Regional deviatoric moment tensor inversion based onLangstonrsquo;s decomposition and Hilbert transformconstraints and its application

Based on Langstonrsquo;s decomposition theory and Minson and Dregerrsquo;s near-field displacement formula, this paper proposes a deviatoric moment tensor inversion method. Waveformrsquo;s envelop function calculated from Hilbert transform is introduced to stabilize the inversion. The method is successfully tested with synthetic data. Numerical experiment result shows that the method has decent robustness and stabilization. Specific results are as follows. (1) While the velocity structure and earthquake location are exactly known, the solution will be accurate and stable (Kagan angle5deg;, the error of double couple component percent, noted as DC%, within plusmn;5%), despite of high noise level even reaching to 30% of original signals. (2) While random disturbances on wave arrival time are limited within plusmn;3 s, the moment tensor solutions inverted in 0.01mdash;0.1Hz frequency range are still entirely stable. About two-thirds of solutions can be considered to be very close to the true solution (Kagan angle15deg;, DC% within plusmn;5%), and about 90% of solutions have a small deviation to the true ones (Kagan angle30deg;, DC% within plusmn;10%). It shows that the method has good compatibility with crustal anisotropy and lateral heterogeneity. (3) The test results under various crust models show that the velocity model has important effect on inversion result. If a 1D model being close to the mean model of true crust structure is used, the inversion can retrieve near-real solution. If the model is a little different from the true model (no more than 10% error), the solution would be close to the real one; if the error exceeds 10%, even reaching to 20%, of original signals, the solution will have notable bias. (4) Earthquake location error mainly affects focal depth determination, accordingly cause spurious non-DC component in final solution. But, with the constraint of pure deviatoric moment tensor, the fault parameters retrieved from inversion have little bias from the real one. (5) In case of sparse data (3 stations at least) and worse station coverage (less than 60deg;), we can still get relatively correct solution from the method under mean crust model. The method is applied to 24 Oct. 2010 Zhoukou-Taikang MW4.7 event in Henan province, China. The optimized solution retrieved by this method is consistent with that estimated from P wave polarity data.