Inversion of negative dislocation model parameters of North China block motion using GPS data Wu Jicang 1 Xu Caijun 2 (Department of Surveying and Land Information Engineering, Tongji University, 1239 Siping Road, Shanghai, 200092) (2 School of Surveying and Mapping, Wuhan University, Luoyu Road, Wuhan No. 129, 430079) According to the introduction of the block relative motion model, the negative dislocation model parameters of the three main fault zones in the area are inverted, so as to distinguish the motion blocking strength of each active fault in the study area, and infer accordingly They are likely to have an earthquake in the future.
Chinese Library Classification: P228.42 The movement of active faults is a major manifestation of crustal movement. The mechanical model of active fault motion can be expressed as the relative rigid body motion of the two blocks divided by the fault plus the negative dislocation distribution on the fault plane. The model assumes that each active block is driven by today's tectonic movement, and there is a long-term stable relative movement between each other. This relative movement may be hindered at the boundary (fault) of the block, resulting in strain, Stress accumulation. When the stress accumulation exceeds the strength of the fault, the fault will move, that is, earthquake.
If it is further assumed that the obstruction at the block boundary exists only in the brittle and hard section of the upper crust, and the soft plastic section in the lower section of the crust is assumed to be free to slide, according to the theory of static elastic dislocation, the obstruction on the upper crustal fault surface can It is expressed by the distribution of negative dislocations on the fault plane. In this way, the crustal deformation at the block boundary can be expressed as the relative rigid body movement between the blocks plus the crustal deformation caused by the negative dislocation distribution on the fault plane. As shown, there is a long-term stable relative motion between block A and block Vab. The boundary between block A and block B is divided by fault F, which is caused by the obstruction of the upper 2 of the fault plane. Crustal deformation can be represented by the distribution of negative dislocations. Therefore, the motion y of a point on the ground is: (1), the left end y represents the point displacement or velocity, which can be obtained by measurement; the right end is a function of a limited number of model parameters; it represents the crustal deformation caused by the negative dislocation distribution on the fault plane. With respect to the calculation formula of / 2 in elastic semi-infinite space, Okada has been in 1985 and 1992,%, is nX1 order observation error vector. Solving x directly by equation (2) is a nonlinear inversion problem, and its solution is uncertain. In this paper, an iterative linear Bayesian inversion method is adopted for the Taihang piedmont and Hebei plain seismic tectonic zone; block W is the Chengning uplift seismic tectonic zone.
In order to invert the distribution of negative dislocations on these three active fault planes, assuming that block I does not move, the velocity of all points minus the velocity of the H058-GPS point located on block I can get all points relative to block I speed. The vector arrows in each indicate that each station assumes that X0 represents the a priori information of the model parameters. That is, for the convenience of calculation, it is generally assumed that the random vector%, all follow the Gaussian distribution, and their expectations are zero, and the variance matrix is ​​2y, 2X. The iterative solution process can be expressed as: where the elements of Ak are calculated as follows: In equation (4), bk is a positive number that controls the iteration step size, and 0 is referenced, giving the geometric parameters of the three faults. The test values ​​are shown in Table 2. The prior values ​​of the motion of each block relative to the rigid body are shown in Table 3. Since the author lacks cross-fault measurement data, it may be assumed that the prior values ​​of the negative dislocation components of each fault are all zero and the prior variances are all 3mm. According to the above-mentioned iterative Bayesian inversion method, give greater weight to the size of the fault position and other geometric quantities, and focus on inverting the distribution of negative dislocations on each fault plane and the relative speed of motion between the blocks. Table 4 lists the a priori value and the inverse value of the negative dislocation and the corresponding mean square error. The posterior values ​​and mean square deviations of relative motion of each block are shown in Table 3. In addition, the sum of squares of data residuals corresponding to the posterior model obtained by inversion is 10 of the sum of squares of data residuals corresponding to the prior model, and obtained after inversion The absolute value of the residual data is mostly within 2mm, as shown in the figure, which is consistent with the accuracy of GPS measurement. It shows that the inversion results are in good agreement with GPS measurement data.
Table 2 assumes the geometrical parameters of the fault (measured according to the "Capital Circle Seismic Tectonic Division 71") fault name fault location width / deep / dip angle 8 °) Table 3 Prior and post-inversion values ​​of block motion / mh1 motion component Block number is fixed. Prior value is inverse, value is inverse, value is inverse, value is inverse, value is a priori, value is inversion. The analysis and conclusion of the inversion result are shown in Table 3. Relative to block I, the block and The motion values ​​of W after inversion are almost the same, all are in the near east direction, and the size is about 3mm / a; the relative motion of block I is east to south, and the size is about 6mm / a, as shown. Table 3 lists the distribution of negative dislocations after inversion of active faults. Among them, the negative dislocation slip component of the Tangshan-Ninghe and Cangdong fault zones is a 3 mm / a tensile fracture component and a 2 mm / a due to the negative position. The misalignment vector is opposite to the actual motion of the fault, indicating that there is still an ascending motion in the Chengning uplift area at the same time, and the fault zone is subjected to micro-tensioning. The components are all 2mm / a, and the tensile splitting component is a 5mm / a, indicating that the fault zone is currently mainly subjected to tensile action; and the east-west Zhangjiakou-Beipiao fault on the north side has a negative dislocation slip component of one The 4mm / a dip-slip component and tensile crack component are about zero, indicating that the fault zone is now mainly subjected to left-handed motion. Intra-plate structure obtained by the above inversion Table 4 Prior value and post-inversion value of fault negative dislocation distribution Fault name negative dislocation component / mD trend U | tendency U2 Zhang split U3 prior value Inversion post value prior value Post-inversion value Prior value Post-inversion value The horizontal axis indicates the station number, and the vertical axis indicates the data residual width after inversion. The arrow indicates the relative motion speed of each block (relative to block I is fixed). The dashed arrow indicates the fault plane. The negative sign dislocation component represents the relative movement of the block in the actual movement trend of the fault and the movement trend of the block after the inversion of the negative dislocation distribution of the fault, and the crustal tectonic deformation since the Pleistocene according to the geological survey. It is basically consistent with the conclusion obtained from the analysis of historical seismicity. As a whole, the southern part of the Inner Mongolia's terrestrial axis area is now subject to crustal movements dominated by extensional effects, manifested by horizontal movements in the Near East direction and current ascending movements in the Chengning uplift area. However, the current crustal movement before the Taihang Mountain fault has a blockage of nearly 5 mm per year in the direction of the crack. It is inferred that the current Taihang piedmont fault zone is more likely to breed moderately strong earthquakes, and the deformation monitoring of the Taihang piedmont fault zone should be strengthened. In addition, the inversion data in this article is only 4 years of GPS data, and the results have certain uncertainties, only for.
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