2-D Acoustic Waveform Inversion In The Laplace Domain

With the further development of seismic exploration technology,more and more subsurface information is obtained from seismic data.Due to the high nonlinearity of the objective function and the lack of low-frequency component in the field data,the waveform inversions in the time or frequency domain is difficult recover long-wavelength components of the velocity model.The waveform inversion in the Laplace-domain is not sensitive to the initial model,and we can obtain more realistic imaging results.This paper makes further research on the Laplace-domain full waveform inversion(FWI),and the specific work is as follows:(1)Forw ard modeling is an important foundation of waveform inversion.In this paper,we inroduced the mathematical principle of the forward modeling in Laplace-domain in detail.We use optimized 9-point difference scheme discrete the Laplace-domain acoustic wave equation,and introduce the perfectly matched layer(PML)absorbing boundary conditions to eliminate boundary reflection.Finally,we construct a large sparse matrix equations,and use the least squares QR(LSQR)method to solve the linear equations.(2)The essence of the Laplace-domain FWI is to search for the best match between the observed wave field and the simulated wave field in the Laplace-domain.In this paper,we use the algorithm of modified Broyden-Fletcher-Goldfarb-Shanno(BFGS),which considering the model itself,gradient and residual functions in the calculation of the approximate Hessian inverse matrix.At last,we achieve the high efficiency and high precision inversion of velocity.Numerical experiments on shallow surface velocity models are indicated,the forward modeling of acoustic wave equation in the Laplace-domain is accurate.It not only the numerical dispersion error range is very small,and the artificial boundary reflections are absorbed efficiently.In addition,using the modified BFGS algorithm in the Laplace-domain,not only the simulation model is very close to the real model,and the speed of convergence is faster significantly.