Convolution-based multi-scale envelope inversion

Ding-Jin Liu,Zi-Ying Wang,Jian-Ping Huang

doi:10.1007/s12182-019-00419-8

Abstract

Envelope inversion (EI) is an efficient tool to mitigate the nonlinearity of conventional full waveform inversion (FWI) by utilizing the ultralow-frequency component in the seismic data. However, the performance of envelope inversion depends on the frequency component and initial model to some extent. To improve the convergence ability and avoid the local minima issue, we propose a convolution-based envelope inversion method to update the low-wavenumber component of the velocity model. Besides, the multi-scale inversion strategy (MCEI) is also incorporated to improve the inversion accuracy while guaranteeing the global convergence. The success of this method relies on modifying the original envelope data to expand the overlap region between observed and modeled envelope data, which in turn expands the global minimum basin of misfit function. The accurate low-wavenumber component of the velocity model provided by MCEI can be used as the migration model or an initial model for conventional FWI. The numerical tests on simple layer model and complex BP 2004 model verify that the proposed method is more robust than EI even when the initial model is coarse and the frequency component of data is high.

Highlights

Building an accurate velocity model is essential for reservoir characterization and seismic imaging
An efficient approach to conduct full waveform inversion is the local optimization method by which the model is iteratively updated using the gradient of the misfit function (Virieux and Operto 2009)
One instinct problem of the local optimization strategy is that the solution tends to fall into the local minimum of the misfit function because of the highly nonlinear nature of full waveform inversion (FWI) (Fichtner and Trampert 2011)

Summary

Introduction

Building an accurate velocity model is essential for reservoir characterization and seismic imaging. Bharadwaj et al (2016) pointed out that the performance of conventional envelope inversion relies on the frequency of the source wavelet and accuracy of initial model, which means the initial model should guarantee that the difference between observed and modeled data is smaller than one dominant period. The convolution factor should be big enough so that the modified envelope data are overlapped, which means the initial model is in the basin of global or local minima. Considering a roughly constrained initial model, the example of BP 2004 model demonstrates the robustness of MCEI

Simple layered model

BP 2004 model

Findings

Conclusion