Earthquake location by distinct constraints for sparse and doubtful data

Earthquakes affected mankind since the days of old, claiming more human casualties than any other nature catastrophe. The determination of the hypocenter location displays one of the key subjects of seismology. Today’s standard approaches provide for trustable location estimates - given a large amount of stations with high quality data and proper assumptions about the sub-surface velocity structure. The same approaches fail, however, when this amount of stations and quality of data is not given, e.g. in the mapping of seismically active zones using low magnitude events: Here, only few stations detect the signals that sometimes barely exceed the noise level. Seismic phases appear hence unclear, rendering the information of arrival times doubtful. Another example are real-time location schemes (e.g. in Earthquake Early Warning Systems): Here, events need to be evaluated and located within fractions of seconds without knowledge of the complete waveform, and data available only from the first few stations that already detected. The objective of this thesis lies in a methodological development that provides for more accurate single event locations in the context of sparse and doubtful data. The less data is available the more the location estimate is determined and affected by the individual datum, its uncertainties and errors. The method of choice must therefore be outlier-resistant (e.g. ignore false picks) and incorporate all parameter uncertainties. When data is few, solutions may further be ambiguous (not due to errors in the input parameters, being exact solutions to a set of even ideal arrival times), meaningly: Multiple, significantly separated location candidates may exist. Also, models are usually only rough and simplified representations of the subsurface structure and will often not explain the observed data well enough. Today's standard approaches often disregard the corresponding uncertainties and, hence, often displace the hypocenter significantly to the true location - outside of the assumed error margins. Mislocations in earthquake early warning or forensic seismology may have far-reaching implications for society and on the political level. This thesis provides therefore a novel location methodology that incorporates the important uncertainties, naturally disregards outliers and thereby leads to robust hypocenter estimates. The work presented builds on the concept of (graphical) jackknifing, which contrary to most of today's standard approaches doesn't attempt to minimize the error in the over-determined system directly, but decomposes the system first into exactly- or even under-determined subsystems. This results in distinct location constraints that are based on arrival time differences between two- or three phases, only. Each constraint identifies a subset of space as possible hypocenter region. The combination of multiple constraints consecutively constrains the final hypocenter region. Since a single constraint relies on a minimum amount of phase onsets, only, solution discrepancies can be traced back to the individual phase data, which allows the data base (e.g. outliers) to be re-evaluated. The global solution is finally recomposed based on the sub-solutions deemed trustworthy, which provides robust and outlier resistant solutions. This concept is built on, supporting for three dimensional station layouts, complex velocity models and a volumetric computation, which render this approach suitable for a wide class of modern applications. A real-time methodology that regards uncertainties in phase picks, phase types and model parameters provides for robust and accurate locations when data is uncertain and sparse. New constraints are introduced, which allow to resolve ambiguities and provide for faster hypocenter and magnitude estimates in Earthquake Early Warning. A new direct search scheme is developed that integrates constraint probabilities over grid cells, which ensures the identification of sharp hypocenter regions independent of the grid's resolution, satisfying the demand for a complete search. The improvement in location quality is demonstrated using several examples ranging from gas-field low-magnitude event monitoring, forensic seismology to examples of real-time locations in Earthquake Early Warning