Incorporating attenuation effects into frequency-domain full waveform inversion from zero-offset VSP data from the Stokes equation

Abstract

With the development of seismic exploration technology, the wave equations used to model the characteristics of wave propagation are becoming increasingly complex. Generally, more than one physical parameter is included in these wave equations, and merely inverting one parameter from these equations cannot help to accurately understand the subsurface structure. To gain further insight into the structure or oil- and gas-reservoir characteristics of the subsurface, multi-parameter inversion is essential. In this study, density, velocity, and viscosity coefficient are jointly reconstructed from the Stokes equation by frequency-domain full waveform inversion based on zero-offset VSP data. The inverse problem is transformed to find the optimal solution to an optimization problem, and the steepest-descent method is used. The sensitivities of the parameters to the misfit function are analysed. Two inversion strategies, namely, the one-by-one parameter inversion and joint inversion strategies, are tried and compared. The joint inversion strategy is proved to be better and thus used in subsequent analyses. In the numerical tests, we compare different frequency-selection strategies and determine the influences of initial models and number of frequencies to the rebuilt models. Numerical tests show that multi-parameter inversion by frequency-domain FWI is feasible and reliable.