Comparison of the Krief and critical porosity models for prediction of porosity and VP/VS

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 925-927 ◽  
Author(s):  
Gary Mavko ◽  
Tapan Mukerji
Keyword(s):  
Short Note ◽  
Pore Fluid ◽  
Amplitude Variation ◽  
Critical Porosity ◽  
Amplitude Variation With Offset ◽  
Sonic Log ◽  
Empirical Relations ◽  
Text Prediction ◽  
Prediction Techniques

[Formula: see text] relations are key to the determination of lithology from seismic or sonic log data, as well as for direct seismic identification of pore fluids using, for example, amplitude variation with offset (AVO) analysis. While there are a variety of published [Formula: see text] relations and [Formula: see text] prediction techniques, most reduce to two simple elements: (1) for each lithology, establish empirical relations among [Formula: see text], [Formula: see text], and porosity for one reference fluid—usually water—and (2) use Gassmann’s (1951) relations to map these to other pore fluid states. In this short note we point out similarities between the critical porosity models of Nur (1992) and Krief et al. (1990) for predicting [Formula: see text]. Both are useful, primarily because they incorporate the above two robust elements. Although derived from different directions, they are nearly identical.

Computation of dry-rock VP/VS ratio, fluid property factor, and density estimation from amplitude-variation-with-offset inversion

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. R669-R679 ◽  
Author(s):  
Gang Chen ◽  
Xiaojun Wang ◽  
Baocheng Wu ◽  
Hongyan Qi ◽  
Muming Xia
Keyword(s):  
Reservoir Characterization ◽  
Synthetic Data ◽  
Pore Fluid ◽  
Inversion Method ◽  
S Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Fluid Identification ◽  
Fluid Property ◽  
Avo Inversion

Estimating the fluid property factor and density from amplitude-variation-with-offset (AVO) inversion is important for fluid identification and reservoir characterization. The fluid property factor can distinguish pore fluid in the reservoir and the density estimate aids in evaluating reservoir characteristics. However, if the scaling factor of the fluid property factor (the dry-rock [Formula: see text] ratio) is chosen inappropriately, the fluid property factor is not only related to the pore fluid, but it also contains a contribution from the rock skeleton. On the other hand, even if the angle gathers include large angles (offsets), a three-parameter AVO inversion struggles to estimate an accurate density term without additional constraints. Thus, we have developed an equation to compute the dry-rock [Formula: see text] ratio using only the P- and S-wave velocities and density of the saturated rock from well-logging data. This decouples the fluid property factor from lithology. We also developed a new inversion method to estimate the fluid property factor and density parameters, which takes full advantage of the high stability of a two-parameter AVO inversion. By testing on a portion of the Marmousi 2 model, we find that the fluid property factor calculated by the dry-rock [Formula: see text] ratio obtained by our method relates to the pore-fluid property. Simultaneously, we test the AVO inversion method for estimating the fluid property factor and density parameters on synthetic data and analyze the feasibility and stability of the inversion. A field-data example indicates that the fluid property factor obtained by our method distinguishes the oil-charged sand channels and the water-wet sand channel from the well logs.

Coupling in amplitude variation with offset and the Wiggins approximation

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. N21-N33 ◽  
Author(s):  
Kristopher A. Innanen
Keyword(s):  
Wave Reflection ◽  
Elastic Parameter ◽  
P Wave ◽  
Converted Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Zoeppritz Equations ◽  
P Wave Velocity ◽  
Higher Order Corrections

Linear amplitude-variation-with-offset (AVO) approximations, which experience a reduction in accuracy as elastic parameter contrasts become large, may be adjusted with second- and higher-order corrections. Corrective terms can be expressed in many ways, but they only serve a meaningful purpose if they provide the same qualitative interpretability as did the linearization. Some aspects of nonlinear AVO can be understood, quantitatively and qualitatively, in terms of coupling — the interdependence of elastic parameter contrasts amongst themselves in their determination of reflection strengths. Coupling, for instance, explains the weak but nonnegligible dependence of the converted wave reflection coefficient on the lower half-space P-wave velocity. This fact can be exposed by expanding the solutions of the Zoeppritz equations in a particular hierarchy of series. Also explainable through this approach is the mathematical importance of what is sometimes referred to as the “Wiggins approximation,” under which [Formula: see text]. This special number is seen to coincide with a full decoupling of density contrasts from [Formula: see text] and [Formula: see text] contrasts at the second order. The decoupling persists across several variations of the nonlinear AVO approximations, including both expressions in terms of the relative changes [Formula: see text], [Formula: see text], and [Formula: see text], and expressions in terms of single-parameter reflectivities.

Yet another Vs equation

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. E35-E39 ◽  
Author(s):  
Jack P. Dvorkin
Keyword(s):  
Shear Modulus ◽  
Wave Velocity ◽  
Carbonate Rock ◽  
Functional Form ◽  
Solid Phase ◽  
Total Porosity ◽  
Pore Fluid ◽  
S Wave ◽  
Critical Porosity ◽  
Text Prediction

The classical Raymer-Hunt-Gardner functional form [Formula: see text], where [Formula: see text] and [Formula: see text] denote the [Formula: see text]-wave velocity in the solid and pore-fluid phases, respectively, and [Formula: see text] is the total porosity, can also be used to relate the S-wave velocity in dry rock to porosity and mineralogy as [Formula: see text], where [Formula: see text] is the S-wave velocity in the solid phase. Assuming that the shear modulus of rock does not depend on the pore fluid, [Formula: see text] in wet rock is [Formula: see text], where [Formula: see text] and [Formula: see text] denote the bulk density of the dry and wet rock, respectively. This new functional form for [Formula: see text] prediction reiterates Nur’s critical porosity concept: The [Formula: see text] ratio in dry rock equals that in the solid phase. It accurately predicts [Formula: see text] in consolidated clastic and carbonate rock. Two motivations for using it are (1) it is simple, and (2) it predicts [Formula: see text] not from [Formula: see text] but directly from [Formula: see text] and mineralogy.

Effect of VS predictors on amplitude variation with offset response

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. N1-N13
Author(s):  
Humberto S. Arévalo-López ◽  
Uri Wollner ◽  
Jack P. Dvorkin
Keyword(s):  
Seismic Data ◽  
Poor Quality ◽  
Rock Properties ◽  
Specific Situation ◽  
S Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Seismic Amplitude ◽  
Text Prediction ◽  
A Site

We have posed a question whether the differences between various [Formula: see text] predictors affect one of the ultimate goals of [Formula: see text] prediction, generating synthetic amplitude variation with offset (AVO) gathers to serve as a calibration tool for interpreting the seismic amplitude for rock properties and conditions. We address this question by evaluating examples in which we test several such predictors at an interface between two elastic layers, at pseudowells, and at a real well with poor-quality S-wave velocity data. The answer based on the examples presented is that no matter which [Formula: see text] predictor is used, the seismic responses at a reservoir are qualitatively identical. The choice of a [Formula: see text] predictor does not affect our ability (or inability) to forecast the presence of hydrocarbons from seismic data. We also find that the amplitude versus angle responses due to different predictors consistently vary along the same pattern, no matter which predictor is used. Because our analysis uses a “by-example” approach, the conclusions are not entirely general. However, the method of comparing the AVO responses due to different [Formula: see text] predictors discussed here is. Hence, in a site-specific situation, we recommend using several relevant predictors to ascertain whether the choice significantly affects the synthetic AVO response and if this response is consistent with veritable seismic data.

Recent advances in seismic lithologic analysis

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 42-46 ◽  
Author(s):  
John P. Castagna
Keyword(s):  
Seismic Data ◽  
Recent Progress ◽  
Seismic Analysis ◽  
Rock Physics ◽  
Pore Fluid ◽  
Analysis Tool ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Fluid Content ◽  
Key Aspects

An objective of seismic analysis is to quantitatively extract lithology, porosity, and pore fluid content directly from seismic data. Rock physics provides the fundamental basis for seismic lithology determination. Beyond conventional poststack inversion, the most important seismic lithologic analysis tool is amplitude‐variation‐with‐offset (AVO) analysis. In this paper, I review recent progress in these two key aspects of seismic lithologic analysis.

Fracture mapping using seismic amplitude variation with offset and azimuth analysis at the Weyburn CO2 storage site

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. B295-B306 ◽  
Author(s):  
Alexander Duxbury ◽  
Don White ◽  
Claire Samson ◽  
Stephen A. Hall ◽  
James Wookey ◽  
...  
Keyword(s):  
Cross Sections ◽  
Co2 Storage ◽  
Horizontal Stress ◽  
Storage Site ◽  
Fracture Zones ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Seal Integrity ◽  
Cap Rock ◽  
Weyburn Field

Cap rock integrity is an essential characteristic of any reservoir to be used for long-term [Formula: see text] storage. Seismic AVOA (amplitude variation with offset and azimuth) techniques have been applied to map HTI anisotropy near the cap rock of the Weyburn field in southeast Saskatchewan, Canada, with the purpose of identifying potential fracture zones that may compromise seal integrity. This analysis, supported by modeling, observes the top of the regional seal (Watrous Formation) to have low levels of HTI anisotropy, whereas the reservoir cap rock (composite Midale Evaporite and Ratcliffe Beds) contains isolated areas of high intensity anisotropy, which may be fracture-related. Properties of the fracture fill and hydraulic conductivity within the inferred fracture zones are not constrained using this technique. The predominant orientations of the observed anisotropy are parallel and normal to the direction of maximum horizontal stress (northeast–southwest) and agree closely with previous fracture studies on core samples from the reservoir. Anisotropy anomalies are observed to correlate spatially with salt dissolution structures in the cap rock and overlying horizons as interpreted from 3D seismic cross sections.

The impact of reservoir scale on amplitude variation with offset

2016 ◽  
Vol 65 (3) ◽  
pp. 736-746 ◽  
Author(s):  
Chao Xu ◽  
Jianxin Wei ◽  
Bangrang Di
Keyword(s):  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
The Impact

Information on elastic parameters obtained from the amplitudes of reflected waves

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1426-1436 ◽  
Author(s):  
Wojciech Dȩbski ◽  
Albert Tarantola
Keyword(s):  
Mass Density ◽  
Seismic Velocities ◽  
Elastic Parameters ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Reflected Waves ◽  
Seismic Amplitude ◽  
Earth Models ◽  
Definition Of ◽  
Proper Analysis

Seismic amplitude variation with offset data contain information on the elastic parameters of geological layers. As the general solution of the inverse problem consists of a probability over the space of all possible earth models, we look at the probabilities obtained using amplitude variation with offset (AVO) data for different choices of elastic parameters. A proper analysis of the information in the data requires a nontrivial definition of the probability defining the state of total ignorance on different elastic parameters (seismic velocities, Lamé’s parameters, etc.). We conclude that mass density, seismic impedance, and Poisson’s ratio constitute the best resolved parameter set when inverting seismic amplitude variation with offset data.

Model misspecification and bias in the least-squares algorithm: Implications for linearized isotropic AVO

2021 ◽  
Vol 40 (9) ◽  
pp. 646-654
Author(s):  
Henning Hoeber
Keyword(s):  
Least Squares ◽  
Model Misspecification ◽  
Forward Model ◽  
Model Parameters ◽  
Omitted Variables ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Omitted Variable Bias ◽  
Least Squares Fit ◽  
Variable Bias

When inversions use incorrectly specified models, the estimated least-squares model parameters are biased. Their expected values are not the true underlying quantitative parameters being estimated. This means the least-squares model parameters cannot be compared to the equivalent values from forward modeling. In addition, the bias propagates into other quantities, such as elastic reflectivities in amplitude variation with offset (AVO) analysis. I give an outline of the framework to analyze bias, provided by the theory of omitted variable bias (OVB). I use OVB to calculate exactly the bias due to model misspecification in linearized isotropic two-term AVO. The resulting equations can be used to forward model unbiased AVO quantities, using the least-squares fit results, the weights given by OVB analysis, and the omitted variables. I show how uncertainty due to bias propagates into derived quantities, such as the χ-angle and elastic reflectivity expressions. The result can be used to build tables of unique relative rock property relationships for any AVO model, which replace the unbiased, forward-model results.

Sign in / Sign up

Export Citation Format

Share Document