Frequency Domain Wave Equation Inversion and Its Application on the Heterogeneous Reservoir Model Data

Zhiyuan Tang

doi:10.5539/esr.v6n1p55

Abstract

Seismic full waveform inversion seeks to make use of the full information based on full wave field modeling to extract quantitative information from seismograms. Its serious nonlinearity and high dependence on initial velocity model often results in unsatisfactory inversion results in paleo-karsts carbonate reservoir characterized by strong heterogeneity. The paper presents an improved strategy of multi-scale inversion to establish velocity field model of waveform tomography. the forward wave equation algorithm was derived in frequency domain, and then the Matrix formalism for the iterative inverse methods is derived by gradient methods to speed up calculation and to avoid convergence to local minimum value. After massive amount of frequencies tests, the appropriate bandwidth are extracted, and the velocity field calculated at low frequency is used as the input of the high frequency. After the iteration, the accurate velocity field is inverted. Finally, frequency domain wave equation full waveform inversion in mathematical and physical models is conducted in order to verify the inverse program. The method of selecting the inverse frequencies is proved to be effective.

Highlights

Seismic waves bring to the surface information gathered on the physical properties of the earth
Seismic full waveform inversion seeks to make use of the full information based on full wave-field modeling to extract quantitative information from seismograms (Dessa et al 2007; Operto et al 2009)
One difference is that the seismic wave-field recorded at the receiver is back propagated in reverse time-migration, whereas the data misfit is back propagated in the waveform inversion (Robertson et al 2007; Vigh et al 2008)

Summary

Introduction

Seismic waves bring to the surface information gathered on the physical properties of the earth. Lailly (1983) and Tarantola (1984) recast the migration imaging principle of Claerbout (1976) as a local optimization problem in Born approximation, the aim of which is least squares minimization of the misfit between recorded and modeled data. They show that the gradient of the misfit function along which the perturbation model is searched can be built by cross-correlating the incident wave-field emitted from the source and the back propagated residual wave-fields (Thierry et al 1999; Brenders et al 2007). In the application of the frequency domain waveform inversion approach, we use seismic data from mathematic model and a caved physical model which is supplied by CNPC (China National Petroleum Corporation) key laboratory. several critical processes that contribute to the success of the method were tested here like, the matching of amplitudes between real and synthetic data, the selection of sequence of frequencies in the inversion, and the relationship between inversion velocity model and wave number reconstruction

Waveform inversion method

Conclusions