Vaughn Ball

Generalized orthogonal attributes for fluid and lithology discrimination

Summary A generalization of principal component analysis produces a pair of seismic attribut es which uniquely maximize and minimize seismic anomaly strength with respect to the background. We call this approach “Generalized Orthogonal Attributes”. Whereas principal component analysis will orthogonalize the background seismic, the method of Generalized Orthogonal Attributes will simultaneously orthogonalize both the seismic background and the anomaly. The introduction of this method is timely given the current industry drive to develop methods that focus on subtle lithologic anomalies in unconventional reservoirs rather than conventional fluid anomalies. The method is also applicable to fluid and lithology responses other than Class III, where traditional principal component analysis has been less effective.

A Model-centric approach to Seismic Petrophysics

A model-centric approach to seismic petrophysical analysis delivers as its products all the components of the forward model: Parameters, Forward Logic, and Resultants. This contrasts with the classic analysis-based approach used in formation evaluation, whose products are interpreted properties such as total porosity and water saturation. While the analysis-based approach is well suited to formation evaluation, its results are disassociated from both the assumptions made during the analysis, and the forward logic used. This results in a disconnect when directly applied to seismic petrophysics.

Thin bed tuning analysis using AVO stratigraphy methods

When conventional methods of seismic stratigraphy are applied to the thin bed problem, the final result is a function which relates a range of thicknesses to a range of impedances. Amplitude versus Offset (AVO) stratigraphy provides and analysis method which can substantially reduce the range of the solution. AVO stratigraphy is not a simple extension of conventional seismic stratigraphy. The essential difference is that petrophysical modeling is introduced in order to parameterize the otherwise unwieldy attributes of density, velocity, and Poissons ratio.

Seismic rock physics in the presence of attribute noise

Classic Amplitude versus Offset (AVO) theory has developed a sound framework for understanding seismic rock physics in a noise-free context. (Foster et al., 2010) However, it has long been understood that noise in the offset domain becomes correlated in the various attribute domains, and can lead to “noise-forming”—the apparent rotation of attribute crossplots. (Cambois, 1998; Hendrickson, 1999; Saleh and de Bruin, 2000) In some domains such as Lambda-rho:Mu-rho reflectivity (LR:MR), noise-forming can actually lead to noisy attributes that are anti-correlated with the expected values (See Figure 1.)

Statistical modeling of seismic reflectivities comparing Lévy stable and Gaussian mixture distributions

The goal of this work is to compare statistical modeling of seismic reflectivities using two heavy-tailed models: Levy stable distributions and Gaussian mixture distributions. Distributions of various parameters, such as reflectivities are required inputs for many Monte Carlo simulations in statistical rock physics analyses for reservoir characterizations as well as formulating seismic inverse problem with non-Gaussian priors. Gaussian mixture models can provide an equally good fit to heavy-tailed reflectivity data as stable distributions, but with a larger number of fitting parameters. Monte Carlo simulations from stable distributions have a tendency to have more extreme outliers than simulations from Gaussian mixture models. Hence problems related to non-physical values, infinite moments, and ad-hoc fixes (truncation, deletion, etc.) tend to occur more often with stable distributions than Gaussian mixture models simulations

Contrasting stress dependence of compressional and shear velocities: Implications for laboratory, logging, and seismic measurements

Stresses are a dominant factor in controlling velocity in any particular rock. Unperturbed in situ stresses are usually different from those found around a borehole or typically applied in a laboratory. Compressional (Vp) and shear (Vs) velocities were measured on five sandstone samples as a function of triaxial stress. Vp is primarily controlled by the stress applied axially or parallel to the direction of propagation. Both axial and lateral or normal stresses have a strong influence on Vs. Isovelocity contour plots over axial and lateral stress space show a complex pattern significantly differing among the different sandstones tested. In spite of this, Vp and Vs are described well by a simple dependence on stress or pressure to the one-third power. Lateral stresses are significantly altered around a borehole much more than axial stresses. As a result, compressional sonic logs should give correct values but shear velocities will be shifted. Also, complex Vp-Vs relationships can be expected if in situ conditions change from the more typical unequal lithostatic stress state to the equal hydrostatic state as zones of high geopressure are approached.