Bayesian inversion for effective pore-fluid bulk modulus based on fluid-matrix decoupled amplitude variation with offset approximation

Geophysics ◽  
2014 ◽  
Vol 79 (5) ◽  
pp. R221-R232 ◽  
Author(s):  
Xingyao Yin ◽  
Shixin Zhang
Keyword(s):  
Bulk Modulus ◽  
Pore Fluid ◽  
Bayesian Inversion ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset

Value of information analysis and Bayesian inversion for closed skew-normal distributions: Applications to seismic amplitude variation with offset data

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. R151-R163 ◽  
Author(s):  
Javad Rezaie ◽  
Jo Eidsvik ◽  
Tapan Mukerji
Keyword(s):  
Seismic Data ◽  
Value Of Information ◽  
Bayesian Inversion ◽  
Information Analysis ◽  
Amplitude Variation ◽  
Mean Values ◽  
Amplitude Variation With Offset ◽  
Seismic Amplitude ◽  
Value Of Information Analysis ◽  
Skew Normal

Information analysis can be used in the context of reservoir decisions under uncertainty to evaluate whether additional data (e.g., seismic data) are likely to be useful in impacting the decision. Such evaluation of geophysical information sources depends on input modeling assumptions. We studied results for Bayesian inversion and value of information analysis when the input distributions are skewed and non-Gaussian. Reservoir parameters and seismic amplitudes are often skewed and using models that capture the skewness of distributions, the input assumptions are less restrictive and the results are more reliable. We examined the general methodology for value of information analysis using closed skew normal (SN) distributions. As an example, we found a numerical case with porosity and saturation as reservoir variables and computed the value of information for seismic amplitude variation with offset intercept and gradient, all modeled with closed SN distributions. Sensitivity of the value of information analysis to skewness, mean values, accuracy, and correlation parameters is performed. Simulation results showed that fewer degrees of freedom in the reservoir model results in higher value of information, and seismic data are less valuable when seismic measurements are spatially correlated. In our test, the value of information was approximately eight times larger for a spatial-dependent reservoir variable compared with the independent case.

Gassmann fluid substitutions: A tutorial

Geophysics ◽  
2003 ◽  
Vol 68 (2) ◽  
pp. 430-440 ◽  
Author(s):  
Tad M. Smith ◽  
Carl H. Sondergeld ◽  
Chandra S. Rai
Keyword(s):  
Bulk Modulus ◽  
Bulk Density ◽  
Pore Fluid ◽  
Direct Result ◽  
Fluid Substitution ◽  
Seismic Attribute ◽  
Amplitude Variation With Offset ◽  
Effective Bulk Modulus ◽  
Porous Frame ◽  
Insight Into

Fluid substitution is an important part of seismic attribute work, because it provides the interpreter with a tool for modeling and quantifying the various fluid scenarios which might give rise to an observed amplitude variation with offset (AVO) or 4D response. The most commonly used technique for doing this involves the application of Gassmann's equations. Modeling the changes from one fluid type to another requires that the effects of the starting fluid first be removed prior to modeling the new fluid. In practice, the rock is drained of its initial pore fluid, and the moduli (bulk and shear) and bulk density of the porous frame are calculated. Once the porous frame properties are properly determined, the rock is saturated with the new pore fluid, and the new effective bulk modulus and density are calculated. A direct result of Gassmann's equations is that the shear modulus for an isotropic material is independent of pore fluid, and therefore remains constant during the fluid substitution process. In the case of disconnected or cracklike pores, however, this assumption may be violated. Once the values for the new effective bulk modulus and bulk density are calculated, it is possible to calculate the compressional and shear velocities for the new fluid conditions. There are other approaches to fluid substitution (empirical and heuristic) which avoid the porous frame calculations but, as described in this tutorial, often do not yield reliable results. This tutorial provides the reader with a recipe for performing fluid substitutions, as well as insight into why and when the approach may fail.

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.

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.

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.

scholarly journals Experimental verification of spatially varying fracture-compliance estimates obtained from amplitude variation with offset inversion coupled with linear slip theory

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. WA1-WA8 ◽  
Author(s):  
Shohei Minato ◽  
Ranajit Ghose ◽  
Godfred Osukuku
Keyword(s):  
Bulk Modulus ◽  
Frequency Dependence ◽  
Hydraulic Properties ◽  
Slip Model ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Avo Inversion ◽  
Fractured Medium ◽  
Spatially Varying ◽  
Linear Slip Model

The elastic compliance of a fracture can be spatially varying, reflecting the variation of microscale properties of the fracture, e.g., aperture, contact asperities, and fracture infill. Characterizing the spatial heterogeneity of a fracture is crucial in explaining the apparent frequency dependence of fracture compliance and in addressing the spatially varying mechanical and hydraulic properties of the fractured medium. Apparent frequency dependence of the estimated fracture compliance is caused when the used seismic wavelength is very large compared to the scale of heterogeneity. We perform ultrasonic laboratory experiments, and characterize the spatially varying compliance along a fluid-filled fracture. We simulate a horizontal fracture, and introduce heterogeneous fluid distribution along the fracture. We perform amplitude variation with offset (AVO) inversion of the P-P reflections, in which we obtain the theoretical angle-dependent reflection responses by considering the linear-slip model. The estimated compliance distribution clearly separates the dry region from the wet region of the fracture. The effective bulk modulus of the fluid is estimated using the derived values of the compliance. We find that the obtained bulk modulus is well-explained by the presence of minute quantity of air bubbles in the water. We also find new evidence of the existence of scattered waves generated at the boundary representing a sharp change in fracture compliance. The estimated boundary between the dry and the wet regions of the fracture, which is detected by AVO inversion, is slightly shifted compared with the actual location. This is possibly due to the interference of the scattered waves that are generated at the boundary. The linear-slip model can represent thin structures in rocks in a wide range of scale. Therefore, our methodology, results, and discussion will be useful in developing new applications for assessing laterally varying mechanical and hydraulic properties of thin nonwelded discontinuities, e.g., fractures, joints, and faults.

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.

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