Long-offset AVO inversion of PP reflections from plane interfaces using effective reflection coefficients

Abstract

A conventional amplitude variation with offset (AVO) inversion is based on geometrical seismics which exploit plane-wave reflection coefficients to describe the reflection phenomenon. Widely exploited linearizations of plane-wave coefficients are mostly valid at pre-critical offsets for media with almost flat and weak-contrast interfaces. Existing linearizations do not account for the seismic frequency range by ignoring the frequency content of the wavelet, which is a strong assumption. Plane-wave reflection coefficients do not fully describe the reflection of seismic waves at near-critical and post-critical offsets, because reflected seismic waves are typically generated by point sources. We propose an improved approach to AVO inversion, which is based on effective reflection coefficients (ERCs). ERCs generalize plane-wave coefficients for seismic waves generated by point sources and therefore more accurately describe near-critical and post-critical reflections where head waves are generated. Moreover, they are frequency-dependent and incorporate the local curvatures of the wavefront and the reflecting interface. In our study, we neglect the effect of interface curvature and demonstrate the advantages of our approach on synthetic data for a simple model with a plane interface separating two isotropic half-spaces. A comparison of the inversion results obtained with our approach and the results from an AVO inversion method based on the exact plane-wave reflection coefficient suggests that our method is superior, in particular for long-offset ranges which extend to and beyond the critical angle. We thus propose that long offsets can be successfully exploited in an AVO inversion under the correct assumption about the reflection coefficient. Such long-offset AVO inversion shows the potential of outperforming a conventional moderate-offset AVO inversion in the accuracy of estimated model parameters.

An analysis of AVO inversion for postcritical offsets in HTI media

“…This results in reflections associated with the critical angle at relatively small offsets, where conventional AVO analysis is not valid anymore. The importance of near-and postcritical reflections is highlighted by several researchers (Downton and Ursenbach, 2006;Alhussain, 2007;Skopintseva et al, 2011), who show that using such reflections improves inversion results. Based on PWRC analysis, Hall and Kendall (2003) and Landrø and Tsvankin (2007) notice that the critical angle is sensitive to the fracture orientation.…”

“…Although equations 8-9 are functions of the amplitude maximum offsets, the critical angle in the isotropic plane is still needed. This information can be retrieved from an AVO inversion in the isotropic plane (Skopintseva et al, 2011). Relative errors in anisotropy parameter estimates obtained from the different types of data are shown in Figure 6.…”

“…A general form of the radius r à PP ðxÞ is introduced by Skopintseva et al (2012). For a plane interface, r à PP ðxÞ is the distance between the source and the receiver along the ray (Skopintseva et al, 2011). The dimensionless normal and tangential components of the displacement vector are represented by u …”

“…where A D ðx n Þ is the normalized reflection coefficient obtained from the data (Skopintseva et al, 2011) for a chosen azimuth and Aðx n Þ is the normalized ERC. Figure 11 shows 2D crossplots of the objective function for an azimuth of 45°.…”

“…Figure 2 shows the amplitude of the ERC normalized by the reflection amplitude at the first receiver x 1 (Aðx; φÞ ¼ χðx; φÞ∕χðx 1 ; φÞ). It is compared with amplitudes of the normalized PWRC A R ðx; φÞ ¼ R PP ðx; φÞ∕R PP ðx 1 ; φÞ and reflection coefficient obtained from reflectivity modeling using the technique described by Skopintseva et al (2011). Reflection coefficients are calculated for the model water/HTI provided by Alhussain (2007), where…”