AVO & Inversion

AVO describes the effect of variations in reflection amplitudes with offset, or more correctly incident angle, which are caused by contrasts in the physical properties of the rocks. The relative change in reflection coefficient is particularly significant when Poisson’s ratio varies greatly either side of an interface. It is this phenomenon which allows AVO effects to be used in the detection of hydrocarbons.

Where the analysis of AVO properties is to be performed on seismic data the processing sequence needs to be carefully designed so that any processes applied are ‘true amplitude’, to ensure that the amplitudes are correctly preserved, and also that amplitude variations are not introduced into the data. It is also important to check the polarity of the data, as standard interpretation in AVO analysis assumes SEG (US) Standard – an increase in acoustic impedance is represented as a positive number or peak in the data.

Spectrum uses the Hampson Russell AVO software to analyze the AVO response in seismic data and perform modeling exercises. We can also produce AVO data volumes in a batch environment, to quickly and economically produce screening volumes.

AVO Modeling
For a complete study of AVO anomalies details of the rock properties present are required. If well log data is available then parameters such as compressional velocity and bulk density can be derived. Shear velocity is also needed, but can be calculated approximately by other methods. Using the information derived from the logs, forward modeling can then be performed and synthetic gathers derived. With Fluid Replacement Modeling (FRM) we generate a series of synthetic gathers for different reservoir scenarios, modeling the amplitude behavior expected in the seismic gathers.

WellModellingExample synthetic gather with different FRM scenarios

Angle Stacks
The seismic data is stacked for different incident angle ranges, which enhances the amplitude anomalies. Comparisons between the near and far angle stacks can be used as a screening tool to highlight areas where differences in amplitude may be due to changes in the fluid content. Data at these locations can then be looked at in more detail.

Intercept & Gradient Stacks
The Intercept (A) and Gradient (B) analysis is based on the following equation:

R(θ) = A + Bsin2θ (Shuey’s Equation)

Where R(θ) defines the reflectivity with respect to reflection angle θ, B is the gradient of the least squares fit to the measured reflectivity versus sine squared of the reflection angle and A is the R(θ) zero offset (or angle) reflectivity. The measurements are made on constant time surfaces versus angle for each time sample in a gather. This holds for angles up to 35 degrees. However, various approximations to the Aki-Richard’s equation are used depending on the angle ranges available

Compressional (P) & Sheer Wave (S) Reflectivity (Rp & Rs)
The Fatti methodology (Fatti and others, 1994) is a more sophisticated AVO approximation than Shuey’s. This methodology is not only more accurate to higher angles-of-incidence, but is independent of any assumption of density and allows any meaningful Vp/Vs as a constraint.

R(θ) = 0.5Rp * (1+tan2θ) – 4Rs * (Vs/Vp)2 * sin2θ

The two pairs of attributes that we can extract from our angle gather data using two-term AVO analysis, compressional reflectivity (Rp, also known as intercept) and shear reflectivity (Rs) or compressional reflectivity and gradient are shown in cross plots from the same source data in figure below.

Rp vs. RS and Intercept (Rp) vs. Gradient Cross-plots

Brine saturated sand inter-bedded with shale, situated within a limited depth range and at a particular locality, normally follow a well-defined “background trend” in AVO crossplot. A common approach in qualitative AVO analysis is to recognize the background trend and then look for data points that deviate from this trend. Changes in rock physics properties such as porosity and fluid have their own associated trends. The background trend is mathematically related to the contrasts in Vp/Vs between sands and shales.

Example of AVO reconnaissance work from Spectrums MC Croatia 2013 dataset.

The area highlighted here is a known gas field, showing the AVO class zone assignment on AB crossplot, which is very conservative – and subsequent plotting of zone distribution.

Spectrum used this method to further investigate amplitude anomalies highlighted in the original interpretation of the Final Stack dataset performed by the Geoscience group.

Attribute Combinations
The various AVO attributes can be combined to produce further AVO attribute volumes. The classic attribute for identifying Class III AVO anomalies is the intercept, gradient product (commonly referred to as AB). The product of A and B is positive for increasing AVO anomalies and negative for decreasing AVO anomalies.

Combining the Intercept and Gradient also gives a representation of Poisson’s Ratio, which can be used to highlight layers which may have hydrocarbon present.

Comparison of Full Offset Stack and Poisson’s Ratio volume over known gas field

Another useful attribute for highlighting class III anomalies is Smith & Gidlow’s Fluid Factor volume which can be generated from the P & S wave reflectivity volumes with Rp-gRs (g=scalar), or from the intercept and gradient with A+B/2. When a scalar is applied to account for the background trend in the crossplot, the attribute is a measure of the fluid effect. The default assumption of Vp/Vs of 2 means that Rp will be consistently smaller than Rs, however the background Vp/Vs values changes both laterally and vertically, so the interval velocities can be used in the calculations to calibrate the Fluid Factor for these changes.

Comparison of Full Offset Stack and Fluid Factor volume

Another example of reconnaissance AVO work carried out on a subset of Spectrum’s MC Lebanese 3D dataset. The Fluid Factor volume was used as an initial screening tool to highlight AVO anomalies, which were then investigated further with gradient analysis, AB crossplot and on other AVO attribute volumes.


Inversion services are provided using the Hampson Russell suite of tools, offering pre-stack Elastic Impedance & Simultaneous Inversion, plus post stack Acoustic Impedance Inversion.

The example shown is taken from Spectrum’s SNS Multi Client dataset. The whole project was a collaborative effort between Imaging Services and the Geoscience Group, from acquisition through to pre-stack Simultaneous Inversion of a small subset of lines in the survey. The model based simultaneous inversion was driven by 8 horizons, which were provided by Spectrum’s Geoscience Group. The inversion study gave a means to further investigate the new deeper potential HC plays in the Carboniferous sequence, with potential source of gas migrating from mature Westphalian coals in Sole Pit basin to the South.

Montage displaying the results from Simultaneous Inversion on SNS MC project.

LMR (Lambda Mu Rho) conversion was run from the resulting P & S wave Impedance volumes output from the inversion. The P-Impedance volume highlights areas of low impedance in the Intra-Carboniferous Fell sandstone, with similar low Lambda-Rho values are highlighted in the same formation. Cross-plotting P-Impedance against Lambda-Rho values allows zone assignment to highlight expected values for gas-bearing sandstones, which were then plotted to highlight possible distribution of these low values across the area.