Seismic Waveform Tomography for 3D Impedance Model with Salt Structure

Abstract

Conventional impedance inversion from post-stack zero-offset seismic data is usually based on the convolution model, and wave-equation based inversion is rarely used, although it is capable to precisely describe seismic wave propagation and invert impedance model with higher resolution. That is because there are more than one physical parameters involved in the conventional wave equation, making impedance inversion complicated. In this study, a one-dimensional (1D) wave equation, containing only the impedance parameter, is adopted and applied for the inversion of 1D impedance model by seismic waveform tomography. However, for a three-dimensional (3D) model, direct application of the 1D waveform tomography may lead to lateral discontinuities. Therefore, we propose to utilize a truncated Fourier series to parameterize the 3D impedance model, and then invert for the Fourier coefficients. With this parameterization scheme, the large- and small-scale components of the impedance model can be reconstructed stepwise by gradually increasing the number of Fourier coefficients. To efficiently and effectively invert the coefficients for the 3D model with salt structure, we propose a joint strategy, in which the low-frequency seismic data is used to invert for the Fourier coefficients representing the large-scale components of the model, while the high-frequency seismic data is applied to invert for the Fourier coefficients representing the small-scale components of the model. Tests on a 3D impedance model with salt structure result in models with high resolution and good spatial continuity, proving the feasibility and stability of the impedance inversion procedure.