AVO analysis and inversion of Aki & Richards equation using Tikhonov solution in order to identify gas-bearing layers

The information driven from wells are capable of determining the reservoir characteristics more preciously and distinctly than seismic data, but such data show much lower resolution horizontally. Therefore, seismic data have gained attention due to their better lateral resolution and their ability to provide the structural information for geologists. The objective of seismic AVO (amplitude variation with offset) inversion is to achieve the physical and elastic properties of subsurface layers using the prestack gathers. Its theory is based on Zoeppritz equations, which provides exact descriptions of the AVO phenomena at elastic interfaces. However, it is too complicated to obtain stable seismic inversion results. Thus, the approximation proposed by Aki and Richards is widely used in inversions. 

Methodology and Approaches:

Aki and Richards approximation has three unknown seismic attributes (the reflection coefficients of compressional velocity, shear velocity and density), which should be derived from seismic data. This study applies the algebra technique to obtain the unknown parameters. A typical feature of inverse problems is that they are ill-posed, and a unique solution may not exist and small errors in the data may cause large variations in the estimation of inverse modeling parameters. One of the best known and most used regularization methods is Tikhonov regularization. This research work estimates the seismic attributes in the Penobscot region using Tikhonov regularization.

Well L30 was drilled in Cross-line 1153 and gas-bearing layers were found in time range of 2000-2036 ms. In general, gas layers could decrease P-wave velocity and slightly increase S-wave velocity. Therefore, the variation of the P-wave and S-wave reflection with offset can be used as a direct hydrocarbon indicator. The reflection coefficient of shear velocity and density could detect the gas layers with high accuracy.