Seismic acoustic full waveform inversion based on the steepest descent method and simple linear regression analysis

Abstract

Full waveform inversion (FWI) is a high-resolution imaging tool in seismic exploration. The steepest descent (SD) method is the simplest local optimization algorithm to update the P-wave velocity model in acoustic FWI, but it takes more iterations than other algorithms due to its inefficient search direction. In this study, we provide a SDSLR method, which can significantly shorten the convergence process of the SD method by using the simple linear regression (SLR) analysis. The SLR analysis has two important effects in this method: compute a SLR model to approximately estimate the recent variation trend of P-wave velocity model and directly predict the inversion result of the SD method of the next iteration. Based on the prediction of the SLR analysis, the SDSLR method can obtain the final inversion result of the traditional SD method with fewer iterations. Three numerical examples have tested the performance of the SDSLR method. Results show that the SDSLR method has great potential in constructing high-velocity anomalies. The computational efficiency of the SDSLR method is similar to that of the SD and L-BFGS methods, while the convergence rate and accuracy of the SDSLR method are clearly better than those of the SD and L-BFGS methods.