Scaled unscented transformation method and adaptive Monte Carlo method used for effects of fault parameters estimation on green function matrix in slip distribution inversion

The elements of Green function matrix are the nonlinear functions of fault parameters estimation, the randomness of fault parameters estimation causes that the slip distribution inversion turns to be the parameter estimation problem of total least squares. Second-order approaching function method, scaled unscented transformation (SUT) method and adaptive Monte Carlo method are designed for biases of displacements in rectangular dislocation model. They are used to analyze effects of the length, width, depth and dip of fault with different variances on the corresponding displacements of unit strike slip dislocation fault, unit dip slip dislocation fault and unit tensile dislocation fault. Results of the simulated fault show that compared with second-order approaching function method and adaptive Monte Carlo method, SUT method has better computational efficiency. The second-order term has dominant effects on nonlinear relationship between displacements and the fault parameter in the rectangular dislocation model. The main biases of displacements are near to fault. The corresponding displacements of unit tensile dislocation are mostly susceptible to fault parameters estimation, followed by the unit dip slip dislocation and unit strike slip dislocation. In addition, the vertical displacement is more sensitive to fault parameters estimation than horizontal displacements.