Seismic Waveform Inversion Using the Finite-Difference Contrast Source Inversion Method

Abstract

This paper extends the finite-difference contrast source inversion method to reconstruct the mass density for two-dimensional elastic wave inversion in the framework of the full-waveform inversion. The contrast source inversion method is a nonlinear iterative method that alternatively reconstructs contrast sources and contrast function. One of the most outstanding advantages of this inversion method is the highly computational efficiency, since it does not need to simulate a full forward problem for each inversion iteration. Another attractive feature of the inversion method is that it is of strong capability in dealing with nonlinear inverse problems in an inhomogeneous background medium, because a finite-difference operator is used to represent the differential operator governing the two-dimensional elastic wave propagation. Additionally, the techniques of a multiplicative regularization and a sequential multifrequency inversion are employed to enhance the quality of reconstructions for this inversion method. Numerical reconstruction results show that the inversion method has an excellent performance for reconstructing the objects embedded inside a homogeneous or an inhomogeneous background medium.

Time Domain Waveform Inversion for theQModel Based on the First-Order Viscoacoustic Wave Equations

“…However, the adjoint wave fields are subject to final time conditions and are generated by propagating the residual data ∑ ( (x , ) − (x , )) from the receiver positions backward in time. Provided that the Lagrange multipliers are determined by the adjoint equation (13), the first three terms of (8) vanish. Moreover, / m = / m according to [17].…”

“…For given current models and actual sources, a forward propagation is implemented through viscoacoustic wave equations (3) and (5) to obtain the forward wave fields k and . And adjoint equation (13) can be solved for the adjoint wave fields 1 , 2 , and 3 with data residuals regarded as sources. The residuals at each time step are injected backward in time.…”

“…For frequency-domain FWI, the attenuation effect can be easily included by replacing the real-valued velocity with a complex-valued velocity using the relationship between complex velocity and [12]. However, frequency-domain forward modeling of wave equations needs to implement a large-scale lower and upper triangular decomposition [11,13].…”