2D multi-scale hybrid optimization method for geophysical inversion and its application

Local and global optimization methods are widely used in geophysical inversion but each has its own advantages and disadvantages. The combination of the two methods will make it possible to overcome their weaknesses. Based on the simulated annealing genetic algorithm （SAGA） and the simplex algorithm, an efficient and robust 2-D nonlinear method for seismic travel-time inversion is presented in this paper. First we do a global search over a large range by SAGA and then do a rapid local search using the simplex method. A multi-scale tomography method is adopted in order to reduce non-uniqueness. The velocity field is divided into different spatial scales and velocities at the grid nodes are taken as unknown parameters. The model is parameterized by a bi-cubic spline function. The finite-difference method is used to solve the forward problem while the hybrid method combining multi-scale SAGA and simplex algorithms is applied to the inverse problem. The algorithm has been applied to a numerical test and a travel-time perturbation test using an anomalous low-velocity body. For a practical example, it is used in the study of upper crustal velocity structure of the A＇nyemaqen suture zone at the north-east edge of the Qinghai-Tibet Plateau. The model test and practical application both prove that the method is effective and robust.

Optimization method of fi rst-arrival waveform inversion based on the L-BFGS algorithm

The fi rst arrival waveform inversion(FAWI)has a strong nonlinearity due to the objective function using L2 parametrization.When the initial velocity is not accurate,the inversion can easily fall into local minima.In the full waveform inversion method,adding a cross-correlation function to the objective function can eff ectively reduce the nonlinearity of the inversion process.In this paper,the nonlinearity of this process is reduced by introducing the correlation objective function into the FAWI and by deriving the corresponding gradient formula.We then combine the first-arrival wave travel-time tomography with the FAWI to form a set of inversion processes.This paper uses the limited memory Broyden-Fletcher-Goldfarb-Shanno(L-BFGS)algorithm to improve the computational effi ciency of inversion and solve the problem of the low effi ciency of the FAWI method.The overthrust model and fi eld data test show that the method used in this paper can eff ectively reduce the nonlinearity of inversion and improve the inversion calculation effi ciency at the same time.