On the method of adaptive waveform inversion with zero-offset VSP data

In this paper, we propose a waveform inversion method to estimate the interval velocity and quality factor Q in time domain using the direct downgoing wave of the zero-offset VSP data. According to the signal-to-noise ratio and the interference of upgoing wave, our method can automatically choose the undisturbed segment of the direct downgoing wave, so it can sufficiently make use the data. A new data weighting scheme is used to make the object function more sensitive to Q. To deal with the ill-posed nature of inversion, we adopt the recently developed multiplicative regularization approach. A nonlinear transform is applied on the 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 example demonstrates the effectiveness of this method, and comparing with the spectral ratio method and the envelope peak instantaneous frequency method, our method is more stable and precise, and less sensitive to upgoing waves.