Seismic traveltime inversion in three-dimensional heterogeneous media

The measured traveltimes of specular reflection events are inverted to obtain a low spatial frequency, three-dimensional model of the reflector geometry and the compressional wave propagation speed. B-spline functions are used to describe the shapes of the interfaces and the lateral variations in velocity. The inversion is performed by optimizing a maximum likelihood criterion using a Newton based iteration. Model updates are obtained by iterative forward modeling and solution of the linearized equation set derived from the maximum likelihood criterion. In the forward problem, the ray tracing equations are solved as a two point boundary value problem with appropriate internal boundary conditions at velocity discontinuities. Analytic expressions for the Frechet derivatives necessary to obtain the model updates are given. Conventional methods are compared to the traveltime inversion technique using synthetic examples. For a relatively simple earth model containing only moderate lateral velocity variations hyperbolic moveout analysis followed by a Dix inversion produces a biased estimate of the velocity and depth. This is a consequence of the simplifying assumptions of the method. In this case, the more general traveltime analysis provides a better result. This is also true for a more complex earth model containing lateral velocity variations and interfaces with large dips and curvatures where the conventional methods fail badly. Picked traveltimes are used as the data in the inversion although the use of the data semblance or the stack power along the predicted traveltime trajectory is also explored. These criterion are shown to be more nonlinear than the least-squares data residual measure. Thus, it is difficult to converge to a global minimum using these criterion and more accurate initial guesses are necessary. An application of the traveltime inversion technique to a 3D marine data set is presented. In this application the effects of the seismic source and the recording system on the measured traveltimes are estimated. The time delay between the first break and the main pulse of the minimum phase source wavelet and the effect of the ghost reflections from the free surface are compensated for in the prediction of the measured traveltimesGeological Science