Abstract:  The propagation matrix theory considers the effects of transmission loss and inter-layer multiple waves on seismic responses. It provides the reflection coefficient spectrum for longitudinal and transverse waves in multi-layer media at arbitrary incident angles. This theory can yield higher accuracy in amplitude-versus-angle (AVA) multi-parameter inversion results than the Zoeppritz equations and their simplified versions. The inversion of the time-domain propagation matrix method requires a significant amount of memory because it involves computing the full-frequency Jacobian matrix. In contrast, frequency-domain inversion only focuses on specific frequencies, resulting in lower memory usage. The propagation matrix method effectively meets the requirements for frequency-domain inversion by solving the reflection coefficient spectrum in the frequency domain. This paper computes the gradient of the objective function in the frequency domain, and employs the L-BFGS (limited-memory Broyden-Fletcher-Goldfarb-Shanno) algorithm to accelerate inversion convergence. To validate the effectiveness of the frequency-domain propagation matrix method, we conduct inversions on both simulated and real data. The application of the propagation matrix seismic prestack inversion method in the frequency domain can stabilize the inversion of layer parameters. Compared to the results from the Zoeppritz equations, the frequency-domain propagation matrix inversion shows higher accuracy.

Key words: propagation matrix theory, Zoeppritz equation, AVA inversion, L-BFGS algorithm, frequency-domain