from their separate ,^ means is 180 gauss; the uncertainty caused by scatter in the individual magnetic field values for this sunspot, therefore, is ±180 gauss. . The final values are uncertain for other reasons also ._ Because ^^ s the splittings are determined from the observed positions of the Zeeman components, uncertabities in wavelength will affect the results. The spectral intensities were recorded at wavelength intervals of 5.88 milli- „ angstroms, so this interval size imposes a limit to the wavelength resolu- tion. If the location of a Zeeman component is defined as the wavelength of its minimum measured intensity, the uncertainty in that location is at ^i least f 5. 88/2 milliangstroms. 73 1 h g a b c d e f IL III 906 908 805 605 IV 151 830 1,070 1,250 1,230 1 ,4'`JV, VI 944 1,330 1,430 1,,680 i1,670 604 YVII, VIII 926 1,400 1,900 1 1,780 1,670 1,360 IX, X 1,6801 2 5010 1,990 2,060 1,770 1,640 1,360 XI 1,510 2,020 2,060 . 1,940 1,680 1,300 XII 1,120 1,670 1,840 1,750 1,450 1,440 XIII 1,060 1,240 1,580 1,210 755 XLV 680' 754 792 , 966 680 XV 755 NORTH FIGURE 4. REVISED LINE-OF-SIGHT FIELD STRENGTHS IN GAUSS FOR SUNSPOT OBSERVATIONS OF JULY 14, 1969 J' l I TABLE 4. DEVIATIONS OF SEPARATE FIELD STRENGTH VALUES FROM MEAN VALUE FOR LOCATION fll j Iry Ll 1 ^i ' 1 1 ^u k K Ll is z^ LOCATION Ill SUNSPOT MEAN FIELD STRENGTH (gauss) NUMBER OF VALUES AVERAGED AVERAGE DEVIATION FROM MEAN (gauss). ,IIIa 908 2 152 I I Ib 805 3 67 IIIc 605 1 0 IIIg 906 1 0 IVa 1,250 4 609 IVb 1,230 3 686 IVg 1,070 5 315 IVh 830 2 75 IVi 151 1 0 V, VIa 1,680 7 155 V, VIb 1,670 7 139 V, VIc 1,420 9 279 V, VId 604 2 151 V, VIg 1,430 10 300 V, VIh 1,330 3 419 V, VIi 944 2 416 VII, VIIIa 1,780 5 126 VII, VIIIb 1,670 8 140 VII, VIIIc 1,360 4 150 VII, VI I Ig 1,900 6 120 VII, VIIIh 1,400 4 376 VII, VIIIi 926 4 284 IX, Xa 2;060 5 104 IX, Xb 1 1;770 5 313 IX, Xc 1;640 10 211 IX, Xd 1,360 1 0 IX, Xg 111990 5 87 IX, Xh 2,010 5 206 IX, Xi 1,680 5 268 LOCATION IN SUNSPOT MEAN FIELD STRENGTH (gauss) NUMBER OF VALUES AVERAGED AVERAGE DEVIATION FROM MEAN (gauss) XIa 1,940 $ 126 XIb 1,680 5 139 XIc 1,300 4 169 XIg 2,060 4 58 XIh 2,020 5 202' XIi 1,510 5 120 XIIa 1,750 5 277 XIIb 1,450 5 313 XIIC 1,440 2 225 XIIg 1,840 5 134 XIIh 1,670 5 131 XIIi 1,120 4 170 "XIIIa 1,210 5 392 XIIIb 755 2 0 XIIIg 1,580 5 360 XIIIh 1,240 5 187 XIIIi 1,060 2 0 XIVa 966 2 15 XIVb 680 1 0 XIVg 792 2 37 XIVh 754 3 151 XIVi 680 1 0 XVg. 755 1 0 m i n n x> n n Il u The uncertainty in field strength corresponding to this wavelength uncertainty is ±75.5 gauss for )5250.2. That value also represents the minimum field strength that can in principle be detected from these spectroscopic data. In practice, the minimum maybe somewhat larger because the resolving power of the spectrograph and the distorting effect of the finite slit width may determine the minimum resolvable separation. The total probable error for the magnetic field values can be esti- mated as the root mean square of 180 gauss and 75. 5 gauss, or 195 gauss. The probable error in the spectroscopically determined field strengths, therefore, is approximately ±200 gauss. SUMMARY OF ERROR STUDY Magnetographs are, in general, subject to large systematic errors. The magnitudes and nature of the errors depend upon the particular type of magnetograph. Numerical error estimates rarely appear in the literature; errors in the range of 10 to 20 percent are generally considered to be moderate (Ref. 40). Most systems are con- sidered to be more reliable for field strengths less than about 1500 gauss than for very large fields. r.. .. It may be possible for a large systematic error to go undetected, although fortunately that is less likely now that results from many dif- LI ferent instruments can be compared. [ In 1962, Stepanov, Shaposhnikova,i i and P'etrova determined that Mt. Wilson measurements underestimated_ 4 a field of 1000 gauss by no less than 700 gauss, on the average (Ref. 12, P. 205) If observations in X5250.216 are used, all previous experience shows that the calibration must be done by comparing the signal levels di as to those measured for the same solar features in another line for which a calibration can be made.loom W 77 7" 1 u s _ 3 Refined error estimates, of course, must wait until the system has been in use long enough for observers to collect a large mass of data and to conduct careful tests for instrumental error. In making a preliminary estimate, no justification exists for assuming the field strengths will have accuracy better than 20 percent of the measured value. Therefore, f20 percent is recommended as a provisional JA minimum error estimate. 'j gg Y 5 k s S ?g s; AY "I ti k i rf. t, k 9 I I ^^ VARIATION OF CIRCULAR POLARIZATION CONSTANT WITH POSITIONON THE SOLAR DISK For real-time rapid reduction of magnetograph signals, the relation between degree of circular polarization and magnetic field strength is assumed to be linear, for fields up to about 1000 gauss. The magnetograph calibration includes determining the slope C 1 for this relation. The value of C l , however, depends explicitly upon position on the solar disk. If the Unno formulation for polarized residual intensities is used, the variation of C 1 with position on the solar disk can be written as a function of known quantities (the Unno formulation is used because it permits C 1 to be written as a linear function of P 0 , the limb darken- ing constant). The expected variation in C 1 across the disk can then be estimated using a minimum number of line-dependent parameters. For small magnetic fields, the relation between the mean circular polarization, Pv, and the magnetic splitting is assumed to be given by = (VH cos 0 Ci (3) where l^ l Equations (3) and (4) are taken from Reference 29, p. 1-17; Equation (4) is Equation (1. 14) of Reference 29. All symbols have the f same meanings as in Reference 29 and will not be redefined here. Because v is independent of µ and P O , the three integrals in .. Equation (4) can be written in a form that is independent of position on y j the solar disk.. V i + S dH(a, v) s f dv Let A = J v T (v , vi) dvI _ [1 + no H(a, v), t Vi S R I vl+S - T(v, v i ) dv 1 ^ j vi - s and vl + S T (v' vi)D= dv.1 + o H(a. v)^}!, v I } 80 ii tc dw 2M Then ILO go Y10 A B+ IAPOD 137- C, - 00 i10 A g 902 tj o A D J4 (B+µ(3O D) (B+RgOD)? C, C! go 11 C, (5) a 8+ go D B and D are easily evaluated, and P O is known. So rquation (5) can be used to find the change in C, for different positions on the solar 'disk. Since the value of C, at µ 1. 00 has not yet been established, the quantity to be calculated will be C C 1. 00) Approximately, C CI (R +A µ) a C R (6) (ClC 4L C, (R (P 1) 81 ti ^ e So if C 1 (µ = 1) is assumed to be known, ^r C 1 (µ =1 )° C1 (1 =1 ) - C1 4t = 0. 9) C1 (µ = 1 ) C A sL 1) 1 pc D x C1 G'=1) C µ( =1 ) C1 4L=1 ) ^0.9 B+0.9 poD (1.0-0. 9) I C1 `Zµ = 0. 8) C1 4L = 0. 9) C1 4, = 0.9) pa D t f C1 (µ 1)= 1) C1 (µ = C1 (µ = 1) [71-8 V+ o. s po D (0.9 - 0. 8) 'E etc. To evaluate D, several spectral line parameters mustbe known: AX - the Doppler width, which must be known in order to evaluate H(a, v) . a - the damping parameter, which is also required to evaluate H(a, v) ?10 - the ratio of line-to - continuous absorption # coefficients. None of these quantities is well known for X5250 in sunspots. Fortunately, however, the values, found from Equation (5) are far more "} sensitive to the better-known quantities µ and (5 O than to the three line profile parameters. The use of photospheric values of AX D, a, and `- 1,1 -lo should not introduce serious errors.y. To investigate this point, a set of maximum and minimum values for C 1 (µ) was calculated by using the smallest and largest values of ,&>,D, a, and no which would be expected on the Sun, for any 82 k: w_'^.,._ .^-_^., ,•_--- ter_. I12 A- spectral line formed in LTE. The results for X5Z50 should lie well within this range. The line profile pare-meters used for this calcula- tion are given in Table 5. The value of Po was 1.70 for both cases. TABLE 5. LINE PROFILE PARAMETER VALUES FOR DETERMINING MAXIMUM AND MINIMUM C, (11)/Cl (1) PARAMETER1 VALUE FOR MAXIMUM VALUE FOR MINIMUM AXD 5.0 milliangstroms 40.0 milliangstroms a 0.05 0.295 r10 5.0 30.0 From Equations (5) and (6), it appears that the smallest possible values that could be obtained for C, (µ)/C j (1) would be found if Po = 0. A set of C, (ji)/C l (1) values was calculated for this case; it is tabulated in Table 6 under the heading, "lower envelope". The maximum and min- imum values found using the parameters given in Table 5 also are given in Table 6. The difference between these sets of values is an over- estimate of the error that would be introduced by using photospheric parameters to calculate C 1 (µ) for sunspots. When p, is less than 0. 5, the maximum error which would be introduced by using photospheric values is certainly only a few percent. It should be emphasized that the range of values covered in Table 5 is truly enormous, and the parameters for any single line can be estimated with reasonable certainty to within much smaller, limits. The results in Table 6 suggest that the C, (µ) values for sun- spot umbrae can be approximated by using the A XD, a, and il, values 83 G. TABLE 6. RANGE OF VALUES OF C l (P)/C l (1) FOR PHYSICALLY POSSIBLE VALUES OF LINE PROFILE PARAMETERS AND FOR 5o 0 t^ MAXIMUM C1 (11 )/C1 (1) MINIMUM C1 ( 10/c1 ( 1 ) LOWER ENVELOPE 1.000 1.000 1.000 1.000 0.917 0.962 0.929 0.'909 0.833 0.920 0.855 0.818 0.750 0.873 0.778 0.727 0.667 0.819 0.698 0, 636 0.584 0.758 0.614 00546 0.500 0.686 0.526 .455 0.417 0.603 0.433 0o364 0.333 0o502 0o335 0.273 0.250 0.382 0.232 0.182 0.167 0.231 0.122 0.092 0.083 0.024 0.003 0.000 4 which are found for X5250 in the photosphere. That approximation must be made because of the scarcity of high-quality umbral profiles of X5251 0 in unpolarized light. The value of Po certainly changes between the photosphere and sunspot umbrae, and this factor is dominant. Fortunately, Po for sunspot umbrae can be determined. Two separate calculations of C, (µ)/C j (1) were therefore made: one for the photosphere and penumbrae, and one for umbrae. For the photospheric calculation, the values of,&X a, and vj 0 were found by fitting an absorption profile to M. J. Hagyard Is observations of X5250 in the photosphere. The values determined 84 l:i dn a were AX D = 12 milliangstroms, a =0. 2, and Flo = 9. For the photo-II l sphere at X = 5250 angstroms, Po = 1. 70 (Ref. 41, p. 171). According s i to Moe and Maltby (Ref. 42), "The intensity ratio between the penumbra 1 and the photosphere shows 14 Ltle or no variation with position on the solar I disk. " The same value of limb darkening constant Po will therefore be good for both photosphere and penumbra, and the line profileg P P P param tersP P will be the same because good penumbral profiles of X5250 are as rare as good umbral profiles. The resulting values of C 1 (µ)/C 1 (1) are I given in Table 7. KQ TABLE 7. C 1 W/C 1 (1) FOR PHOTOSPHERE AND PENUMBRAE . a fi a ^ } 5 1 u C1 (11)/C1 (1) 1.000 1.000 0.917 0.957 0.833 0.908 0.750 0.855 0.667 0.796 0.584 0.729 0.500 0.652 0.417 0.566 0.333 0.464 0.250 0.345 0.167 0.202 0.083 0.016 s r_^ For the umbral calculation, the same values of A k D, a, and { ,qo will be used, but a new P o must be found. Wittmann and Schroter j (Ref. 43) give center-to-limb intensities of sunspots at X == 4680 angstroms and 6400 angstroms. On the authority of Figure 3 of 1 Ii !I 85 a l P Iu (4680 angstroms) INTERPOLATED Iu (5250 angstroms) Iu (6400 angstroms) 1.00 3.68 3.77 3.94 0.90 3.66 3.75 3.93 0.80 3.63 3.72 3.90 0.70 3.60 3.69 3.87 0.60 3.56 3.65 3.183 0.50 3.52 3.61 3.78 0.40 3.47 3.55 3.70 0.30 3.35 3.33 3.59 0.20 2.98 3.12 3.40 0.10 2.24 2.50 3.02 j r; Reference 44, the values for X 5250 angstroms can be found by linear interpolation between the two sets of Wittmann-Schroter values. The results are shown in Table 8 TABLE 8. CENTER-TO-LIMB INTENSITY DISTRIBUTION FOR SUNSPOT UMBRAE AT a = 5250 ANGSTROMS - 4 ^A u Iu (u) / I U (1), So =: 0.093 Iu (u)/Iu (1) FROM TABLE 8 1.00 1.000 1.000 0.90 0.991 0.993 0.80 0.983 0.987 0.70 0.974 0.978 0.60 0.966 0.968 0.50 0.957 0.958 0.40 0.948 0.942 0.30 0.940 0.884 0.20 0.931 0.828 i 0.10 0.923 0.664 { go value is less accurate in this range) I i h 't A simple equation of the form of Equation (7) does not permit a good fit over the entire range of µ values, but an acceptable fit for 1. 0 ? µ 0.4 can be obtained by setting (3 o = 0.093 (ui = 0.086). In Table 9, the j values of I (µ)/Iu (1) for (3 = 0. 093 are compared to the interpolatedu o ^ measured values. ^- TABLE 9. VALUES OF UMBRAL LIMB DARKENING FOR $0 = 0.093 COMPARED TO MEASURED VALUES t r { .'^1 The value Ro = 0.093 was used to calculate C1 (µ)/C 1 (1) for -gi g## r, umbrae. The values of C 1 when µ is less than 0.40 should be given less weight because the approximate limb darkening relation is less f accurate in that range. The line profile parameter whose value in umbrae is most uncertain is probably rho. Values C l were calculated using i1 0 = 9, the photospheric value, and Flo = 40, since v10 may be much larger in ^ 1 87 1 R umbrae. The results for both rio values are given in Table 10; they are almost identical. _ 3 TABLE 10. C 1 (p)/C 1 (1) FOR-SUNSPOT UMBRAE u C, (u)/C I (1), no = 9 TC I (u)/C1 (1), no = 40 1.000 1.000 1.000 0.917 0.915 0.913 0.833 0.827 0.825 0.750 0.740 0.737 0.667 0.652 0.648 0.584 0.562 0.558 0.500 0.471 0.467 0.417 0.380 0.376 0.333 0.286 0.283 0.250 0.192 0.190 0.167 0.098 0.096 0.083 0.000 0.000_ (SO value is less accurate in this range) t .. Y i Should it become necessary to do so, a supplement to Table 10 for µ < 0.4 can be calculated, using a value of Po which gives a better fit to the umbral intensities near the limb. j The values of Tables 7 and 10 are shown plotted in Figure 5. The relation for the umbra is almost linear. I I ,^ i 88 ov JW 1.0Y y PHOTOSPHERE, UMBRA PENUMBRA _' 0.8 G , r- 0.6 0.4 - y - 0.2 01 r , 1.00, .80 0.60 0.40 0.20 0 FIGURE 5. C1 (u) /C 1 (1) AS A--FUNCTION .OF_P__OSITION ON_ SOLAR DISK ,i 1 PROGRAM TO LOCATE AND PLOT MAGNETIC FIELD NEUTRAL LINES Two of the properties which are of the greatest interest in solar magnetic field maps are the regions where the magnetic field gradients are steepest and the locations of the boundaries between field regions of opposite polarity. The regions of steep gradient are easily located on magnetic field contour plots because they are the regions where the contours are most closely spaced. However, the boundaries between opposite-polarity field regions (the boundaries will be called "neutral lines" for brevity) are generally less distinctive in appearance on contour plots, and it is convenient to provide a separate program to plot the neutral line locations directly from magnetograph data. A FORTRAN program to make such plots has been written for the Univac 1108. The position of each neutral line is identified by selecting the coordinates of pairs of adjacent points for which the measured signals are opposite in sign. The program in its present form will analyze a square grid of data 128 points on a side and will store 1998 coordinate values. Places where the signal !changes sign because of the sign reversal of the magnetograph calibration curve for large magnetic field values will be identified by the program as portions of neutral lines. When the field strength values at which the calibration curves change sign have been established, the program will be modified to ignore signal sign changes for field strengths in the reversal range. w The program compares points in two adjacent horizontal data rows. Beginning with rows I and 2, the signs of pairs of points are compared by taking groups of four data points at a time. The points are labeled as shown in Figure 6; their signs are compared in the order P1, P2; Pl, P3; P2, P3; Pl, P4. If all four points are of the same sign, 1 r 90 ;n a 1 - A ""Moto V I Pfr F191 KE 6. POM-1 LASELIM PAT MS FOP. IMMIX LUM PfWQFAY, V,;Jnt^,, 11i 4n-d P4 rel-abeled PI and PZ, and the next verti c--A pair W th'-, Oght P3 and P4 for a new iour-point group. The ,,;omparfoon fo vqx-fated across the data row. When two points of oppopftc- oign vrc found, their coordinates are stored. In order to oft,Y,4 In rnornory, the program then stops testing values in. a pow-ti(.111'ar four-point ;.4roup anxJ moves to the next group. This explains why, In. the final ptotti, thr; lines which connect points of opposite sign ffmy tako any of the foliv direction-f3: they simply record the relative posi- 13(onij of Clio moy).,Ibertj of the first pair of points of opposite sign which was found In ew"h groll.p of four points. When the first two data rows have been tw%nnod, Clits proccom is repeated with the second and third rows, and the ('101 noquonco J," ropeated until the entire frame has been scanned or until I It A SS,o M frvf- I, f%eveel; I% ti Ne values has been filled. Aft or tho ficanning has been completed, the coordinate values of tho palvm of pointa of opposite sign are plotted by connecting them w..J.Ah Hfiorl. 711no(j. A line drawn joining the midpoints of these short volillociJap. JAV1013 W1,11, traco the location of a neutral line to the precision t"I' llowod by tho tij,)rttial v0 00ltition of the data. To assist in determining tho of Clio plotted points, grid lines are drawn at every folixt)"I dft-ca row and colaq,111. I ^^ R t^ vl v { The program was tested on a frame of magnetograph data which was obtained from the Kitt Peak National Observatory and which has t ' been used for testing other magnetograph analysis programs at MSFC. This particular data set forms a grid 120-by-120 data points in size. 3 Three cards were missing rom the data dec k ; one of these containedg ^ -_ r data which crossed a neutral line and produced a gap in the upper X right-hand corner of the final plot. Except for this gap, the plot agrees -, in every detail with the neutral line pattern obtained from the data by E the Kitt Peak Observatory. It also agrees with a hand plot of the data. - The plot of the test data is given in Figure 7. Figure 8 is a flowchart of the test program, which reads data from cards, and Figure 9 is the listing of the test program. For use with real MSFC magneto- graph data, the piTc gr_am will be modified to read the appropriate magnetic tape formats. a i :a 3 i n 92 ti ^| °^ { ^ | \^ ^^. 40^ ^ -- -- rq lotj ^^^ ^ . ^\ ^ ^\\ ^ ^ I f \^ ^ ^ . \ /} \ /i. 7;:;^71 i ^ \ ^ }, ^ j ^. | ^ ^° j } / ^ \ 120 80 I% tr j I CtD i READ RMS NOISE L— LEVEL FOR ! FRAME 3 ILOC = 1 READ FRAME DIMENSIONS IMAX AND IMAM AND SIZE ISIZE I ALLOTTED TO ZERO GRADIENT COORDINATE ARRAY t I ISZ1 = ISIZE-1 READ FIRST TWO ROWS OF DATA. X1 (I), X2(I) NMAY = r IMAY - 1 s c NY] = l I D NY2 = NY1 + 1 a ^ NMAX = IMAX —1 ' I = 1 u k C N X I -` I NX2= I+1 z e r FIGURE 8. FLOWCHART OF TEST PROGRAM 94 ru ^ Sid? xi ^ w x s:: a. x^ t b y ' ,dew ^_p gsXa{^. r^ N y^ nfu fi^Pa a. b k l j ri Pi = X1(I) 1 P2 = XZ(I) P3 = X1(I+1) P4 = X2(I+1) ; NLX(ILOC) = NX1 PI AND P2 OF N0 NLY(ILOC) = NY1 NLX(ILOC+1) = NX1 SAME SIGN? NLY(ILOC+1) = NY2 + _, ILOC = ILOC+2 u • E f^ YES a NLX(ILOC) = NX1 'ILI NLY(ILOC) = NY1 NLX(ILOC+1) = NX2 N^? Pl AND P3 OF ILOC > ISZ1? N0 A— NLY(ILOC+1) = NY1 SAME SIGN? ILOC = ILOC+2 YES YES { 2 NY1 > 70. YES B i ILOC > ISZI? NO A NO YES r ^, ^ WRITE MESSAGE ^^ AND TERMINATE. j { NY1 2 70? YES B RUN ; ;t ..i NO WRITE MESSAGE AND 1 TERMINATE RUN rl FIGURE 8 - Continued '95 41 t 1 :. X. } ._. a.v. .... a x,....... _. _.,:... _ :... ...., . ^ .. :.,.__ ,W. _::- ..a.r..ra..w..:,....,...^.c.a.w._a:.......m u.ue^.:..w,..a......, _..,...:.... .._ .r.._.. ... ^.^ ... ....... ... . .. ` r A x 2 f _ NLX(ILOC) = NX1 4. P1 AND P2 NO NLY(ILOC) = NY2 OF SAME SIGN? NLX(ILOC+1) = NX2 NLY(ILOC+1) = NY1 ILOC = ILOC+2 ..,..,_ YES F ' NLX(ILOC = NX1 A NO ILOC z ..w. NLY'(ILOC) = NY1 NO PI AND P4 ISZl NLX(ILOC+1) = NX2 OF SAME SIGN? *.^. 7 NLY(ILOC+1) = NY2 YES sa YES,... • 1 k _ B YES NY1 >_ 70? 4i A NO ILOC NO ISZ1? NO YES I = I + 1 I > NMAX? A WRITE MESSAGE ` ^, AND TERMINATE • 9^ ++ YES j C RUN .^ s B YES NYl > 70? PI = Xl(IMAX) r P2 = X2(IMAX) NO ) WRITE MESSAGE NLX(ILOC) IMAX AND TERMINATE P2 AND P3 NO NLY(ILOC) = NY1 RUN OF SAME SIGN? NLX(ILOC+1) =IMAX' NLY(ILOC+b = NY2 A ILOC = ILOC+2 YES ,. . 3 a NO ILOC Z _.3 ISZ1? S YES F5 i I FIGURE 8 ' - Continued 4 f 96 iw. 77 3 a r '^ 5 J- I NO WRITE MESSAGE ES +NO NY1 2 70? AND TERMINATE B RUN r k y; YES ti a B II = T 4 t I' e( 7 XT(II) = X2(II) i s C II II + 1 NO II 2 IMAX? W .. YES READ NEXT ROW ` OF DATA D NYl — NO NYl_ > NMAY? NYl + 1 YES Li PRINT AND PLOT B NLX AND NLY VALUES Ll STOP - i FIGURE 8 - Concluded i f{ _i s _ 97 Ji?EP C EPA CIFNT6 CCNTCURS IN MICWFTOr!RfPH CA T/ VEP I! 'ICN FCP TEST WITH KPND MIENFIOEPAPH CATO C IMENS I ON X111 28)•- X.211291 + NL Y I 7100fl I t NLV 1 2010 1 C 110 E N S I C N A QAAV 1 22) CS TA fA R PJVfl)*l=19221124HHARCCOPY ONL V • ONE COPY •18*EV ORE= F K W q = 5 RE AC (K v Es 1) RPSN J C I FEAC RMS NOISE LEVEL F OR FRAME FORMAT IFIC*V) ILCC= I a A CCUNTEP FCR aZERCR EROCIENTS r. EA C (K t7 E 9 4E 1 1140 X• I MAM. 15 1ZF 4' FORMAT 13IIf) C NO. OF q CWS• NO. OF CCLUMNS • NO. OF NEUTRAL LTNF POSITIONS TC ry STCrEC I S TCI?E - I C REAC 15T 2 V CWS C l: CATA FEAC fK r-E• 461 4 XI IT ) • I= I • IMAXI 0EAC IKPE• 4F) I X 2 1 1 ) 9 I= 19 IMI X I 146 F rOMA T 1.1 24FE.cly I yj I SET V CCCRCT•AYE COUNTER INC START SEAR C H OF CRAUF x IMAM Cc S NVI= 1 • h-mil NY2= NVI ♦ 1 71 C SUPT OF iC O ACIENTi EVALU A TION LOOP NMA X= IMAX - I cr IV I= If, Kloiax C ET X CCCACINATE COUNTER NXI= I N 12= 1 ♦ 1 P1= X I II) ^' R2 = 2t1 i^. , P?= X I 1 41 1 IF IPI 1 1174 • ! • IU? IP3 IF I P 2 1 4• !• ! 1114 IF 1F7. 1 '• ? • 4 4 NL X f IL C C I= NXI k' LYIILCC)= N V I ^'L X I I L 0 1)= N V I WRITE IKWP• !131 P1 • P7• NXIO NVI F DPMA T I IM • 2( El 2 . w e EX 2AIF• F)-) ILCC= IL CC 2 IF E ql F I N I - 7 0 1 6. 7. 7 F WRITF lKWR• Al K V I a F rRMO T I IN 9 E9H&RRA Y RE C FRVEC F OR ?E :?O r-RACIFNT COnRCINATFF IS FY ILLEC NY1=• I ! I WRITE 4KWR• 11} It FOR M AT CIH • ITHYERMINITE RUN) CC TO 9?9 IF tv)) 112• 12P W 11 2 IF 1PI1 129 12• 11 FIGURE 9. LISTING OF TEST PROGRAM ORIGIN Al PAGE IS 98 00'R QUALITYOF 11? IF IF?) 1?9 129 12 1? NLXIILCCI= NY f NLVIILCCI= NYI NLYIILCC + 11= NY2 NLYIILCC + I)= NY WRITE IKWRr 30) P19 P T 9 NX19 NYI ILCC= ILCC + 2 IF 1 IL OC-ISZ1 ) 1119 c 9 5 1 ! 2 IF IP2) 1159 IE. 114 11E IF IP T ) 159 IS9 l 114 IF 1091 149 159 IF It NLXIILOCI= NXI NLYITLC^)= NY2 NLIIIL0 + 11= N X 2 NLYIILCC + 11= NYI - j WRITE IKWR9 =01 P29 P?• NX19 NY1 I L C C = ILCC + 2 IF (ILOC-IS711 1119 °9 5 15 IF IP1) IIG© 1f9 11E 11F IF IP4) 16v IQ9 10 110 IF IF4) 1G9 IV* IF( IF NLYIILCC)= N Y I NLYIILCC)= NY1 ALX'IILOC ♦ 1)= N X 2 NLYIILCC • l)= NY2 WRI T E IKWR9 ? U1 PIt P4 NX1r NYI ILCC = ILCC + 2 IF I ILOC-IS7) 1 Ir9 5 9 S IC CONTINUE P1= x11IMAx1 F2= X2IIMLXI IF IP1) 1189 189 111g^ 118 IF_ 6021 1e. 189 17 117 I, F-I P.P7) 179 189 1 17 NL YIILCC)= INAX NLYI ILCC 1= NY1 NLYIILCC + 11= IMex NLYI ILCC + I)= NY2 ILCC = ILCC + 2 IF (ILCC-2S?I) 1P.9 189 HIS IF INYi-101 IVF9 79 .7 1f,S .) 116E WRITE (KWR9 8) NY1 WRITE ( KWP9 11)C. C TO 9990 18 IF INYI-NFAV) 1 0 9 79 7 i! 19 Cr 217 Ii= 19 IjA Y X1III )= X2(TT1 ?0 CONTINUE Ll C RE1C NEXT RCW CF C A TOFEtC IK REv 4F) ( X21L ) 9 I= 1. TMAXI o CCNTINUE C THIS CCMPLETFS S£1RTH FOR 37FRO CQ§CIFNT4 POINTS 7 IFIN_ ILCC - 1 401TE IKWRr 1321 IFIk - 1?2"FORMAT IIH • SHIF-IN =r TILE) WRITE IKWR@ .211 Ll FIGURE 9 - Continued PAGE lU ORIGINAL POOR QUALITY^F 99 i ME 1421 FORMAT I 1 05FX CCCRC O F ZERO [RICTENT POINTS A;E1 WRITE ( K WR • 271 INLX I I) • I= 1 • Tf IN) 22 FORMAT IIH • 51IS9 SX)l WRITE /K WR • 231 23 FORMAT (IH •3ShY CGCRC OF ZERO ERACTEAT POINTS ARE ) WRITE ( KWR• 221 (NLY(I)• U4 1a IF IN) 3 PLOT TAPE CALL KENT 199 ARRAY) CALL CRICIV([ • 0•Gr12U.(' • C.Ur1Z!` • f•u•Li • u * ire 1 1 IFI= ILCC-2 CC 800 I= 1. IFI• 2 J X-!NlXtI1 `^ "ALL KSCLVIIX • NXP, IERR1 0X1= NXP 7 CALL VSCLV1IX. NXP, TERRI —NXPNX2_ Y_ INMAY41)-NLY(I) f ,ALL YSCLVI(Y• NVP• IE RI NYI= NVP Y. INMAV+I) - NLYII+11 a CALL YSCLVIIYv NVP• IERR1 NV2= NYP CALL _LINEVtNX1•NV1•NX29NY21 8110 CONTINUE .-« CALL ENC,408 goo STCc * ENC FIGURE 9 - Concluded f - Li 4 0 LD ell mI'IvRo 2I00d 30 SI JVd rivmolno tj 100 VIM ; pCONCLUSIONS AND RECOMMENDATIONS , Even the best magnetograph results are subject to large uncer- is intainties. It unwise to assume the uncertainties results obtained with a new system are less than *20 percent. They may be larger. To reduce some of the uncertainties ofcalibration and inter- - ^y p retatio_ n, it is recommended that the magnetograph be modified toy r operate using a line other than the neutral iron line at 5250. 216 angstroms. The new line, of course, should be carefully selected to introduce a minimum number of new uncertainties. If compelling instrumental reasons exist for requiring the new line to be near 5000 angstroms in wavelength, both x.5253 and X5324 would be worthy of closer investigation. Because the amount of Zeeman splitting is k proportional to the square of the wavelength, lines of wavelength longer than 5000 angstroms would tend to produce larger splittings and 4 therefore could be advantageous choices. A number of red spectral 4 lines have been suggested by various authors as possible magnetograph lines; two neutral iron lines which should be investigated are x:6173. 348 (lower excitation potential = 2. 213 electron volts) and X6302. 508 (lower excitation potential = 3.671 electron volts) (Ref. 12, p. 179). A number of other candidates may exist. k Evaluation of the characteristics of possible new magnetograph .: lines type inshould begin with a preliminary study of the summarized Table 3. Lines which are not rejected in the preliminary study must then be further examined to prove that their properties ar:, compatible with the assumptions implicit in the magnetograph calibration analysis. As was shown earlier in this report, attempts to calculate line profiles LJ for sunspot models may reveal such incompatibility. The profile i _ - 101 i v t Vm{ ] 1 ,1^ 3 calculation thus forms a test which should be applied to each line which __- . ais seriously considered for magnetograph operation. ,,} When the magnetograph is operated using X5250, it is recommended ` that no reliance be placed on calibration systems which require, even indirectly, the calculation of residual intensities of that spectral line in magnetic fields." g t e 102 _.., 1 i REFERENCES - SECTION 2 1. Minnaert, M., G. F. W. Mulders and J. Houtgast, Photometric r Atlas of the Solar Spectrum 3332,x, to 8771A, Schnabel, Amsterdam, 1940. 2. Moore, C. E., M. G. J. Minnaert, and J. Houtgast, The Solar Spectrum 29351 to 87701, N. B.S. Monograph No. 61, December 1966. ,. 3. Obridko, V. N., Soviet Physics-Astronomer, 9, 77, 1965. 4. Obridko, V. N., Soviet Astronomy-AJ, 9, 398, 1965. 5. Moe,_ 0. K. , and P. Maltby, Astrophysical _Journal Letters,- 1,, ^. 189. 1968. 6. H6noux, J. C., Astronomy and Astrophysics, 2, 288, 1969. r 7. Yun, H. S., Solar Physics, 16, 379, 1971. 8. Beckers, J., Solar Physics, 9, 372, 1969. 9. Gbhring, R., Solar Physics,_ 8, 271, 1969. ! 10. ` Moe, 0. K., Solar. Physic 4, 267, 1968, 11. Staude, J. , Solar Physics, 12, 84, 1970.w 12 Bray, R. J., and R. E. Loughhead, Sunspots, Chapman and # LL4 Hall, 1964. 13. Corliss, C R., and B. Warner, Astrophysical Journal Supple- ment, 8, 395, 1964. ^t; 14. Withbroe, G. L., Solar Physics, 9, 19, 1969. 15. H6noux, J. C., Solar Physics, .4, 315, 1968. 16. Beckers, J. M. , and E. H. Schroter, Solar Physics, 7, 22, 1968 r 17. Lamb, F. K., "The Effect of Collisions on Spectral Line. Formation .in Solar Magnetic Regions". Solar Magnetic Fields, IAU Symposium No. 43, ed. by R. Howard, D. Reidel, 1971. . 103 l^ REFERENCES - SECTION 2 - Continued 18. House, L. L., "Coherence Properties of Polarized Radiation in Weak Magnetic Fields", Solar Magnetic Fields, IAU Symposium No. 43, ed. by R. Howard, D. Reidel, 1971. 19. Harvey, J. W., Solar Physics, 28, 43, 1973. 31 20. Harvey, J. W., Solar Physics, 28, 9, 1973. 21. Zwaan, C., and J. Buurman, 'Magnetic Field Strengths Derived from Various Lines in the Umbral Spectrum", Solar Magnetic Fields, LAU Symposium No. 43, ed. by R. Howard, D. Reidel, 1 971 22. Wittmann, A., Solar Physics, 23, 294, 1972. 23. Wiehr, E., Solar. Physics, 9, 225, 1969. 24. Chapman, G. A., and N. R. Sheeley, Jr., Solar Physics, 5, 442, 1968. 25. Harvey, J., W. Livingston, and C. Slaughter, "A Line-Profile Stokesmeter: Preliminary Resuit p, on Non-Sunspot Fields", Line Formation in the Presence of Magnetic Fields, NCAR, Boulder, 1972. 26. Stellmacher, G. , and E. Wiehr, Solar EhXsics, 18, 220, 1971. lit 27. Harvey, J., and W. Livingston, Solar Physics, 10, 283, - 1969, vi I 28. Staude, 1. , Solar Physics, 17, 331, 1971. 29. "Real-Time Solar Magnetograph (First Generation)", ed. by J. R. Watkins, NASA, George C. Marshall. Space Flight Center, MISC-SSL-70-5 #3, December 1970. 30. Beckers, J. M. , and E. H. Schr6ter, Solar Physics, 4, 303, 1968. 31. Beckers, J. M. , and E. H. Schrifter, Solar Physics, 4, 142, 1968. 104 e n REFERENCES - SECTION 2 - Concluded. U 32. Deubner, F. L., and R. Liedler, Solar Physics, 7, 87, 1969. H-1 33. House, L. L., and L. C. Cohen, Resonance Lines in Astro- physics, NCAR, Boulder, 1968. ^I 34. Moore, C. E., A Multiplet Table of Astrophysical Interest, Contr. from Princeton University Observatory No. 20, 1945. Cl 35. Unno, W., Pub. Astronomical Society of Japan, 8, 108, 1956. 36. Dunn, A. R., Solar Physics, 26, 83, 1972. 37. Grigorjev, V. M., and J. M. Katz, Solar Physics, 22, 119, 1972. 38. Beckers, J. M. , "The Measurement of Solar Magnetic Fields", r Solar Magnetic Fields, IAU Symposium No. 43, ed. by R. Howard, ;.^ D. Reidel, 1971. 39. Dunn, A. R. , "AnalyFis of Sunspot Spectral Data", Teledyne Brown Engineering interim Report SE-SSL-1428, October 1971. 40. Kotov, V. A., "Systematic Errors of the Crimean Vector Ma.gnetograph", Solar Magnetic Fields, IAU Symposium No. 43, ed. by R. Howard, D. Reidel, 1971, 41. Allen, C. W., Astroph sical Quantities, U. of London, 1963. 42. Moe, O. K., and P. Maltby, Solar Physics, 8, 275, 1969. 43. Wittmann, A., and E. H. Schroter, Solar Physics, 10, 357, j 1969. 44. Maltby, P., Solar Physics, 13, 312, ,_ 1970. 105 _ r, WON _:. _ T _..,^ , ^; ^^ 'NI. TABLE OF CONTENTS i fit Page a INTRODUCTION ._ . _ . . ,^ ^ 110 MAGNETIC FIELD NEUTRAL LINE PROGRAM . . . . . . . 111 t MAGNETIC FIELD GRADIENT PROGRAM . . . . . . . . . 120 RESULTS OF PLOT PROGRAMS 129 t' NOISE REMOVAL PROGRAM . . . . .. . . . . . . . . . 133 I TRANSVERSE MATRIX GENERATION PROGRAM . . . 140 r. j 3 107 Y f } ...._.......... rte. . nw __..... __ y. .....-. .._ .:: .:__ _.:. ... __ . _. i 11 1 LIST OF ILLUSTRATIONS Figure Title Page 1 Point Labeling Patterns for Neutral Line Program . . . . . . . 0 112 r ' __.. - v 1 2 Listing of Neutral Line Plot Program 114 3 Listing of Magnetic Field Gradient Plot s. e Program . 123 4 Sample Neutral Line Plot. . . . . . . . . . . 130 5 Sample Gradient Plot . . . . . . . . . . . . 131 6 Magnetic Field Contours for Data Plotted in J ,. F Figures 4 and 5 . . . . . . . . . . . . . . . 132 j .¢ 7 Magnetograph Data Tape Format . . . . . . 134 8 Listing of Noise Removal Program . . . . . . 136 9 Listing ofTransverse Matrix Generation i Program . 140. Ll 108 bLIST OF TABLES Table Title Page 4 1 1 Gradient Plot Program Symbols . . . . . . . 121{ 411 , 2 Contour Labels for Figure 6 . . . . . . . 129 3 Data Statements for Spike Noise Removal Program . . . . . . . . . . . . 135 s i, j 1 4 Y F-1 , log mss:. INTRODUCTION This section contains documentation for four programs written for the Univac 1108. Two of them have been described in Teledyne Brown Engineering Interim Report No. EE-MSFC-1815 (May 1974). Some minor changes have been made to these programs, so updated descriptions and current listings are given here. These two programs plot selected portions of Real Time Solar Magnetograph data: one program displays locations of magnetic polarity changes, and the other shows relative steepnesses of magnetic field gradients as a function of location in the data matrix. The third program removes isolated large data values from the data array and replaces each of the removed values by the average of the values surrounding it. The "corrected" array is then written on a new tape in the same format as the original data. The fourth program is a simple routine which combines the "U" and "R" matrices from the; original magr ,,^tograph data to form the matrix of values corresponding to transverse magnetic field data. This new matrix is written on a new tape in the same format used for the longitudinal data. 1 3 n! -" k _l 1 I IMAGNETIC FIELD NEUTRAL LINE PROGRAM This program locates and pl, cs the locations in the magnetogram I at which the magnetic field changes polarity. At these points, the sign 4; 1, of the magnetograph signal changes, so the program really plots the locations where the signs of adjacent signal values are different. The position of each neutral line is identified by selecting the coordinates of pairs of adjacent points for which the measured signals 1 are opposite in sign. The program in its present form will analyze a ' square grid of data 128 points on a side and will store 1998 coordinate -^ values. Places where the signal changes sign because of the sign reversal of the magnetograph calibration curve for large magnetic - field values will be identified by the program as portions of neutral lines. When the field strength values at which the calibration curves ' change sign have been established, the program will be modified to ignore signal sign changes for field strengths in the reversal range. The program compares points in two adjacent horizontal data 1 rows. Beginning with rows 1 and 2, the signs of pairs of points are i compared by taking groups of four data points at a time. The points are labeled as shown in Figure 1; their signs are compared in the order f P1, P2; Pl, P3; P2, P3; P1, P4. If all four points are of the same 1 sign, points P3 and P4 are relabeled P1 and P2, and the next vertical pair to the right becomes P3 and P4 for a new four-point group. The comparison process is repeated across the data row. When two points of opposite sign are found, their coordinates are stored. In order to save space in memory, the program then stops testing values in a particular four-point group and moves to the next group. This explains why, in the final plots, the lines which connect points of opposite sign r Irk 111` G ex i1 .. z{ 4. s^ data row 1 P1 P3' data row 2 P2 P4 FIGURE 1. POINT LABELING PATTERNS FOR NEUTRAL LINE PROGRAM may take any of the four directions: they simply record the relative positions of the members of the first pair of points of opposite sign which was found in each group of four points. When the first two data rows have been scanned, the process is repeated with the second and third rows, and the full sequence is repeated until the entire frame has been scanned or until the array reserved for coordinate values has been filled. After the has been thescanning completed, coordinate values of the pairs of points of opposite sign are plotted by connecting them with short lines. A line drawn joining the midpoints of these short connecting lines will trace the location of a neutral line to the precision jallowed by the spatial resolution of the data. To assist in determining the coordinates of the plotted points, grid lines are drawn at every fourth data row and column. The p rogram uses as data the magnetograph output tapes in their formatafter undergoing initial processing. In this format, the transverse and longitudinal components are written on separate tapes. Each magnetogram consists of 9 records: a label record of 19 words, and then 8 records of 2049 words each (a counter plus 2048 signal value rs). In some cases, a few words at the beginning of each snag- netogram were lost when the original tapes were processed. The tape read portion of this program contains a short routine to correct for this condition. i 112 Two values must be supplied in order to execute the program. 4 Both of these are entered in DATA statements within the program. The first is the number of longitudinal matrices contained on the tape. E LLJ This quantity is given the variable name of IPP and is entered as an integer variable. For example, for a tape containing 12 longitudinal FTI LU matrices, the DATA statement would have the form DATA IPP/12 / s Only longitudinal matrices are processed by this program. The determi-' u nation of transverse field strengths from data recorded in the format s here field beused requires that a transverse value calculated as the K - square root of the sum of the squares of its components. The algebraic signs of the transverse field values therefore cannot be determined, F and polarity reversals cannot be detected. j 11 The second datum to be supplied is the mean background noise flevel for the frame of data. This variable is called RMSN; for the matrices that have been processed so far, the value RMSN = 0.05 is 4 l usually satisfactory. RMSN is a real variable. The DATA statement ' which specifies RMSN would be written DATA :RMSN/.05/ ll for a typical data frame. A listing of the program is given in Figure 2. A sample plot 11 is shown in Figure 4, i .. P, 113 o'' r nNow e a 07Tiff- 1^ C IZERn GRAOTFRTT L6NTw1113- IN" -OcA?;NE-Tn APB n / 00101 20 DIMENSION N L X(20001, NLY1 20n019AR RAY1221.TEMP(S000).Y(32, 178) 00103 30 OtMFNS1OM LTIME(9) 00104 4• DIMENSION A(201 OCIOS- 5• o4 TA (AR R AY111.1 0 1, 22)/ 244H ► RnC OPY ONLY, ONE. COP Y ^1606N0OI07 he DATA IPP/17/ 00111 T• n4TA HL/P/ - 00113 80 DATA RMSN/.nS/ 00115 99 KRE n 5 00116 n1• KI/R n 6 00117 110 CALL OPE N IP, 1. 'it _ 00120 120 IMAX- 129 00121 130 IMAY- 12P 00122 14• ISI7F- 2000 00172 IS• C N0, OF ROWS, NO. OF COLU M NS, NO. OF NEUTRAL LIN E POS)TlnNS TO BE 00122 I60 C STORFD 00123 17- IS7.1 n IS17F - 1 0012 4 _ IA$ CALL IDF f"T 0. ARRAY) 00124 19• C DATA ARE WRITTEN ON TA P E. F R OM RIGHT TO LEFT, IN RON OROF R . A - 0C174 2n• C ROWS AT A TI N E. P RECFOED BY A RECORD CONTAINING 19 WORDS 00124 710 C OF HFAnER INFORMATION 1a: 6C175 220 no 999 IP n I. IPP 00125 00130 236 240 C 300 READ HEADER INFnRMATIUM CALL RFDTPR ter 2. IER, NW, 19g A) OC131 25• IF (MW-1 9 ) 300 ► 1. 300 — 0013 4 260 1 WRITF (KwR, 9901 NW 00137 270: 990 FO R MAT (III , 34N W n . 15) 00137 00140 28* 290 C RMSM IS RMS NOISF. LEVEL FOR FRAME IF (IER - 1) 391, 39 fl . 391 _ 0CI43 300 391 IYRITF IK w R. 3921 IER, NW 00147 310 192 - -_ FORMAT (IH , 2110) - 00147 324 C READ 1ST 2 R F CO gn S nF MAGNFTnGRAM OPIaO 33• 390 DO 65 T- 1. 2 00153 3441 ICY n 1 0015 4 35• WRITE (K Y,'R. 98e1 tCT - DOW 360 9AR FORMAT (IH , 4HICT-. IS! 00160 370 J- 7448•(1-1[•1 - --..._^_. . OC161 384 19 CALL RFnTPR 18 2.1ER. NW. 1, ICNT,7048.TFMP(J ► ) 0(1 162 390 WRITE (KWR. 9P9) NY), IrNT OC166 904 989 FORMAT (IH ,3HNWs,17.SV.SHICNTw,lrl 00167 414 ! IIF (MW-7 n 49) 13^• 129. 130 00172 474 130 WRITF (K W R. 392) NW, IrNT 00176 434 KK• 2049-Nw ♦ ) 00177 440 JX- 1 { 00200 450 DO 121 K n KK. 704q 00203 4A6 7EMP(K1- TFMP(JYY OC70 4 470 JX . JX • 1 00205 480 171 CONTINUE 00207 ' 490 K20 KK - OP210 500 00 131 K• 1. K7 on213 Ste TEMP(K) - 0. FIGURE 2. LISTING OF NEUTRAL LINE PLOT PROGRAM q i ORIGINAL PAGE 1., 114 OF POOR QUALITY i 00214 S2• 131 CONTINUE tj 00216 530 1129 IF (IER-1) 3 9 59 4650 9 395 -00221 Sale 344 WRITE (KWR, 392) IER. NN 00225 $S• 4650 IF (1-1) 6S, 46S, 65 _ 00230 56• 4165 IX a 100 00231 570 ' !Y • (Y - SC - F I 00232 540 IDELYn 25 7 00233 S90 N. FLD(2 9 109 TFMP111) 00234 600 IDAYS• 200*FL0(26,I,N) ♦ IOOOFLD(2791,M)+80*FLn1?A$I,N) 00234 610 1443*FLn(29,1,N).20•FLD(30,1;N) ♦ ID*FLD13I.1.NI+8•FLD(32,I,M)j it 1 00234 620 244*FLD(33,1,N)+2*FL0(34.19N)+FLDI3S.I,N) 0023S 63^ N^ L0 ( l 8 .7. TEMP(tII - - - 00236 64+ j FL0130,40)e FLn112.4gTfMP(I1) 00237 6S• IHOURSO 20*FLD(10,1,N) ♦ IO*FLD(31.I.N)+o*FLn(32,1,N) OC237 66• 1+4*FLD(3391,N)+2OFLD(34.1,M)~ FL0 1 3S,I.N1 a 1 00240 67• No FLD(20, 7, TF.MP(1)) 00241 640 I IMIN• 40•FLD(29,I.N)•2OoFLn(30;IrN)•IO•FLp431.I,N) -- OD241 600 I4R0PLnf32.t.N1+4iF 3 Hl+T$-FCDT 3 4 9I,NI+FID(1 91i OC242 70• No FLD(27,7,T£MPIi)) a f 00243 710 ISEC n 40*FLP(29,I.N)•2MFLD(3091,NI410*FLD(31119N);a*FLnfl2.I,N) 00243 720 I+4*FLD(33,1.N)*2OFL0134,19N)OFLD(35,1,N1 6 A L._. OD244 73• ENCODE ( 41), LTIME1 InAYS• IMOURS. IMIN, ISEC 00252 74• 140 FORMAT (T4, SH nAYS 9 17,6H Hn URS 9 18 9 8H,MINUTE i, t0 9 8H SFCOMnS1 { ---0253 7S• I - CALL FRAMEVI3) .._.__ —_ T i 254 760 CALL PRINTV (54, LTIME, IX, TY) i { 00255 770 CALL STOPTV 3 )- 1 00756 790 165 CONTINUE 00260 7941 i ILOCn _1 G 00261 Ro• ICE I p Iv "-00267 el• C TCT 1S Nn. OF RECORDS ;READ - FRDFT TAPE- 00261 1120 C IC 15 M0. OF TIMES READ FROM TAPE IS EXECU T ED I}f c 00261 830 C IC SHOOLr AE EQUAL TO ICT 1 00262 A4• To 129 1 00263 AS* no bA .1J n 2, 37 $ 0026 6 R60 n0 74 KK II 1, 124j - 00271 970 Y(JJ, KK) • TEMP(l) t, 00272 8R• Is I ♦ I x 00273 89• 170 CONTINUE 00275 90• 168 CONTINUE ! OP275 91• C REMOVE STRIPF 00277 — 920 DO 4 r 56 IM n I. 32 x aa7f+7 .__ 93 0 ix n (IM-11.128 • 11t ` 003n3 940 TEMP11x1 n TE M P(1X ♦ 11 t 003n4 95• 4r56 CONTINOF F 4 00304 96• C SET,X 000RnINATF COU N TFR AND STA R T SEARCH OF FRAME OC3n6 970 NMAx• 1MAX - 1 1 003n7 9p• 11 n 2 `-Ott3D7 990 C START SE A RCHING COLUMNc 2 THROUGH 16-{ 00310 100• 11MAY= IMAM - 1 3 00310 101• C I SPIKE. NOISE FILTER1 Q0311 1026 211 O O 40SA Jim 1, 31 003I N 1030 no 4051 KK n 1. 127 00317 1046 XTEMs A89(RMCN-ARS(y(JJ,KK))) 1 - X03?(T IMS• IF ( x TF M -3.•RMSm) 4051. 40 5 1. 'qt)53 00323 1060 4052 YTEMO Ap5(RNSN•AR51Y(JJ+T9KKI)1 )- 00374 107• IF (YTFM-3.rRMSN) 4 ,143. 4 053, 4051 ORIGINAL PAGE IS OF' POOR QUALIFY FIGURE 2 - Continued 115 Irm 00327 1080 4054 YIJJ,KK1 — RMSN/1.50 i 00330 1090 GO TO 4051 r 60331 1100 4053 ITEM n AB5(RM9N-AAS(Y(JJ.KX+II)j 1 00332 111• IF IZTEM-3.•RMSN) 4055 9 4 055. 405100335 1120 4855 7ZTE M • A S S(R M SN-AB5(YtJJ • 1 KK+ ) r 00336 11140 IF (ZNUEM-3 .•RMSN) 4054. 4954. VOSI 00341 11 4• .41151 CONTINUE 4L, 00343 115• 411;40 CONTINUE 00345 1160 DO 9 JJ • 11, Ib Q0345 117• C PREPARE TO GET CORRECT COORDINATES FOR VALUES TO BE STORED _ 003 4 5 119_• C MISUNDERSTANDING, AA011T ORDER IN WHIC H TA P E 4AS WRITTEN00345 1190 C SO MUST EXCHANGE X AND Y y[OORD A F TfR THEY ARE OETERMINEO 00350 1200 NXI n JJ + (IC - I)-•16 00351 1216 MX2 n NXI + 1 00352 1220 no 1O I . 1. 127 » ` 3c: 00352 1230 C I SET Y COOROINATF COUNTER0034 5_ _ 174• NY1- i 00356 125• _ ----NY20 1 + 1 00357 1260 Pl- Y(JJ, 1) 0.0360 127• P20 YLJJ. 1 + 11 00361 1290 P3 n Y(JJ • I, 11 00362 1290 P4• YIJJ+I. 1+11 _ 00363- .130• PP• ABS(Pl1—RMSN .-" w 00364 1310 IF (PP) $07, 907. An14 0036 7 1320 P92 PP. C. ow 00370 133• P63 IF ( P I) 904, 902. 903 00373 1340 904 P1 • -PP 0037 4 135• GO TO 902 A1 a k 00375- 136• 9!13 P l . Pp K00376 1370 902 PP O ABS(P2)-RMSN -- 44 OP377 1390 IF (PP1 804, 901, 905004n2 I149s 07 403 140• n4A. A OS, Ppa 0. IF ( P 2) 9 05. 901, 916 004n6 1410 9115 P2 0 -PP PO407 -.142• GO TO 901 ` 09410 143• 916 P2= PP ._ i 00411 1440 901 PP! ABS(P31-RM5N 00412 1480 IF IPPI 8 06, 9129 807 00415 1460 A-16 PP= 0. xrw 00416 147• An? IF (P3) 9 17, 9129 90A 00 ,471 1490 917 P3n -PP 00422 -* 1490 GO TO 91? C0423 1 Sf! 90A P3 0 PP 00424 1516 912 PPP ABS(1*4)-RMSN° 004 75 1520 IF IPP) 909, 911_. RD9 00 4 30 153• AnA li a00431 154• Pf► 9 (P4) 9 09 , 911w 91C 60T13^4 .155• 9C9 a4• - PP 00435 I560 GO TO 911' 00436 1570 910 PCr PP 00 4 37 l5R• 911 IF (PI) IC4, 3, ID3 00442 1590 Ir3 IF (P2) 4 . 1. 3 E 0044 5 161+• I n4 IF (P2) 3, 3, 4' 00450 IbtO 4 aLX(ILOC)i fly 00 4 51 1626 MLYIILncI* Nxl 1 OC1452 163• %lLX(ILnC + 1 1. MY2 FIGURE 2 - Continued I { ORIGINAL PAGE Ib OF POOR QUALITY 116 E t^ r' ^y 00453 1640 NLY(ILOC ♦ I). NXI - 0045" 165• WRITE ( KWR, 301 P1 • P2 • NXI, NT-I 00462 166* 30',FORMAT I!H , 2(EI2*5.5X). 2(16; 5X1) .---00'1'63' 167* ILOC n ILOC ♦ 2 0046 4 1.68* IF (ILOC - 15)1) 10, 5, 5 _.. _ _0047_2 170* 6 WRITE (K W R * 8) hY1 00475 171 '+ 8 .. _ .. _FORMAT !6H NYIs, 17) * I 00'176 1720 WRITE f KOR * '411 ) - 00500 173* WRITE (KWR, 412) 00502 174+ 411 FORMAT (25H ARRAY RESERVED IS FILLED) 17S* 412 FORMAT 1 - 15H .-. TAR-NINWYE - Ruk-) J 00504 1764 946 IF (ICT-8) 907. 7 * 7 ^._ 00504 177* C GO TO END OF MAGNETOGRAM 00507 1790 907 CALL REDTPR (892.IER,NW,I*ICNTi20489TEMp(l)) 00,5)0 1790 WRITE (KWR, 989) NW, ICNT 0051 4 180* ICT n ICT ♦ 1 - c os ts JAI WRITE ( K1A'O " 0681 ICT 00520 1820 IF (ICT - A) 9079 7, 7 110520 IA3* C GO TO END OF MAG NETOGRAM9 THEN S T ART NEXT ONE 00 , 623 1894 3 IF (PI) 112, 12, 113 005 7 6 195* 112 IF (P3) 12 9 129 13 00531 1864 113 IF IP31 139 120 12 3^ -- -TA-7 • 13 N L X (I L O C) = My! 00535 188 4 ''rL,Y(ILOC)a NXI D0536 I894 NLX(ILOC + )1= NYl t 00537 1904 NLY(ILOC ♦ I). NX2 604o 191* WRITE (KWR 30) P I,{ _ 00546 1924 ILOCO ILOC + 2 J f 7 -130 IF (1LOC-1'471) 14 9 5, 00552 194* 12 1F (P21 I15, 15, 114 ^...^ 00555 195* 115 IF (P3) IS, 159 14{ 00560 196 114 IF (P3) !4 9 15; 15 .005[^ 3 9 *1 7 4 14 NL XfILOC1 n UY2 0056 4 1 980 NLY(ILOC) n NXI 00565 1994 NLX(ILOC ♦1) '• NYt ODS6 6 2000 NLY(ILOC ♦ 1 la NX2 00567 0QS75 2010 WRITE (KWR, 30) P2'9 P3, N XI, NYI f -02* ILOC n ILOC ♦ 2 _ J 00576 ^Q3* IF (ILOC - I S c1 1 0 5, 5 00601 2040 15 IF fPl) 110 9 10, 116 r- 0 4 - ^05 + 116 IF (P4) 16• 1C• IJ 00607 2064 110 IF (P4) 10 9 ti), 16 00612 2074 16 N LX(ILOC) NYI 0-0613 2080 NLYfILOC)= NX 1 }f r 00E14 2094 NL X(ILOC ♦ lla NYZ 1 00415 210• NLY(ILOC ♦ I)= MX2j - 006 j6— - 2 114 WRITE fKWR, 30) P1 • P4, NX1, N$i00624 212* !ILOC n ILOC + 2 ..k 006+25 2134 IF (ILO[-1571) I CI * S. S1 C 00630 2144 10 C'ONTINiIE 00632 215* 9 CONTINUE 1 vOb34 2164 IF (ICT - A) 20, 2 171. 7 7 - — 207 i00637 2J' O0 I19 JJ• _ ---_.t* i6 OC642 2180 110 170 KK n 1 9 170 006 4 5 2190 Y(JJ, KK1. Y(JJ+16 9 KK) FIGURE 2 - Continued ORIGINAL PAGE IS OF POOR QUALITY t 117 i9 I' 3-1 00646 2200 120 CONTINUE 00650 2210 119 CONTINUE 00652 2220 IC - 1C + 1 00653 273• CALL REDTPR(A; 2. IER. NW r is IC N Tr 20489 TE"Pl Il l 0 _ IKWR. 9891 NW ICNT`224 00661 00660 2250 ICT - ICT • ICY ♦ ) "^ 226 • RITE ( KWR. OAS) ICT 0066 4 2270 IF (NW-20491 230. 22 9 9 230 00667 2290 -230 WRITE (K W R. 392) NWy ICNT 00673 2290 KK• 2049-NW + 1 _ 00674 2]0 • ,fa ) 00675 231• _.— — __.-^ DO 231 K- KK. 2049 20700 2321 TEMPIK). TEMP(J) 00701 233• in J + 1 GO702 2341 231 CONTINUE 007n 4 2350 K2n KK-1 _ oy7p5 2AL0 110 232 K n 1. K2 "* 00710 2376 TCMP(K)• 9. 00 7 11 23A0 7,12 CONTINIIF 0071 3 2390 229 IF ( IER -11 39.3. 394 ► 393 0071 6 2480 393 14RITF (KWR. 3971 IER, NW OC772 2410 ],94 1- 1 ^_41Z72j ... 242 0 no 165 JJ. 1 7 9 37 00726 2430 00 166 KK n l• 12A 00731 2440 Y(JJ. KK)- TEMP(II 00732 245• I• i ♦ i 00733 2460 1J66 CONTINUE 00735 2470 1165 CONTINUE C97 —s 2400 C REMOVE STRIPE 00737 2.490 110 4051 IM- 71. 32 00742 250• IX n iIM-1).1 00743 2510 TEMPIIXI- TF MP(TX + 1) 0074 4 2520 415 CONTINUE 00746 2530 its 1 AM6 _ 254 • C GO SFARCH FIRST 16 COLUMNS AGAIN 00747 ?550 GO TO 2.11 00750 2560 Oct 00 219 JJ n 1. 16 00753 257• nn 770 KK- t• 175p_r,7st Env `'(JJ. KK) n Y(JJ+16 9 KK1 C07S7 2590 72n CONTINUE 00761 26D• 719 CONTINUE 00763 261• 1C • 1C +1 00764 2620 1CY% IC ^ a OC765 2630 II• 006 4h ?44• GO TIn >:t 00766 2650 C THIS COM P L°rFS SEARCH FOR *2FR(f G RAOJF.NT # PO1NT5 _007A7 2660 7 iF'IN• 1L O C -1 ^077w , 2670 NRITF (K'4 R. 1321 IFIN CC773 26A0 137 FORMAT (lH . SHI F I N -. 110) OC773 2690 C INVERT X AR4AY FOR PLOTTINf. OD77`4 2700 no IA,01 I s to IFIN OC777 2710 N1(- rILXIII _01000 2720 "ILXIII• IMAX+1 - MX '# , i' 7730 IR-I CONTINUE. - `- 010.01 2740 C PLOT TAPE" 0100 3 275e CALL ,R1OIV(2r'1•Qrl7B.prn.p.125.OrorOr4.09-SrSr^I0^^t1:.+4.a4) +t0s FIGURE 2 - Continued ^R.^G^^, pAGE ^ Fqua •i- M 1 F t C 1001 2760 1!F1. ILOC-2 01Of15 277+ D0 AQO i n 1, 1Fi s 2 ' 0 010 278+ Xi• NLX (I) I 01011 279+ CALL XSCLVI (X, NXP, IERR) 01012 2A')• N;X1- NXP y! Q1013 ZAP• Xjs NLX(1+1) t 01014 282+ GALL XSCLVI(Xp NXP, IERR) - 1015 ?,A3+ NX2 n NXP - 01016 294+ YiY- (NMAY+1) - NLY(I) 01017 2A5• CALL YSCLVI (YY, N YP, IFRO)0'1020 2A6+ NY 1 n NYP .' jet C21 287+ YY n INMAY+I )-NLY`(I+1 ).._._ 01022 2980 CALL YSCLVI(YY• N YP, IERR)011023 2R90 NY2• NYP `' ( 011024 290+ CALL LINFV(NX1s NY1 9 NX29 NY2) 0!1025 291+ 400 CONTINUE - ' 011027 2920 999 CONTINUE `— 010 31 ^f `3 +► CALL E N D J 0 R _. - -------- -- 01037 '1940 STOP '_. 01033 295+ END FND OF CnMPILATION; NO DIAGNOSTICS* 1 { t s IG^ PAO ,POM _ FIGURE 2 Concluded,- r QUA f i 119 MAGNETIC F I ELE ^j o] a i R i i E r x One way to represent magnetic field energy distributions in sunspots is to plot values of magnetic field gradient as a function of position in the spot. A second special-purpose program has been written to generate such displays. The value actually plotted is not the value of magnetic field gradient; instead, it is the difference between signal values of adjacent grid positions. This procedure was chosen for several reasons. First, it gives the most direct representation of the actual data. Second, the plotted values are independent of uncertainties in the field strength calibration of the signal. Third, evaluation of distances on the solar surface and foreshortening corrections are not required, so the plot is independent of the assumptions which must be introduced to make those calculations. Fourth, if differences only are used, the evaluation of anumerical derivative is avoided; that procedure is notoriously unstable. The final plot is.presented in the original magnetogram grid format, so it can be easily compared with contour plots and with photo- graphs of the scope display at the time of observation. A label page giving the date and time of the observation is written for each plot. Difference values in three size ranges are plotted. The scale factor used for demonstration was , the approximate mean noise level of the observations, XNSE, but any interesting scale factor could be 3 substituted. The plotting symbols were chosen to give an appearance of increased density as the signal difference value increased. The difference ranges and corresponding symbols are listed in Table 1. Y. The magnetograp signal data are read from magnetic tapes in the same format as are used for the neutral line program. In addition MW e s, 120 TABLE 1. GRADIENT PLOT PROGRAM SYMBOLS GRADIENT DIFFERENCE SYMBOL. 2 USE < difference < 5 XNSE o 5 XNSE < difference < 10 XNSE + difference > 10 • XNSE to the data tape, a mean noise level or other plotting scale factor must be specified. This value is supplied in a DATA statement by assigning a value to a variable called XNS; the appropriate noise value, XNSE, is later calculated from XNS. In the sample given here, XNS 0. 05. As in the neutral line program, the number of matrices to be processed is supplied in a DATA statement. Again, the variable name assigned to this quantity is IPP, and again it is an integer variable. This program processes either longitudinal or transverse data but cannot do both types in a single run. If longitudinal data are to be plotted, the magnetograph data tape, after initial processing, is used as the data source. IPP is the number of longitudinal matrices on the tape. A third DATA state- ment must be included: DATA LT/l/ and will cause the program to select the correct procedure for reading I and plotting the longitudinal data. If transverse data are to be plotted, F the data tape must be generated by the fourth program described in this section. IPP is the number of transverse matrices to be plotted, and LT must be supplied by the DATA statement i DATA LT /2 No separate data deck is required. The logic of the program is like that -of the neutral line plot 0 program, except that value differences instead of sign differences are ti i_ i i_ 1 I^rl^ 121 recorded. Sequences of small grids, numbered P1, P2, P3, P4 as shown in Figure 1, are used to evaluate the differences across the magnetogram. The plot symbol is assigned to the coordinates of either P1 or P2. The coordinates of P1 are used if one of the differences (P1-P2), (P1-P3), or (P1-P4) is plotted; the coordinates of P2 are used if (P2-P3) or (P2-P4) is plotted. The value plotted is the largest difference found in the small four-point grid. No difference values smaller than 2- XNSE and no isolated difference values larger than 6• XNSE are plotted. A listing of the program is given in Figure 3, and a sample plot is shown in Figure 5. 7I 4 1 4 Wen 00100 OcI ne 00100 octal 00I03 to 2• 3• 4• so he r. 6RADIENT GGNTOWAS IN MAGNET96kAN C BLANK IS PLOTTED IF GRADIENT V ALUE 15 LESS THAN 2X NOISE'S C O IF-6RADIENT 15 2 TO SX NOISE,' • IF GRADIENT 15-MORE THAN C IOX NOISE. ALL GRADIENTS MORE THAN 2X NOISE ARE PRINTED* DIMENS-1 -ON XTWO(IOOO)oYTWO(1000)oIFIVE41000)tYFIVE41000) DIMENSION XTEN(500)#YTEN(5001*TEMP(S000) * Y(32 9 1261 oolos 8• RRAY 42B),—GTEMi5l DIMENSION FLOX(12). FLDY(12, 00106 9• DIMENSION A119) 00107 10• DIMENSION LTIME19) 00110 It* DIMENSION TEME 120491 00111 12• DATA IPP/38/ 3 ia• OAtA (F t-14-r-4-4-v 12 1412-0" 4 calls 114 • DATA FLDX(2)/6H 00117 Is• DATA (FLOW). I n 4. 12)/9*6H 00121 16• DATA (ARRAY(!). to I S 221/24H HARDCOPY ONLY, ONE COPYr 1806H 00123 17* DATA HL/e/ 00125 18• DATA LT/I/ ---Go i 2s--- 19• G 6T A) 4 ' L QNrm t T 11 9 I NAL 9 'j I F ZRANSVEWSE 00127 20* DATA XNS/.O5/ 00131 21• KRE n 5 00132 220 KW4- 6 00133 23• CALL OPE N (66 I S 6) 00134 esi33 24• 25• IMAX• 128 Ij. ^v 00136 26• ISIZE n 1000 00136 27• C 1 NO* OF ROWS, NO. OF COLUMNS, NO. OF GRADIENT VALUES STORED 00137 28• ISIS loco 001 40 29• IS2w 1000 001 14 1 30• IS3 n $00 ON 4 2 3f+ 1SIZE - +— 00143 32• CALL !DENT 19, ARRAY) 00144 33• i DO 7 117 IP• I S IPP 00149 34• C READ HEADER INFORMATION 001 14 7 36• ODD CALL HEDTPR 18, 2, IER, Nw l- , -1-9, A) 001sn 36s IF (N*-19) 300, 1. 300 Be! 370 1 WR 1 TE---f K W R v 0 1001 4* ---- 00156 38* P90 FORMAT IIH , 3HNNe, 151 00157 39• IF IIP-30) 997. 700. 700 00;162 40• 700 CONTINUE 001 63 4 1• IF M-11 170m 170. 171 00166 142• ',170 XNSEAS A17 ) -(XNS-A(131) 00 1 170 44* 171 XNSE • SORT(A(8)*SQRT(XNS)) 00170 45• C XNSE IS MEAN NOISE LEVEL 00171 46• 172 TXNS n XNSE*2.00 00172 47• FXNSw XNSEO5*00 00173 48• DXNS n XNSE610.00 FIGURE 3. LISTING OF MAGNETIC FIELD GRADIENT PLOT PROGRAM 01t1G1N4, PAGE 0P POOR QUALITY is i E i 123 kJ ) 0 a 175 SO N FLDX ( 3) n A(4) 002P11 520 391 WRITE (K W R, 392) IER. NW 00205 53• 392 FORMAT (IH , 2110) 00206 S40 390 WRITE IKWR, 671 (A(l). 1- 1, 19) 00214 S5• 67 FORMAT IIH , 611 X . 01211 00215 560 WRITE (KWR. 167) (A111, IN 1. 4) 00224 58• WRITE (K W R, 169) (A(I), is S, 11) - 002!37 590 169 'FORMAT (lH .5fE12.S,2X),2fII0s2Xl) 00233 600 WRITE (KWR. 168) (AM, I n 12 9 191 00241 61• 168 FORMAT (1H , S(E12.Sv 2X)) 002,41 62♦ C READ 1ST 2 RECORDS OF MAGNETOGRAM 002;45 640 1CT - 1 002, 46 650 WRITE fKWR, '988) ICT 00251 660 988 FORMAT I1H ,4HICT-, 15) 00252 67• J- 2048+(1-1) + 1 f- 00253 eegG4 68- 690 19 CALL REOTPR (8, 2, IER, NW, to ICNT, 2048, TEMP,(J)) CNZ -- 002, 60 700 ---- --- _ 989 FORMAT (iH , 3HNW-, 17, SX, 5HICNT n , 151. 00261 71• IF IN*-20491 130. 129, 130 00264 720 130 WRITE (KWR, 392) NW, ICNT 00270 73• 00 122 I8. I, 3 00273 740 -315 122 TEMEIIB) n TEMP(IS) _ ..Hi e --.- -- --- -- -- _- % 00276 76• 00 123 Ie- 11, 2049 00301 770 TEME 118)- TEMPIIM81 00302 78• Imes IM8 + l 00303 790 123; CONTINUE 7 0/0^3f 0S^ 800 DO 124 ION 4 9 10 . -404+0' _ _ 44 ♦ 124 T C M C I 1 0 1 - X N-%&- ...____ -".___ ___-.. ----_ -.-__._.-..-. - 00312 820 DO l25 !8 n 1, 2049 00315- 83• 125 TEMP(IR)- TEME(18) ,^.. 00315 640 C REMOVL STRIPE 00317 A50 129 DO 4056 1M- I. 16 00327 860 IX- (IM-11+128+J-1+111 1?03ts - ---8 7T-' - -----Tim I 1 X ) 0-I %"-- - _ -.-- - — - 00324 See 4056 CONTINUE 00326 99+ IF (IER-1) 395, 4650, 395 00331 900 39S WRITE (KWR. 392) IER, NW 00335 91• 4450 IF 11 -1) 65, 465, 65 00340 —003"1 92- - --9341-- 465 IX - 100 -. _ 11V- .4Ir_'_- 00342 940 IDELY- 25 003 4 3 95o Na FLUI29 109 TEMPO)) 00344 -960 IDAYS- 200*FL0 ( 26.1,N)+I00 - FLU127 . 1,N)+AOOFLD(28,1,N) F00344 1970 1+40•FLD(29,I.N)+20-FLD(30,I,N)+10-F60131919N1+8• LD(32.I.Nl Qeu 00344 980- 2+4•FLU(33,1.N)+2'FLD134,1,N)+FLD135,19N) 00346 100* FLD(3U,49N)- FLD(1294,TEMP(l)) 1= 00347 1010 (HOURSn 20*FLD130,1.N1+10*FLO(31.I.N)+8-FLD(32,I9N) 00347 102• 1+4•FLU133,1,N)+2*FLD13491,N1+fLD(35,i,N) 00350 1036 No FLD120. 7. TEMP(11) 4300351 104 • 1MINn 400FLD 1 2991iN1 + 20*FLD(_3.0'..I.N)+IO*FLD(3191,N) _ 84331_, .. _ 0"-- ... _^_ { sof 6 W 1 32 .1 N } ►4' Ft 81 -iJY ra lit -i Li1(i Y r — --- FIGURE 3 - Continued ORIGINAL PAGE IS GE 'POOR QUALITY, 124 1 YJ t 00352 1060 No FLU(27.7.TEMP(l)) - ' 00353 1080 (44•FLUI33.I.N1+2•FLD(34.1.N)+FLD(3591.N) 00354 !090 ENCODE 140, LTIHE) IOAYS. IHOURS ♦ ININ, ISEC ^r 00362 110• 40 FORMAT (14. SH DAYS & 1796H HOURS9180H MINUTES. I S O M SECONDS) 00363 111,• CALL FRAMEV(31 P$_ 00364 1120-- CALL PRINTV (54. LTIME. IX, IY) 00389 !130 00366 114• 65 CONTINUE 00370 115• ICU I p^ 00370 116• C ICT 15 N0. O F RECORDS READ FROM TAPE ¢ 00370 1170 C IC IS NO. OF TIMES READ FROM TAPE IS EXECUTED ,,•_ ^] 00370 1180 C IC SHOULD BE EQUAL TO ICY - ! -- --- ----'_ { tj-T--21- } 00371 1200 I n 129 00372 1210 DO 68 JJ- 2. 32y } 00375 122 • DO 70 KK • 1, 128'f( F 00400 1230 Y(JJ. KK) n TEMP(l) 00401 124 ^ ' yz • 69 CONTINUE00404 1260 Is I N --- 00406 l2A e----- -- ---- _ _—. ^a 0(+!104 127• C SET X COORDINATE COUNTER AND START SEARCH OF FRAME • NMAX n IMAX -1 ` 00407 129• J10 1 00410 130• J2. I — 094 ! !-- +a{^ a^.1 00 4 12 132• Its 2 - 1 4 33• G STARTS U A- 1 -1- 1 C LIMNS 2 TNRUUGN ► b00 12 1 E L 00 4 13 134• NMAY n IMAY - l 00'413 135• C SPIKE NOISE FILTER 00 4 1 4 136• 211 DO 4050 JJ- 1. 31 _--.$44 t7 -- ' l a i+— -- n n 4951- K- -1 ,-127 00422 139• XTEM n ABS(XNSE-ASS(YIJJ.KK))) 00.423 1390 IF (XTEM-3.+XNSE1 4051. 4051. 4052 00426 1400 4OS2 YTEM- ABS(XNSE-ABS(Y(JJ+1.KK))) 00427 141• IF (YTEM-3.•XNSE) 4053. 4053, 4051 00 4 32 1426 4054'Y(JJ,KK ► - XNSE 00434 1440 4053 ITEM• ARS(XNSE-ABS(Y(JJ.KK+I))) 00 4 35 1450 IF IZTEM-3.0XNSE) 4055. 4056, 4051 00 44 0 1-46• 4065'ZZTEMm ABS(XNSE-ABSIYIJJ+I.KK+i))) 00 ,441 147• IF IZZTEM-3a*JNSE) 4054 9 4054. 4051 00 4 44 1480 4051 CONTINUE —9fi4^ltr---tV9 ►--- -------- 00450 150• 00'9 JJ n 11, 16 004501510 G PREPARE TO GET CORRECT COORDINATES FOR GRADIENT VALUES TO 00460 1152• C BE STORED 00 4 50 153 • C MISUNDERSTANDING ABOUT ORDER IN WHICH' TAP E *AS WRITTEN 00450 154 0- C SO MUST EXCHANGE X AND Y COORU AFTER THEY ARE DETERMINED (JJ, ^.. 1 --0{►M5 ^ N X-F+--ld 4-I-C -,1 1aµ .__. _ . - • •---- --- ._ _ .. .. _ _ _ _ _ 00 45 4 ► S60 NX2r NXI + 1 00 4 55 1570 DO 10 I. 1, 127 00455 1580 C SET Y COORDINATE COUNTER 004A0 -1690 NYI- 1 00 4 61 160• NY2. I ` ♦ 1 0 FIGURE 3 - Continued ORIGINAL PAGE IS OF POOR QUALITY 125 e F, u r^ n 00622 2120 IF (J1-IS2) 109 S. 5 N M X00675 1130 311 WRITE IKWR9 261 X29 NY 1. G A 00632 1140 XTENIJ3)s NYI 00633 1150 YTENIJ31s NX2 00634 2160 J3n J3 + i t ---89b35— •>t-1-".-------•- ---1-^--N,a^ Fb 3 > 10 r -6 ^ rr - . _.: _ . ___ _ _ -._ ^ _ --- • _ FIGURE 3 - Continued ORIGINAL F nim POOR QU I!l 126i rt' E 00463 162• P1s Y (JJ. 1 + 1) '' OP;Iisl i 6 i' ° i- Y (J d 1 ^ l > ._ 00 4 65 1640 P4 n Y(JJ + 19 1+1) i 04466 1650 GTEM(l) n P1 - P200 ,467 1660 GTEM(21 n P1-P3 i 00470 1670 GTEM13) nP1-P4 00471 -----169 00441- 1680 GTEM(4) n P2-P3 61 l 00473 1700 T - GMAXs ASS(GTEM(I)) 00474 1710 16 n 1 00475 1720 DO 299 12 n 2. 5 r 00500 1730 IF (A85/GTEM412))-GMAX) 299, 301. 301 00503 1740 301 GMAX • GTEM(12) { 1YrF11 - - 0050S 1760 299 CONTINUE 00507 1770 IF 116-4) 297, 298, 298 00512 1780 297 IF (GMAX-TXNS) 10, 295, 295 00512 1790 C COORD OF PI WILL BE STORED 00-5I5 1800 295 IF (GMAX-FXNS ► 294, 302, 302 9v5 a s - i B F+ - 4 - --- - - .x 00525 182• 25 FORMAT IIH ,4HNX1s,17 9 9M NYJ=,1799H GMAX n *E12.5) 00526 1930 XTWOIJI)s NYI 00527 184• YTWO(J1)s NXI ' 00530 1850 Ji n J1 + 1 00531 1860 IF lJl-IS11 10, 5, 5 t' 00637 188• 303 WRITE (KWR, 25) N X19 NY19 GMAX 00544 1090 XFlYE(J2)s NYI 00545 1900 YF1VE(J2)s NXI c 00546 1910 J20 J2 + 1 X' I 00547 ^- 1920 IF (J2-152) 10, 5, 5 ^BSf►? -- 00557 92, 1940 — R 1 X- ° <<- r^-WQ r 2ST -N-X4 r.NY L►-fiMIJC__-- ----- -- XTEN(J31s NYI 00560 1950 YTENIJ31s NXI 00561 1960 J3 s J3 + t 00562 1970 IF (J3-IS3) 10, 5, 5 t 00565 1980 298 IF,(GMAX-TXNSi 10. 307, 307 --685fi5- . --199+-- --E ---E66i)D- 6f-P2 WILL-Hf °Si6RF.N -.-- _ --- -- . _-. _ _ . 00570 2000 307 IF (GMAX-FXNS) 308, 309, 309 00573 2010 308 WRITE IK W R, 261 N X29 NY19 GMAX 00600 2020 126 FORMAT (lH ,4HNXZz,J7g9H NY1m91799H GMAXs9E12•S) 00601_: [030 XTWOIJIIs NYI 00602 204.0-- YTWO(J11s NX2 — 88603- 206 4 -- ` 00604-- 1060 IF (JI-ISI) 10 1 5.--5 i 006,07 2070 309 IF IGMAX - DXNS) 3109 311. 311 00612 2080 310 WRITE' IKWR, 26) NX2, NYI_. GMAA_ j 006117 1090 XF'I VE (J21 s NYI + 006'20 Zl0• YF,IVEIJ2)s NX2 ) SIM I I U 1 01 I . - . I Ll I I. I ! -1 ^l ^l 00440 21840 S IF INXI - 70) 6 9 6 8 906 004 14 6 220• 8 FORMAT (6m NYI n o 17) 006 4.7 221*- - -WRI-TE tKWRv 27) J 1 9 J29 J3 00654 222s WRITE (K W R, 11) oc6S6 i2230 *1-1-T-E tK-WR o 1-2) 00660 22440 11 FORMAT (40H k31 ARRAY RESERVED FOR GRADIENTS IS FILLED•) TERMIN*TE RUN, 1 00662 225 0 2260 K 906 PeRM*:f 1 H IF (ICT - 8) 9079 79 7 00662 22! 7• C GO TO EN O OF MAGNETOGRAM 00665 2280 907 CALL REDTPR (8, 2, IER, NW, Is ICNT, 204 8 , TEMPM) 00666 2290 WRITE f-K*Rj 989) NW, ICNT 00672 230• ICT n ICT 00676 000JI6 00701 00703 00705 2320 233* 2344 * 935• 236• IF (ICT-8) 907 9 7s 7 C 60 To END OF MAGNETOGRAM, T,HEN START NEXT ONE 10 'CONTINUE 9 CONTINUE IF IILT - 6) 20 9 2019 7 g o 66eafim 00713 g37^ 23as 28 H9 dalto 1. Do 120 KKw I t 128 00716 239* YIJJ, KK) m Y(JJ + 16 9 KK) 00717 9400 120 CONTINUE 00721 241• 119 CONTINUE 00723 21420 IC n IC + I ID67 2 11 i430 CALL REBTPR ( a TCH 04724 2440 C REMOVE STRIPE 00725 246* DO 4057 IM • Is 16 00730 2460 IX n lim.1)*128*111 00731 2470 TEMP(IX)m XNSE 00732 214 8• 40b7 CONTINUE -W-34 2490 WRITE (KWR. ICNT 00740 2600 ICT n ICT # 1 007 4 1 251• WRITE (KWR, 988) ICT 00744 2S2* IF (NA-2049) 230s 229, 230 00747 2S3* 230 WRITE fK W R9 392) NW, ICNT 00753 2540 KK• 2049 - NW + 1 2550 — 00755 2560 00 231 K- KK, 2049 00760 267♦ TEMP(K)a TEMP(J) 00761 2589 jam j + I E 2 3 rn.Tf-cOO7b2 2 9*-^ 00764 260• K2m KK - I P32 W"t 1 s K 2- ---- --- 00770 262* TEMP(K)2 Do '1 0?71L 263W 232 CONTINUE 00773 2640 229 IF (1,L R-1) 393. 394, 393 00776 6 5 s 393 WRITE (KWR, 392) IER,:NW 01002 266* 394 In I 2 6 ? s —90 165 dj 1,L-r-33— 0I006 268• DO 166 KKs Is 128 01011 t. 69* Y(JJ9 KK) n TEMP(I) 01012 2700 In I + I 01013 27l* 166 CONTINUE 01015 272• 16S CONTINUE FIGURE 3 Continued ORIGINAL, p.4(;- I PoopU QLTAU* 127 I 01017 2714 • C GO SEARCH FIRST 16 COLUMNS AGAIN 01021 0024 01027 01030 01032 276• 277• 278 n 279• 280• 261 220 219 00 219 JJ n 1. 16 Do 220 KK n 1. 128 Y(JJ. KK) n YIJJ 4 16 9 KK) CONTINUE CONTINUE " as" 0036 gale 282 n I ET I rz w I ICT n 10 01036 283• 11. 01037 284• GO TO 211 01037 Z85 n C THIS COMPLETES C A LC OF GRADIENT VALUES 01040 286• 7 WRITE (KWR, 27) JI, J2, J3 61845 ile?s 3H44 ,4-5-g rj* 3W-J2W.I6-.6X0Md".tai 01045 288• c INVERT X AND Y ARRAYS FOR PLOTTING 61046 289• Jim JI . 1 01047 290• DO SCO t o 1. J1 01052 291• NX n XTWOM 01053 292• . a 9 a^ Nye YTWO(I) NTWO; 1 k ^ NMAN' s fNK6. A;0 1 a oloss 294• YTWO(I) n NMAY +I-NY 01056 295• 800 CONTINUE 01060 296• J2 n J2 —1 01061 297• DO 799 f u to J2 01064 296• NX n XFIvE(II 0!a ri__ 1299+. 91066 300• XFIVE(Ij n NMAX + I -NX 01067 301• YFIVE(I) n NMAY #1 -NY 01070 302• 1799 CONTINUE 01072 303• i nJim J3-1 0107!3 304 n DO798 t o 1. J3 4)4"6--- 9 T E N 4 1 4— 0107 1 7 306• Nye YTENII) 01 I0',(1 307• XTENJI) n NMAX + I-NX 011uil 308• YTEN(I) n NMAY + I —NY 01102 309• ;798 CONTINUE 01I04 310• CALL WUIK3L (-I#0o0e128*0o0o0@128.0#IHO,FLDX*FLDY.JltXTWO,YTWO) C ALL: _ __4 0 0 * 0 W_ I_ Q 9 2 04 9 1 W - F , 0 X ^ E 1 0!$ r J'3 0 XF_I Vf # At F_L V E 01106 Size CALL WUIK3L 4Mo0*00128o0o0o0e128oO#IH*.OLDXgFLDYoJ3,XTENeYTEN) 011 93 7 313• 997 CONTINUE 01111 314• CALL ENDJOB r. t. 01112 315• 998 STOP 01113 316• END ENU OF COMPILATIO N : NO DIAGNOSTICS* RESULTS OF PLOT PROGRAMS Figures 4 and 5 show results of the two plot programs for the same frame of data (23 October 1973, 23h 41m 9 s U. T. ). Figure 4 is, the neutral line plot and Figure 5 the field gradient plot. Figure 6 isl a contour plot of the same data frame, made by the Computer Sciences Corporation. (The orientation of Figure 6 is reversed both vertically and horizontally from Figures 4 and 5.) The contour intervals of Figure 6 are labeled according to the code given in Table 2. TABLE 2. CONTOUR LABELS FOR FIGURE 6 1 LABEL FIELD STRENGTH (gauss) A -2:581 x 103i B -1.290 x 103 C -6.452 x 102 D -2.581 x 102 E -2:581 x 101 F 0.000 G +2.581 x 101 H +2.581 x 102 I +6.452 x 102 J +1:290 x 103 K +2.581 x 103 The position of the solar limb shows clearly in each of these three figures. (The vertical streak in Figures 5 and 6 is a flaw on the magnetograph vidicon tube. The gradient plotting program now contains a routine which removes this streak. ) In addition, the active region shown contains two neutral lines which run across the regions w of steepest magnetic field gradient. There is also some evidence, 3 in Figures 4 and 6, of 'a weak but complex field structure near the limb. 129 i a ^^ i ^u 3 '^` 110 *: I 4 Vl% Ir l^ I Il too 90 I l I I ro I' ki (I fl Cl 0 FIGURE 5. SAMPLE GRADIENT PLOT 131 -mad iii, d Witt "goo", _^ ^^ ' ^ ~^ ^^ -v ^^ ^^-^ ^^ ^ ` / ^. + ^^ ^^ F^GURE 0. MAQNETIC FlELD C0NT0URS FOR DATA PLOTTED lQ FlGURE^ 4 AND 5 ^^ 8 = l3^ ^ . ^, ^ ^ N01 SE REMOVAL PROGRAM Some of the data matrices contain noise values. which appear as single values much larger than any other values near them. This program removes each of these values, replaces it by the average of r the points surrounding the removed value, and writes a new tape containing the corrected matrices in the same format as on the original A tape. Both longitudinal and transverse matrices can be corrected in one pass . The program also removes the vertical streak which appears « m Figures 5 and 6. This stripe always occurs m column 111 of the ^ data matri. as it is read in .(the matrix is stored reading from right to left across the frame). Because the location is always the same, the, stripe can be removed as soon as the matrix has been. read. The ^ value in the location X = 111 in each line is replaced by the value '" X = 112 in the same line... t ,. The isolated values to be removed are identified by comparing them to criterion values which are supplied as data.. Two criterion `;', w values are needed, one for longitudinal data and one for transverse. The data tapes used are the..magnetograph data tapes after the initial. m processing, so the data values are signal values, not field strengths. Also, the transverse criterion value is the criterion for the U or the. ^^^ R component, not for the resultant transverse field vector. It is assumed that the same criterion value can be used for the U and R m matrices. (^ ^' After a matrix is read, the. proper criterion value is chosen, and the absolute„value of each matrix data point is compared to the ^ ^ criterion value.. If the matrix vaa:ue ismore than six times.. the r ^ ^^;: '^ _133 S ^ '. -.-, "' ^^ ^ ^ €) p ^^ 1^ criterion value, the adjacent matrix points are examine d. If one or y u more of the adjacent values is greater in absolute value than six times ^ the criterion, the tested value is assumed to be valid. ; Tf none of the ! ^ adjacent values is greater- in absolute value than six times the criterion, ^ ..^ s the tested value is assumed to be invalid and is replaced by the average ' ; ^' of the adjacent values. 9 1 The magnetograph data for the program.. are taken from the .-.. data tapes after initial processing. These tapes have the general ^., ^' b: forma± shown in Figure r . ." a HEADER !t LONGITUDINAL DATA MATRIX ^^^ MAGNETOGRAM INTENSITY DATA MATRIX #1 U MATRIX (ONE COMPONENT OF TRANSVERSE DATA) R MATRIX (OTHER COMPONENT OF TRANSVERSE DATA) ^._ ^^ ^t ^^ '? HEADER ^" #; ' LONGITUDINAL DATA MATRIX +N ^- F` MAGNETOGRAM INTENSITY DATA MATRIX ^' #2 U MATRIX - ; r R MATRI X 11 ^ ^ I , ^^ HEADER ._^ LONGITUDINAL DATA MATRIX r MAGNETOGRAM INTENSITY DATA MATRIX M ^ #NMAT U MATRIX ,' R MATRI X ^( ^ END OF .FILE..:. .., FIGURE 7. MAGNETOGRAPH DATA TAPE FORMAT `^^ .,^ ^ ^; 7 ,. . i 134 w ^- ^.^ . -_,_.^ ^.. TABLE 3. DATA STATEMENTS ^'OR SPIKE NOISE. REMOVAL PROGRAM ---- MODE EXAMPLE VARIABLE (REAL OR OF DATA NAME VARIABLE DEFINITION INTEGER). STATEMENT NMAT Number of magnetograms Integer DATA NMAT/7/ on tape (i.e., number of groups of matrices as shown in Figure 7) XNA Criterion value. for Real DATA XNA/.005/ longitudinal data = six times largest valid isolated signal value XNB Criterion value for Real DATA XNB/.002/ each component of ' - transverse data = six times largest valid isolated signal value. expected in. U ^' and R matri ces HINT DINT = 1.0 if intensi ty Real DATA DINT/00/ matrices are present, - on tape and = 0.0 if no intensi ty mai;ri ces were recorded ,, On any tape,.. the longitudinal matrix may or may not be present, ' y y y p sent, and the -U-R matrix t aer ma sor ma t not be resent. nThbs ro ` ram will voce s s anP Y Y P P g P Y combination of matrices if the correct data are supplied. (It is assumed, however, that the intensity matrices are either always present or always absent. All tapes processed bo far have complied with this assumption. };n addition to the tape, values must be furnished to the program through four DATA statements. The contents and formats of these statements are described in Table 3. - ,, ^' k ,^ i 0 ^:=f; r r e3, a tt x '^ { ^. .^ .I ^^ .:; ^ ^ '^: i ,, r 4 r, ^' ^ e ,, a ^^ .. After the matrix has been corrected, the program writes it on taps in the same format in which it was read and reads the next matrix. a The tape which is produced contains NIvSAT groups of matrices; each. ... group contains the same number of matrices as were in that group on the original tape. ^^ 4 A listing of the program is given in Figure . 8. „^ ^ i ^. x f tF _ ,^ i, ^. z ,.. -^ ^- 9a1R0 1+ ^ REMOTE SPIKE NOISE,^ALUES ' JOIOI 2 •' DIMENSION TEMPt163841^A1151 . IAI4l^Yt128^1281 00103 3• DIMENSION TEMEltC491,, x0104 4• pI MEND IO.N _ XI1.S.E1 Y 1 ._ _,'_--., - •-_.r^_ :_ ._.. _ . 00104 5♦ ' C NMAT= N0. OF MAGNETOGRA M S ON OATH TAPE 00.105 6+' DATA NMAT/7/ '""' OClfi7 7+ DATA XNA /. 00583/ 0.0111 8^ ^ DATA XNB/.J0156/ ^ G011 . 1 9♦ C XNA IS LIMIT FOR L .MATRIX 0011.1 10• C XNe tS 1-Ii^l.i:7..-E.O.R T :MATRIX __..____:_.__ ^ , !, 00113 11+ DATA DINT/1•G/ ^^ ,Y ( , FIGURE 8. LISTING OF NOISE. REMOVAL PROGRAM F ; ' ,; ORIGINAL PAGE IS ; ;^ ' . . ^ OF p(X?R, QUALITY .136 -^ - ^ ^ ^" . e.... _..__W_. - - _ .: .. ^ . . .;.....^...k., _.^. _ ,..__ _ M- ,: __ .. _ _ ^'! t^ ^: ' ^, ` _ Ot)113 12 • ^ DINT .^^ 1.F..^N4_LN..ZE .LS.lTY__MATRICESa_s,I..IFJNTE- .N.S.I.L^l1ATR1CF5 ;^', ^0113 13• C PRESENT 1!ee 00115 14• KREn 5 ^o OC116 15• KWR• 6 JC117 I6 ♦ CALL OPEN (8.1.3) ,, ! 00120 17• CALL REV;IND l91 -- •^ i 00121 !B • CALL 4P.E^t_J9^- .1;._5.1. _ _ . _.. __ _+.._._.._ __ .. _-------. 00122 19r CALL REwIND191 .-^ 00123 2Ur Dp 100 1MAT n I. NMAT OOd2^ 21• C READ HEADER 00126 22• 1 CALL REDTPR 18.2 ► IER^NW^2.IA111^7.A111^2^TA^31^8^A(A11 'OOI27 23• CnLL W R ITER t9,2.tER.2^IA/11 ^7^A111,2.tAt31.8^^(811 ^-' 00130 24t .. .._1F_ .INy ll .._.191. L a . 1.7.• 1 _ .... .__..:_----_._. _.. '4 t OC133 25• 17 WRITE (K w kr 211 NW ^ 00136 26• 2l FORMAT 14H NW n . 15) ?0137 27• 26 WRITE ( KWk ► 1671 lAlll. IAl21. AII1^ Al2! ^ 00145 2@• 167 FORMAT IlH ^ 2 I119 ► 1%),21Al2^2X11 g ` ^ 00146 OQ156 29• 3pA 169 WRITE iKWk. t691 IIA 1 I1.1 n 3, 71 .1A131^IA1411 FORMAT X21 (10.2X11_1_IH r 5_1E1 2.5 ^ 2 X 1 _ __. .._—..__]C 157 3tr WRITE (KV+k. 168! lAlI1.1= 6. 151 -- — _ ''` ^^ 00165 32• 168 FORMAT IIH ^ B(E12.5.2x11 00166 J3• WRITE (KWk. 2991 IAl21^ (MAT 00172 34r 299 FORMAT llH . ?lIlO^ 5X11 L'0173 35r 1F f0INT1 2. 2. 3 ' ', 9176 36• 2 IF lIAl2.le5.1. 4. 5. 5 _-.----_-.__._.._. _._ __ __. _. ^? 00201 37• 4 ItiUN n 1^ OC2,;2 3d+ XNSE1l) n xNA 00 20) 39s GO TO 50 0020 4 4U• S dF (IAl21-611 6. b, 7 ' CO207 00210 4I• 42r b !HUN n 2 ! XtJSE1J ^+...XMB... __. _. ,— .— - . __ 00211 43• xNSEf2)• xN8 00212 44• GO TO 5p OG213 45r 7 (HUN n 3 002!4 46r XNSE(11 n XNA'^^^ rJ0215 47r x^'3E121 n XNB(s^ 00216 4Br XN3E13) n XN9 _ __ ._ 00217 49• G0 TU 50 t OC220 SCr 3 !F (IAl21 - 51 8. 8^ 9 JC223 Slr 8 !RUN n 2 ^! 00224 52r _ xIJS E (11 n XNA 00225 53r xNSEl21 n XNAt G0224 54r GO 70 5P . - —_..__ - _ j 00227 55r' ' 9 !F I IAl21-611 IU. 10^ 11 ^': ^^ 90'232 56r" 10 1HUN n 3 CG233 57r` XNSFIII n xNA '$ 00'234 SBr xNSEl21 n XNB. '_:j 00235 59.r. %NSE 1 31 n XNB 09236 60• GO TO S p _._ _ I 00'237 61 • 1 1 (,HUN n 4 ^ 00'240 b2• XNSEtII n XNA 00241 63r XNSE121 n XNA 64• XNSE131s %NB -0242 243 65♦ XNSE141 n xNB - _. _ _^_^ ' ta0245 67• 5Q DO 51 1 n Ir (RUN 'r ORIGINAL PAGE IS FIGURE 8 -Continued OF POOR QUALITY _ ^, ^. . _ .^ ^ x^ , . ^ ^ ' 002 4 5 ... 6:esL— .. _.^ ._ _--- .RE.AD ..ktA-I-R.1-1L - -- — - . _ _. _. . _... _... - --_. _—. f I JOf.250 69r J= 1 ^ 001251 7qr 52 CALL. REDTPR(8,2+IER•NW,I^ICNT•204H,TEMPI J )1 } ' 00'252 71,r WRITE IKWR. 969) NW• (CNT 00;256 72r 989 FORMAT llH • 3HNW n •I7,5X•5H:CNT n •15) ! pO^y56 73r C CHECK FOR WRCNG_RECCR p LENGTH iN 1ST RECORD " 00;25 7 7 q .^ _ ..^_ _I F-• -UPI -N^-^-2^ay-s-^-3-3J^+-s4-•--_}^.tl-.. _..--- ____. — ..---^^- ^, 00;262 75r lap WRITE (KWR• 9891 NW, !CNT ' liCj' 266 7br WRITE lK'+^H• 113x) ( TEMPt1L )• IL s 1• 2n1 U0^274 77^ 1139 FORMAT 1511H • E12.51) 00275 7Nr 00 122 i g = 1. 3 9 ""! OQ300 7qr 122 TEMEIIBI= TE M PIi g ) '" 00302. 6pr _._ _. _ 1Me:. 4_ -_ . ___ .._—_ _..__-.._ _-_-- --^_._. ._-.-- _ _ G0303 81r 00 !23 I g n I1. 2048 j ^i 00306 82r TEMElIB)= TEMPIiMB) )j ap3U7 83• IMB n IMg + 1 r' 00310 A4r ! 1.23 CONTINUE ^' ^iw,,.,,.;^-.r., -•— -..^ P^^ aQ31 5 86 + 1.24 TE-ME-1 .1 B) = XNSE 1^-1..I- ... .. .------.. C ^' 00317 87r DO 125 iB- 1. 2C48 00322 8B ♦ 125 TEMPII6) n TEMEIIB) j ^ OC32y 89r WFt1TE lK4^K• 113.) (TEMPIIL), IL n 1. 20) ,, 00332 gar 59 J= J + 2048 ^3 ,, 0!+333 9lr 53 CALL REDTPRI A , 2•IER•NW , I ,ICNT•2048 • TEMP I J)) J^ G0334 92t WH 1TE Lx_HR^ .9.8.4.1.. t^1.W, _i C.NT ... 00340 93* IF ((CNT-8) 12. 129. 1?9 '110 34'3 9'4r 12 J n J + 2(}48 ' GC34'.4 95r GO TO 53 x: C I P ^^ ^^ (^C345 9' 7r 1 29 DO M 4D56 S I M l , ) 2A ^ ±^ 60350 9'e+ IX n I1M-li• n I29+}11 .1' _i UC351 9'9• TEMPIIX)= TEMiP lIX + 1) ;-^ a i p1;352 10'Ur- 4056 CONTINUE + ( 00352 lUlr { WRITE MATRIX LNTO Y ARRAY '' ' I CC354 102+ 1.Y' 1 ^' ^ 80355 103r '12ADO 6 8 JJ• l • ^ ^ 60360 104• DO 70 KK n 1. 12A ,^ a 110363 145 YIJJ•KK)= TEMPItY) '° h OC364 LObr 1Y n iY + 1 00365 107+ 7p C UNT I NUE J0367 IUBr 6B CONTINUE ^...^ QG367 109r C SPIKE NO15E FILTER pC371 11Qr 21 l -D0 4050 JJ = 1 • 1.27- . Op374 1llr D0 4451 KK n 1. 127 ^X0377 112 XTEM= ABSIXNSEIi)-AHSIYtJJ,KK))) ^^^ !)C 4 00 113r XMG n Y(JJ.KK ) ^' Q0 4 01 114« IF (XTEM-S. r XNSEI 1 ► 1 43 5 1 • 413 5 1 • 4052 „.,.. #^ v ^; C. [14(14 115r y052 YTEM n AHSIXNSEII)-ABSIY I JJ + I,KK)11 !^ ^,: O,G405 116+ IF IYTEM-S.!XNSL:1.I 11 4.05 3• 4n53, 4051 .^ ,. O^C410 117r 4(154 TTM1 = (Y(JJ•KK+1)^YIJJ+I•KK)+VIJJ+I•KK+11:)/3.. ' .(10411 ller IF LJJ-i) 39JC• 30Q0• 3UL)1 'l ^f. _00414 1.19.• 3,?01 TTM2 = ITTMl + Y1JU-1• KK)+YIJJ-1•KK+1)1/3• *^^^^ OC 4 15 120 n GO TO 3nr,2 k OQ416 1?ir 3dC?"^ TTM2 n TTMI ...^k ^ C0417 122* 3CJ02 IF 1KK-_l.) 3DG3• -3003• 3CQ4(, ^; 00422 123r 3t^04 TTM3' lTTM2+YlJJ, KK-11 + Y(JJ+1. KK-111/3. ^. ^ ^ .; ,^ •FIGURE 8 -Continued " ^"^ ^ ; .<>. ' u { i ^ ^_.._^ ,, y + _ _ ^., ' _^.^:^^'r^+^..^^ ^'^^^' ^ _ 138 , }r{ ^^ M^ r^ ,L/r^^ t^^'^^ ^ ..»u.....,a._^.._ . -.«. ..^:::.- .„.. .:..^-.,^ ,,.^^ ._....:.s. ,..., ,.-. ^,...:-^..,,.. .- _,,.. ..ate_ - _ - ,^ {1 i I i z . O.O y 2 3 00 4 26 .12.4 •, 125• _._ .. __ _. 3006 LE__L^1..1 •_11._3D.C.S.^. 3 n n 5. 3 D n b TTM4= (TTM3+Y(JJ-1• KK^11I/2^'---___._...... ^._^^— 1, GC^427 OG 4 30 126+ 127+ 3'x05 GO TO 3 g lf! ' TTM4 = TTM3 OG 4 31 128 GU TO 3p1;^ „_ QQ^(32 129r 3.003 TTM 4 ' TTM2 DD 4 3 3 13 G s _3 010 . X (_J J ^--. -KK-ls __LIPL4 ._._ ..... __ s OC434 l31• WH1TE (K W R• 4 u49) JJ• K K •_ .X M G• Y ( JJ• KK) .k, fJ0442 132 4049 FORMAT (1H • 15. 5X. 15. 2(5X• E12.5)) 1 DG943 OQ44y 133• 134♦ 4x53 GO TO 4p5) ZTEM= A55(XNSE(11-ABS(YIJJ• KK ♦11)1 ^ ;• ^ OC445 135* IF (ZTEM^S•*XNSE(I)1 4055 4C55. 4051 ^r ^ 00450 ! 36l YD55.. . Z.LIE . M_= A8.5.( ,1(NSE.(. L) _ A85.1^ ( _ JJt 1 • K.K.+ 1 L.1-L __._ _ ^^^ L0 4 51 137• IF (ZZTEM-S.^XNSE(11I 4059. 4054. 4051 GCy54 13'6+- 4051 CONTINUE '( JQ456 13,9 4054 CONTINUE ^ (iC`i56 14!0* C REWRITE CORRECTED Y ARRAY IN TEMP. e ` _, , OQ460 141* I' Y= 1 i OQ4b1 142• .. QO. 17.1 JJ-.._Jra_ J2b __.... •^ - OQ464 14'3* UU 1 7 0 KK= 1. 175 a^467 G0470 14',4• !45♦ TEMP(IYI n Y(JJ.KK1 1Ys IY ♦ ) .i flL^471 14',6* 17C^ QONT INUE `, .{ 171 _._ _ ^ ' ^ ^00473 00 4 75 148+ C WONTINUE R .I T E T_A.P E _ _REt O B Q. ___ _ 149 J= 1 Up47b 15'0* ICNT s 1 t ^^• Up477 15'I+ 55 CALL WRITF..R (9. 2rIER^1^iCNTi2048•TEMP(JI) ( iCNT - 81 54. 56. 56 ;^^ ^;^ D0503 15,3+ 54 J F = J • 2048 . ^ ^ 00504 15'4* 1CNT:_. LLNT._^ 1,.._ _ .. -_ .._ ,; t7C505 15'5+' -_ GO TO 55 ' ' r OQ50b 15jb +- 56 N RITE (K(VR• 571 IMAT ^ ``^' 00,511 ISJ* 57 FARM AT (1BH WROTE MATRIX N0• • 14! Q0,512 t5'6* 51 CONTINUE. OR514 159♦ 100 CONTINUE 0051.6 16.0•. CALL. .CLOSE 19a^.1.._ • ^^ ^G51T 161+ _ STOP .. i ^G520 16?«' END t ^^t, = ^^ ENO Oi _-COMPILATION; NO DJAGNOSTICS. ^ ^ , .^ ^ FIGURE 8 -Concluded ,^ { 'f _; I f ^j ^ ORIGINAL, PAGE ^^ „^ OF POpR QUASI ^€^ 13 9^;^ j t ^` ^" TRANSVERSE MATRIX GENERATION PROGRAM This is a very simple program which reads a magnetograph data tape, selects the U and R matrices, and calculates the transverse component T of the signal according to T = (U 2 + R2) 2 , for each matrix' ^^^^ ^ point. The matrix of T values is then written on a new tape. .The tape written by this program is not in the same format as the' original s ^._. tapes; it consists only of header records. and T matrices, , ^.,^ The data tapes for this program are the same as for the other programs described in this section. Two data values must be supplied. .^ly .through DATA statements; these are NMAT and DINT. The definitions of these variables and formats of the DATA statements are exactly ^,^ the same as for the Noise Removal' Program. Note, in particular, r,f that NMAT is the total number of magnetograms pn the tape, whether .^- r or not all those magnetograms contain transverse data matrices. 'On the output tape, however, headers and matrices are written only for those magnetograms which contained transver se data. ,1A listin of the ro ram. is iven in F ure 9. "^^g P g g g ^ OOt00 1• C WRITE TA P E FOR Pl0'TTING TRANS y ERSE FIEL p PATTERNS OOIUi 2. OiMENStON Uil6]841; R12Q481, HT12D487 fl OOiD] ]• DIMENSION AI151, lA(4) ^. a 0010] 4• C NMATn N0. OF MAGNETOGRAM5 ON DATA TAPE +y ^DOlD4 5• DATA _NMAT /147 ' •----•- $11-T-A--N E-M-T-L$r0-f- } 00.106 7 n C D1NT•D iF NO INTENSITY MATR111 PRESENT, •1 IF INTENSITr MATRIx ^, 00106 9. C E SENT KRE nOOLLD 9 S ^^,^0011 j 10• ^ KWR n 6 ^1,^ 001 12 f 1 • {ALL OPFN l H, 1 , S) L ^ -•^-eo+ta ----t-;<.- . _._.. _ ^+^^.-t- rFr

Magnetometer experiment power profile

Abstract

Extracted data

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