Inversion Methods For The Focal Mechanisms Of Small Earthquakes And The Stress Field And Their Application

As we know, the study of tectonic stress field is important to the study of geoscience and its practical application. Similarly, focal mechanism solutions of earthquakes play an important role in the study of tectonic stress field. Introduction of the concept "seismic moment tensor" makes the displacement generated by an earthquake and the seismic moment tensor describing its focal mechanism have linear relationship. If the displacement field generated by the earthquake and the Green’s functions representing effects of propagation path are given, we can easily obtain seismic moment tensor (i.e., focal mechanism) by waveform inversion. However, the technique of waveform inversion is only suitable for far-field data or large earthquakes, and at most extended to regional data or moderate earthquakes. For synthetic Green’s functions in near-field distance fail to approximate real media response, the technique of waveform inversion becomes unsuitable for near-filed data or small earthquakes. Up to now, no consistent methods and techniques in resolving focal mechanisms of small earthquakes with near-field data have been accepted like the technique of waveform inversion. Thus, exploring new methods for resolving focal mechanisms of small earthquakes is the first of our jobs. Generally speaking, there have been existing two approaches to tectonic stress field from focal mechanisms which are based on two different assumptions:(1) assuming the direction of maximal shear stress be consistent with the slip of fault; (2) assuming the average direction of the stress axes of a huge amount of focal mechanism solutions be the direction of tectonic stress field. The above methods both have their disadvantages while advantages individually, so exploring new approaches to resolving tectonic stress field from focal mechanisms becomes the second of our jobs.An inversion technique for focal mechanisms of local and regional earthquakes, named Generalized Polarity and Amplitude Technique (GPAT), is proposed based on the progress already made over decades, and its feasibility and capability of resisting disturbance are tested by a series of numerical experiments. At first, an inversion equation system is constructed with the vectors consisting of the polarities of the P first motion and the maximal amplitudes of generalized phases based on the concept of wave field, and a technique for solving the equation system is specified. Then, a series of numerical experiments are conducted for the effect of various factors on inversion results, including distribution of observation stations, number of the stations, random noises, errors in epicenter location, errors in focal depth and errors in velocity model. We test these factors’effects independently, and finally, a special experiment is designed for comprehensive effect of all the factors. The experiments show that the GPAT is feasible, and has rather good capability of resisting disturbance.Forty-nine earthquakes are employed to test for the practical ability of the GPAT in inversion of the focal mechanisms, moment magnitude and focal depths. In order to test for the suitability of the GPAT for local, regional and far-field events, the events with magnitudes of about ML0.2 to Ms7.0 are selected, and the epicenter distances of observation points are kept from around 5km-8000km. The inverted results show that the GPAT mechanisms should be right to reasonable uncertainty ranges, the GPAT moment magnitudes are subjected to be trustable, and the GPAT depths seem to be about 0.6km deeper than the routinely determined depths on average. On the whole, the GPAT is believed to have a good performance in inversion of focal mechanism, moment magnitude and focal depth. After sufficient test of the GPAT, we applied this method to resolving focal mechanisms of 1671 earthquakes recorded by QiaoJia array installed in Qiaojia segment of Xiaojiang fault in Yunnan province. The minimal magnitude of these earthquakes is ML-0.7, and the maximal is ML4.7.After having learned the research progress, and especially having recognized the essence of the existing comprehensive-fault-plane-solution method, we tried a new method, called Tensor-Averaging Method (TAM), based on the physical understanding that seismic moment tensor is equivalent to stress glut. The new method admits that average direction of the stress axes of a huge amount of focal mechanisms should be in agreement with that of the stress field. In this case, it is unnecessary to identify real rupture plane, so TAM has extremely high computational efficiency.We designed numerical experiments to test the feasibility and capability of resisting disturbance of TAM. At first, we assume the uncertainty of the focal mechanisms or noise level are 5%,10%,20%,30% and 50%, respectively, the mechanism types to be tested are of vertical strike slip, normal slip, reverse slip and vertical dip slip, and the numbers of focal mechanism solutions are 1000,100 and 20, respectively, in order to test the effect of the uncertainty of focal mechanisms on the inversion result. The testing result shows:(1) The effect of uncertainty is little different from type to type; (2) the bias of the inverted result will increase with the uncertainty level increasing; (3) the bias will increase with the number of the focal mechanism solutions decreasing. Then, we assume that the bias of local stress fields relatively to regional stress field are at levels of 10%,20%,30% and 50%, respectively, and the number of the focal mechanism solutions and the mechanism types are the same as above, in order to test the effect of heterogeneity in stress field on the inversion result. The testing result shows:(1) the effects are little different from type to type; (2) the bias will increase with the heterogeneity level increasing; (3) the bias will increase with the number of the focal mechanism solutions decreasing. The above experiments indicate that we can use TAM to get reliable results in case that disturbance is at a reasonable level and data is enough. Thus, the TAM is feasible, and has good capability of resisting disturbance.To test the practicability of TAM, we inverted 1671 focal mechanism solutions of small earthquakes which had occurred within the Qiaojia array to determine the direction of the stress field. The results show, the direction of the stress field is consistent with that of local GPS velocity field, and close to other existing research results, implying that the results from TAM is practically reliable and thus TAM is practicable enough.TAM’s obtaining the convincing results is not only support to TAM itself but also to GPAT.