AVO, inversion or AVO inversion? Hampson-Russell’s software solutions

By Rebecca Goffey, Hampson-Russell Software & Services (A CGGVeritas Company)

As geophysicists, reservoir characterization is our goal. We aim to transform seismic traces into pseudo well-log measurements from which we can infer reservoir properties, such as porosity or fluid content. To achieve this goal, we use one or more techniques from a repertoire of well established tools. The choice of which to use depends on a range of factors, including data availability, hardware and software resources, as well as expertise. AVO and inversion are both tools that increasingly are being combined to form a range of newer AVO inversion techniques. But how did we get to this stage? In this article, I will focus on AVO and inversion methods, how the boundary between them has blurred, and the innovative software being used to benefit from the overlap.

Historical perspective
Historically, AVO and inversion have been treated as two distinct methodologies. AVO, an acronym for "Amplitude Versus Offset", was originally developed by Bill Ostrander in the early 1980s. The method involves the interpretation of the amplitude of P-wave seismic data as a function of offset or angle to imply fluid effects. It is now widely used, particularly in the search for gas. By using complex AVO equations, AVO allows us to estimate S-wave type information from P-wave reflections at different offsets.

Naturally, AVO methods have their limitations. Rock physics effects create one of the biggest: the inability to distinguish between fizz water and commercial hydrocarbon saturations. All our hopes for saturation discrimination lie in the density term, and true AVO inversions can get us there.

Seismic inversion methods have been in use since the 1970s and are based on the convolutional model that treats a seismic trace as the convolution of the seismic wavelet and the earth’s reflectivity. Inversion attempts to reverse this process by removing the wavelet, resulting in values for the P-impedance in the subsurface. We can then relate this P-impedance to lithology and porosity.

We can trace the history of inversion through the evolution of inversion algorithms used as industry standards over recent decades. The first post-stack inversion methods, such as Recursive Inversion (Lindseth, 1978) were simplistic, and limited by their lack of wavelet definition and inability to recover the low frequency components. Subsequent Model Based Inversion techniques (Hampson & Russell, 1991) removed these limitations and gave rise to high resolution, accurate inversion results. Today there are a whole host of inversion algorithms available to the interpreter.

All post-stack inversion methods suffer from a common limitation: the input stacked dataset does not represent the true earth reflectivity. We assume that our stacked data is equivalent to a normal incidence (zero offset) dataset. But this is not true when stacking data that contains AVO effects. Thus the resulting inversion is not true P-impedance. We need AVO inversion methods to overcome this.

Combining AVO & inversion methods
Over the last decade, numerous papers have been published introducing new combined AVO and inversion concepts. Software companies have eagerly adopted these and developed their software accordingly. Today, we’ve reached the ultimate in AVO inversion: full pre-stack (aka simultaneous) inversion. If this is today’s gold standard, how did we get there?

Industry trends in AVO, inversion & AVO inversion

Lambda-Mu-Rho
In 1997, Goodway, et al. published a paper on an AVO inversion method based on Lamé’s parameters (rock physics descriptors). This method, known today as Lambda-Mu-Rho, or simply “LMR”, is the first step on the AVO inversion route we are exploring.

A standard AVO method is used to compute estimates of P-wave and S-wave reflectivities directly from pre-stack data. These two datasets are then inverted, using standard post-stack inversion techniques, to P- and S-impedance respectively. Once P-impedance and S-impedance have been derived, we can get estimates of the Lamé parameters, typically lambda-rho and mu-rho which, in turn, relate to fluid and rock properties. Cross plotting methods are widely used in the interpretation of these inversion results.

Elastic Impedance
During the 1990s, it became increasingly common for processing companies to deliver range limited (near, mid and far offset) stacks to their clients. These stacks benefit from the improved signal-to-noise ratio that results from stacking data. Naturally, interpreters wanted to invert this data. But what should they invert the data to? Only zero offset data can be inverted to acoustic impedance.

Connolly solved this conundrum in 1998 by proposing Elastic Impedance (EI) as an angle dependent analogy to acoustic impedance. Based on the Aki and Richards equation, the EI method was the first to truly combine elements of AVO theory into inversion. As a natural extension to P-impedance, the EI concept made it easy for software designers to adapt pre-existing inversion algorithms to accommodate the inversion of near and far angle stacks.

Elastic Impedance inversions benefit greatly from the AVO effects they incorporate. The inversion results are now dependent on P-wave and S-wave velocities, and density. The results are no longer just lithology tools but respond to fluid effects too.

Limitations
One of the potential limitations of using post-stack inversion algorithms for LMR and EI inversion is that the inversions are performed independently. So, for example, we invert S-wave reflectivity to S-impedance without any consideration for how we have inverted the P-wave reflectivity data, and yet P-wave and S-wave velocities are closely related. This can result in unrealistic Vp/Vs ratios and negative LR values.

What is simultaneous inversion?
There was one final step to reach today’s gold standard: full, pre-stack inversion. This new pre-stack inversion technology aims to obtain reliable estimates of P-wave velocity, S-wave velocity and density, from which we can predict both fluid and lithology properties. By including the AVO effects present in pre-stack data, our inversion is no longer restricted to being primarily a lithology prediction tool.

There are only a few pre-stack inversion software products on the market, all of which work in subtly different ways. In 2007, Hampson-Russell released their unique simultaneous inversion algorithm within their long-established, industry standard STRATA inversion software program. What makes their algorithm special is that it operates on the full pre-stack data, unlike some algorithms that are restricted to range limited stacks.

Simultaneous inversion perturbs an initial first-guess P-impedance model to estimate S-impedance, density and more reliable P-impedance values. We do this in such a way that if we forward model from the resulting impedance and density volumes, using AVO equations such as Zoeppritz’s equations, the resulting pre-stack synthetic CDP data will very closely match the actual pre-stack CDP data.

We make various assumptions to get to the results, one of which is that we can describe a linear relationship between P-impedance and both S-impedance and density. Here we see an example of these relationships from real log data. We assume that the linear regressions (red lines) hold for the wet trends but not for the anomalous (hydrocarbon bearing) zones. We invert to determine for ΔL terms on the cross plot images below. 

Cross plots of log data to define the background relationships that will constrain the simultaneous inversion. Left: Ln(density) versus Ln(P-Impedance) /  right: Ln(S-impedance) versus Ln(P-Impedance)

Why have recent software innovations excited our industry? The answer is “for lots of reasons”:
• Vp/Vs ratios
• Density term
• Derive more accurate LMR results
• Apply to time-lapse datasets
• Apply to multi-component datasets

First, simultaneous inversion will give us an estimate of the S-impedance, allowing us to derive Vp/Vs ratio volumes. These alone are extremely useful for locating hydrocarbons as Vp/Vs ratios drop in the presence of oil and particularly gas.

Cretaceous example: the Vp/Vs ratio is very low in the gas reservoir interval highlighted by the red box.

Another benefit of Hampson-Russell’s new innovative technology is the ability to estimate density. Depending on factors, such as acquisition geometry, depth of interest, data quality etc., we can derive density information during a pre-stack inversion. This may help to distinguish between fizz water and commercial hydrocarbon saturations.

With this new software algorithm in hand, geoscientists can also revisit earlier inversion techniques and apply them with more accuracy. For example, we can use P-impedance and S-impedance from simultaneous inversion to estimate LMR parameters.

LR v MR cross plots for the same dataset, derived from simultaneous inversion (left) and “independent” inversion (right). Negative values of LR (blue zone) are computed using independent inversion results. Lowest LR values from simultaneous inversion (yellow zone) are positive.

One of the key innovations of the new Hampson-Russell algorithm is that it can handle the joint inversion of PP and PS data. Since multi-component data is the way forward in mature basins, this algorithm opens up a whole host of interpretation techniques for the future. Similarly, the unique inversion algorithm has been adapted for the inversion of time-lapse seismic data, allowing geoscientists to invert base and multiple monitor surveys simultaneously.

Summary
The last two decades have seen the introduction of, and huge developments in, a range of reservoir characterization technologies. Our favoured techniques of AVO and inversion have evolved from new concepts to industry standard techniques. EI and LMR are now firmly established, more so than other AVO methodologies not discussed here, such as the Fluid Factor (Smith & Gidlow, 1987) and Poissons’ Impedance (Quakenbush, 2006).

All these methods continue to evolve, increasing in both complexity and accuracy. Today’s gold standard of a full, pre-stack (simultaneous) inversion represents the ultimate combination of AVO and inversion technologies. STRATA – Hampson-Russell’s inversion software – now contains full pre-stack inversion

Software innovations such as simultaneous inversion haven’t happened in isolation. Advances in computing hardware, such as faster chips, larger data storage etc., allow us to do the once impossible: number-crunch through huge volumes of data. Those of us that supply software to the oil industry continue to innovate: the current market demands that we do so.

Contact details:
Rebecca Goffey
Hampson-Russell (A CGGVeritas company)
Regional Manager – Europe, Africa & FSU
Parkshot House, 5 Kew Road,
Richmond, Surrey, TW9 2PR, UK
T: +44-20-8334-8091
F: +44-20-8334-8191
E: rebecca.goffey@cggveritas.com

Mr. Yuriy Smirnov
Hampson-Russell, Moscow
T: +7 495 789 8420
E: supporthrs.moscow@cggveritas.com
www.cggveritas.com/hampson-russell