InSAR Inversion Considering Model Error For Hypocenter Parameter

Rapid development of Interferometric Synthetic Aperture Rarar (InSAR), greatly enriching crustal deformation observation data, enables the geoscience research community to probe into the various geophysical phenomena related to earthquake fault in a fully new perspective. When extracting hypocenter parameter, geodetic data can effectively compensate for intrinsic limitations of other observations such as surface rupture data and seismic record. Hypocenter parameter can not only be used to analyze the seismogenic fault mechanism and regional tectonic stress, but can also provide a basis for studying rupture and expansion of the active fault, evolution of the characteristic fault, mechanism of the postseismic deformation, strain absorption and adjustment of the continental lithosphere, stress changes and seismic hazard assessment in the future. Consequently, the accuracy of hypocenter parameter holds a more and more attention of geoscience scientist. To determine a more precise hypocenter parameter, this dissertation creatively carries out the work of InSAR inversion considering model error for hypocenter parameter.This article first establishes the mathematical model of InSAR inversion for hypocenter parameter, and studies its intrinsic features. According to the rectangular dislocation theory and Laplace smoothing constraint method, functional model, stochastic model and mathematical model with equality constraint appropriate for InSAR inversion for hypocenter parameter are proposed. Method of the generalized inverse analysis is introduced into focal slip distribution inversion to give the calculation formulas of data resolution, parameter resolution and variance for the coefficient matrix of the functional model. By taking strike, thrust faults and Dangxiong earthquake as examples, the effects of adding observation data and adding constraint condition on the mathematical feature items are studied. The results show that adding observation data can to a certain extent increase the rank of the coefficient matrix, but cannot improve its morbidity; adding constraint condition can significantly increase the rank of the coefficient matrix, can improve its morbidity, can to a certain extent reduce the data resolution, but can significantly increase the parameter resolution, and can reduce its variance from hundreds of meters down to centimeter level. These results can provide a theoretical basis for inverting InSAR deformation observations for focal slip distribution. During focal slip distribution inversion, adding constraint condition is indispensable. This article then explores the effects of mathematical model error on InSAR inversion solutions of hypocenter parameter theoretically, performs the synthetic inversion tests, and investigates the distinction of functional model error and stochastic model error. Sources of model error in the InSAR inversion for hypocenter parameter is summarized, and model error theory of linear inversion from surveying data statistical analysis and method of Monte Carlo error estimation in the nonlinear inversion are introduced. By taking strike, oblique and thrust faults as examples, the effects of the functional model error and stochastic model error on inversion solutions of hypocenter parameter are analyzed by calculations of nonlinear inversion for hypocenter parameter and linear inversion for slip distribution, respectively. The results show that the functional model and the stochastic model containing errors can bias the hypocenter parameter solutions, and reduce the corresponding precision, consistent with results from theoretical prediction. Model error estimation and identification methods in the InSAR inversion for hypocenter parameter are discussed, and the distinction of functional model error and stochastic model error is investigated. The result indicates that effective separation of these two errors in InSAR inversion system of hypocenter parameter still faces larger challenge.This article then presents the model error compensation method in the InSAR inversion for hypocenter parameter, implements the synthetic inversion experiments, and gives recommended inversion strategy. Model error compensation method from surveying data processing is summarized in detail, and strategy of adjusting stochastic model to compensate for model error in the InSAR inversion for hypocenter parameter is proposed. By introducing variance component estimation (VCE) and robust estimation theory and methods from surveying data processing, VCE algorithm, robust estimation algorithm and robust VCE algorithm suitable for linear and nonlinear inversion for hypocenter parameter are designed, and the corresponding concrete implementing procedures are presented respectively, where the equivalent variance-covariance function is used to construct the corresponding weight function. At the same time, compensation abilities of these methods are measured by exhaustively synthetic inversion experiments. Smoothing constraint condition equation is translated into virtual observation equation by relying on the virtual observation principle, smoothing factor is then expressed in the form of unit weight variance divided by virtual observation variance, and VCE method is used to work out the weight of observing data sets and smoothing factor, simultaneously. Three types of algorithms are elaborately compared, their compensation strengthes are also analyzed. If the observing data set contains gross error, robust estimation algorithm can better reduce or eliminate the negative effects of gross error on source parameter solutions when nonlinearly inverting for hypocenter parameter, but has certain limitations when linearly invering for slip distribution, where robust VCE algorithm is required. If two or more data sets contain gross errors, robust VCE algorithm performs better than VCE algorithm on ability of compensation for model error. And then the recommended inversion strategy in the actual InSAR inversion for hypocenter parameter is proposed.This article then studies the October6,2008Dangxiong Mw6.3earthquake and November10,2008Dachaidan Mw6.3earthquake extensively. For Dangxiong earthquake, Envisat and ALOS image data with different tracks and different wavelengths are processed to extract high-quality InSAR coseismic deformation, robust VCE method designed by this study is used to reduce or eliminate the effects of model error on source parameter solutions. The results show that the focal slip mainly occurs in the depth range4.5-11km, the average rake angle and slip are-112.58°and0.50m, the maximum slip of1.53m is located in the depth range6.1-7.1km, and the corresponding seismic moment is4.22×1018N m (Mw6.38). Hypocenter parameter solutions from VCE have a certain bias. Biases without (robust) VCE are larger than those with VCE, and deviation of rake angle is-4.195°. Precisions without (robust) VCE are also significantly worse than those with (robust) VCE. For Dachaidan earthquake, Envisat image data is processed to extract high-quality InSAR coseismic deformation, nonlinear robust estimation is used to determine the focal fault geometry, and further linear robust VCE method is adopted to derive the fine focal slip distribution. The results show that the focal slip mainly occurs in the depth range10～20km, the average rake angle and slip are104.2°and0.2m, the maximum slip of0.64m is located in the depth range13.8-14.6km, and the corresponding seismic moment is3.74×1018N m (Mw6.35). Due to that the drived InSAR deformation field contains fewer gross errors with smaller magnitude, whether do robust estimation has little impact on the precision level of the parameter estimation when nonlinearly inverting for hypocenter parameter, but (robust) VCE is needed to fix the reasonable smoothing factor when linearly inverting for fine focal slip model.This article finally explores the weight of coseismic deformation observation data when inverting for hypocenter parameter. VCE method can better determine the weight ratio among different observation data sets, value of which is neither equal, nor equal to value calculated according to prior variances. Weight ratios from nonlinear inversion for hypocenter parameter and linear inversion for focal slip distribution are not equal and differ widely in magnitude, and should be estimated by VCE principle, respectively. The weights of the observing data points neither increase as far from the fault, nor increase as close to the fault. The criterion of assessing weight by distance from the fault trace is not reasonable. Considering mathematical model error, robust estimation principle can provide a fittable way to determine weight for each observing data point.