Estimating Frequency-dependent Seismic Attributes By Matching Pursuit: a Case Study

Summary

This paper investigates the use of spectral decomposition for extracting information on fluid properties. Traditional theory for detecting fluid response is based on the pure elastic Gassman theory, and the resultant seismic effects are frequency-independent. Using dynamic fluid substitution, we demonstrate that the frequency response of seismic reflection and its resultant attenuation and dispersion are directly linked to fluid saturation. To extract this information, we develop an accurate two-stage spectral decomposition method by matching pursuit. This allows us to calculate a range of frequency-dependent attributes, such as, absorption coefficient and amplitude gradient in the frequency domain. Application to real data shows a good link between the anomalies and hydrocarbon saturation. The results highlight that careful data processing and modeling are necessary to understand the complex effect of different fluids on the spectral response and enable robust interpretation.

Introduction

Most studies of seismic response to fluid saturation are based on Gassmann''s theory and reflectivity modelling with the Zoeppritz equations, which turned out to be frequency-independent. Recent years have seen the development of technologies which exploit the phenomenon of frequency-related seismic attributes, such as attenuation and dispersion, for predicting reservoir fluid (Castagna et al., 2003; Ebrom, 2004; Odebeatu et al., 2006), and the underlying theory for most of these studies is based on empirical knowledge extrapolated from laboratory measurements.

Chapman (2003) developed a multiscale theoretical model to perform dynamic fluid substitution, which yields an effective medium with its elastic properties varying with frequency. Subsequently, Chapman et al. (2006) have discussed how to calculate the frequency-dependent seismic reflection response, and shown that the resultant frequency-related properties, such as attenuation and dispersive characteristics, are directly linked to fluid mobility within the rock frame. These studies provide a theoretical modeling framework to understand and analyze the seismic frequency response to fluid saturation.

To derive frequency-related attributes from seismic data, it is convenient to use spectral decomposition techniques. There are several techniques available to perform spectral decomposition, such as windowed Fourier transform (WFT), continuous wavelet transform (CWT) and matching pursuit, etc. (Avijit and David, 1995). Since WFT and CFT cannot represent the high frequency component with sufficient accuracy due to the restriction between frequency and scale, matching pursuit is considered to be a better alternative although it is relatively computing-intensive (Mallat and Zhang, 1993). Here, using a dictionary of Morlet wavelets (Morlet et al., 1982), we develop an accurate two-stage method by matching pursuit for spectral decomposition. This allows us to calculate a range of frequency-dependent attributes. Testing on synthetics and real data verifies the approach.

Dynamic fluid substitution

In the case of reflection from a single interface, Gassmann''s theory predicts that changing the fluid saturation in one of the layers will change the impedance contrast and therefore the amplitude of the reflection. This effect is independent of frequency. Chapman (2003) have presented the mathematical procedure for calculating the frequency dependent elastic constants, and the resultant seismic reflection and transmission responses are outlined in Chapman et al. (2006).