A hybrid approach for tomographic inversion of crosshole seismic first-arrival times

Abstract

A sequential hybrid approach was presented here to invert crosshole seismic first-arrival times. The proposed tomographic scheme combined a simple simulated annealing algorithm with a linearized smoothness-constrained least-squares inversion. The simulated annealing was implemented to obtain a background velocity distribution used by the linearized inversion for the initial guess. The linearized component was based on the functional description of traveltimes. This indicates a nonlinear function, the eikonal equation, providing traveltimes for a given slowness model. Thus an explicit ray tracing was not required by the linearized scheme. The velocity updates were obtained by a matrix inversion based on an iterative conjugate gradient-like LSQR algorithm. Second-difference regularization was used to stabilize the solutions. The Jacobian matrix giving the partial derivatives with respect to the model parameters was constructed by a finite-difference approximation based on the perturbation of the cell slowness. The traveltimes for both the hybrid and linearized schemes were calculated by a fast finite-difference eikonal solver. The hybrid scheme was tested by using both synthetic and field data sets based on the crosshole geometry. According to the tests studies, the tomograms resulted from the hybrid approach better imaged the subsurface velocity distribution. Also the hybrid optimization was characterized by quicker convergence rate than the conventional optimization based on only the linearized inversion. The tests with the synthetic data set also showed that the hybrid approach yielded a solution having lower rms residual, smaller Euclidean distance and lower relative errors in the cell velocities.