Acoustic full-waveform inversion of surface seismic data using the Gauss-Newton method with active constraint balancing

Abstract

We propose a full-waveform inversion algorithm using the Gauss-Newton inversion method with active constraint balancing that uses the spatially variant damping factor and source normalized wavefield approach for surface seismic data in the frequency domain. The active constraint balancing technique automatically determines the optimum distribution of damping factors that control the stability and resolution in Gauss-Newton inversion by using a parameter resolution matrix and spread function analysis. Through numerical experiments, we present that the active constraint balancing scheme provides stable inversion results without a severe loss of resolution compared with the conventional Gauss-Newton method. The reconstructed image using the active constraint balancing method more closely resembles the true image for the region with low sensitivity. Also, the estimated value converges faster to the smaller RMS error level than those estimated by the conventional Gauss-Newton method. We also implement the normalized wavefield method to overcome the lack of precise knowledge on the source. The source normalized wavefield approach effectively removes the potential inversion errors from source estimation because the source spectrum is eliminated during the normalization procedure. Our inversion algorithm, using the source normalization scheme, provides excellent inversion results even though the data are generated by two slightly different source wavelets. We present that the frequency selection scheme proposed by Sirgue and Pratt, which is based on the average amplitude of the whole received data, provides a useful guideline for selecting the proper frequencies for our inversion. Our novel inversion algorithm successfully reconstructs the velocity model within 10-30 iterations despite its starting from a homogeneous or linearly increasing velocity model. In addition, for testing the performance of our inversion algorithm on a more complicated structure, we apply the algorithm to the SEG/EAGE overthrust model. Successful inversion is achieved as the reconstructed image approaches the true model with the consistently converging RMS error even though insufficient data are used.