On the Method of Adaptive Waveform Inversion with Zero‐Offset VSP Data

Abstract

In this paper, we develop a waveform inversion method to estimate the interval velocity and quality factor Q with zero‐offset VSP data. The inversion is done in the time domain and the objective function is constructed using the undisturbed segment of the direct downgoing wave. According to the signal‐to‐noise ratio and the interference of upgoing wave, our method can adaptively choose the undisturbed segment of the direct downgoing wave as long as possible, so it can make use of the most of the data. A new data weighting scheme is proposed to make the objective function more sensitive to Q. To deal with the ill‐posed nature of waveform inversion, the recently developed multiplicative regularization approach is adopted, which can adaptively determine the regularization parameter as the iterations proceed. In addition, a nonlinear transform is applied to the unknown model parameters to constrain them within their upper and lower bounds. For reducing computational cost, the analytic expressions of the elements of the Jacobian matrix are given. The application of this method on the synthetic VSP data and real data demonstrates the effectiveness of this method, and indicates this method is less sensitive to random noise and upgoing waves.

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