Elastic Attribute Generation From 3 Points Elastic Inversion
Authors: Rauch-Davies Marianne , Portniaguine Oleg 
Published: October 2008

Abstract
The concept of Elastic Inversion (EI) has been generally accepted over the last few years in the exploration and production environment. EI reconstructs elastic attributes, such as Poisson's ratio, Vp/Vs ratio and other attributes using angle stack AVO data. This paper discusses a 3-point elastic inversion method.
As its name suggests the 3-point inversion needs three impedance values at each location for calculating various elastic attributes. First, three angle stacks are calculated and inverted individually to reflectivity impedances using standard seismic software. The three resulting reflectivity impedances are associated with angle-dependent elastic impedance by Connolly's (1999) formula. Unfortunately, this EI formula is strongly dimension-dependent, which makes application of it difficult since it predicts very large values of EI for small angels and small values of EI for large angles.
In 2002 Withcombe derived a dimensionless version of Connolly's formula. It contains quantities Vp, Vs and normalized by the background (average) values of Vp, Vs and. The background values are derived either from the mudline or from existing logs. We obtain stable results using a slightly modified version of Whitcombe's and Connolly's formulae. Here, we present and discuss real-data results on a Frio reservoir.

The Elastic Inversion Concept
Elastic Inversion reconstructs elastic attributes, such as Vp/Vs ratio, Poisson's ratio and other attributes using angle stack AVO data. First, three angle stacks are calculated, e.g. at near (5-15 degrees), middle (15-25 degrees) and far angles (25-35 degrees). Next, each of these angle stacks is inverted to reflectivity impedances, using standard seismic software. The following method is used to associate the three resulting reflectivity impedances with angle dependent elastic impedance.
Unfortunately, Connolly's EI formula is strongly dimensiondependent, which makes application of it difficult since it predicts large values of EI for the small angles and small values of EI for large angles. Whitcombe (2002) derived a dimensionless version of the EI formula:(Mathematical equation available in fullpaper) which contains quantities Vp, Vs and normalized by the background (average) values of Vpo, Vso This is the formula used for this elastic inversion. Assuming that K=2, and taking the logarithm of EI and rearranging the terms, we have:(Mathematical equation available in full paper)

Seismic example
The Frio reservoir is a stratigraphically trapped sand and shows a large drop in acoustic impedance when gas saturated. This results in a typical bright spot around the gas reservoir. However, amplitude alone does not seem to define the limits of the gas sand sufficiently and elastic attributes were calculated.
Figure 1 shows an amplitude horizon map at the top of the Frio reservoir. Around well-2 amplitude anomalies are present, which are most likely caused by the gas. However, this figure does not clearly show the extent of the reservoir.
Figure 1: Amplitude map at top of Frio sand. (available in full paper)
Figure 2 displays the elastic attribute Poisson's ratio.