Analysis of seismic anisotropy parameters for sedimentary strata

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. D495-D502 ◽  
Author(s):  
Fuyong Yan ◽  
De-Hua Han ◽  
Samik Sil ◽  
Xue-Lian Chen
Keyword(s):  
Seismic Anisotropy ◽  
Sedimentary Rocks ◽  
Measurement Data ◽  
Transversely Isotropic ◽  
Theoretical Expression ◽  
Strong Correlations ◽  
Backus Averaging ◽  
Anisotropy Parameters ◽  
Intrinsic Anisotropy ◽  
Gas Bearing

Based on a large quantity of laboratory ultrasonic measurement data of sedimentary rocks and using Monte Carlo simulation and Backus averaging, we have analyzed the layering effects on seismic anisotropy more realistically than in previous studies. The layering effects are studied for different types of rocks under different saturation conditions. If the sedimentary strata consist of only isotropic sedimentary layers and are brine-saturated, the [Formula: see text] value for the effective transversely isotropic (TI) medium is usually negative. The [Formula: see text] value will increase noticeably and can be mostly positive if the sedimentary strata are gas bearing. Based on simulation results, [Formula: see text] can be determined by other TI elastic constants for a layered medium consisting of isotropic layers. Therefore, [Formula: see text] can be predicted from the other Thomsen parameters with confidence. The theoretical expression of [Formula: see text] for an effective TI medium consisting of isotropic sedimentary rocks can be simplified with excellent accuracy into a neat form. The anisotropic properties of the interbedding system of shales and isotropic sedimentary rocks are primarily influenced by the intrinsic anisotropy of shales. There are moderate to strong correlations among the Thomson anisotropy parameters.

Relationships between the anisotropy parameters for transversely isotropic mudrocks

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. MR195-MR203
Author(s):  
Fuyong Yan ◽  
Lev Vernik ◽  
De-Hua Han
Keyword(s):  
Elastic Properties ◽  
Seismic Anisotropy ◽  
Measurement Data ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
The Other ◽  
Quality Analysis ◽  
Directional Bias ◽  
Empirical Relations ◽  
Anisotropy Parameters

Studying the empirical relations between seismic anisotropy parameters is important for the simplification and practical applications of seismic anisotropy. The elastic properties of mudrocks are often described by transverse isotropy. Knowing the elastic properties in the vertical and horizontal directions, a sole oblique anisotropy parameter determines the pattern of variation of the elastic properties of a transversely isotropic (TI) medium in all of the other directions. The oblique seismic anisotropy parameter [Formula: see text], which determines seismic reflection moveout behavior, is important in anisotropic seismic data processing and interpretation. Compared to the other anisotropy parameters, the oblique anisotropy parameter is more sensitive to the measurement error. Although, theoretically, only one oblique velocity is needed to determine the oblique anisotropy parameter, the uncertainty can be greatly reduced if multiple oblique velocities in different directions are measured. If a mudrock is not a perfect TI medium but it is expediently treated as one, then multiple oblique velocity measurements in different directions should lead to a more representative approximation of [Formula: see text] or [Formula: see text] because the directional bias can be reduced. Based on a data quality analysis of the laboratory seismic anisotropy measurement data from the literature, we found that there are strong correlations between the oblique anisotropy parameter and the principal anisotropy parameters when data points of more uncertainty are excluded. Examples of potential applications of these empirical relations are discussed.

Comparison of seismic anisotropy of sedimentary strata at low- and high-frequency limits

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. MR1-MR10 ◽  
Author(s):  
Fuyong Yan ◽  
De-Hua Han ◽  
Tongcheng Han ◽  
Xue-Lian Chen
Keyword(s):  
High Frequency ◽  
Seismic Anisotropy ◽  
Sedimentary Rocks ◽  
Low Frequency ◽  
Layered Media ◽  
Ray Theory ◽  
Frequency Limit ◽  
Anisotropic Properties ◽  
Velocity Anisotropy ◽  
Backus Averaging

The layer-induced seismic anisotropy of sedimentary strata is frequency-dependent. At the low-frequency limit, the effective anisotropic properties of the layered media can be estimated by the Backus averaging model. At the high-frequency limit, the apparent anisotropic properties of the layered media can be estimated by ray theory. First, we build a database of laboratory ultrasonic measurement on sedimentary rocks from the literature. The database includes ultrasonic velocity measurements on sandstones and carbonate rocks, and velocity-anisotropy measurements on shales. Then, we simulate the sedimentary strata by randomly selecting a certain number of rock samples and using their laboratory measurement results to parameterize each layer. For each realization of the sedimentary strata, we estimate the effective and apparent seismic anisotropy parameters using the Backus average and ray theory, respectively. We find that, relative to Backus averaging, ray theory usually underestimates the Thomsen parameters [Formula: see text] and [Formula: see text], and overestimates [Formula: see text]. For an effective layered medium consisting of isotropic sedimentary rocks, the differences are significant. These differences decrease when shales with intrinsic seismic anisotropy are included. For the same sedimentary strata, the seismic wave should perceive stronger seismic anisotropy than the ultrasonic wave.

A physical model of shear‐wave propagation in a transversely isotropic solid

Geophysics ◽  
1994 ◽  
Vol 59 (3) ◽  
pp. 484-487 ◽  
Author(s):  
Chih‐Hsiung Chang ◽  
G. H. F. Gardner ◽  
John A. McDonald
Keyword(s):  
Wave Propagation ◽  
Physical Model ◽  
Shear Wave ◽  
Seismic Anisotropy ◽  
Sedimentary Rocks ◽  
Physical Property ◽  
Transversely Isotropic ◽  
Velocity Variation ◽  
Common Phenomenon ◽  
Isotropic Solid

It is now understood that seismic anisotropy is a comparatively common phenomenon in sedimentary layers. The elastic properties of most sedimentary rocks have been shown to be anisotropic. (Anisotropy means that the physical property of the material is a function of the measuring direction). Seismologists are generally concerned with velocity variation with the direction of propagation.

Seismic critical-angle anisotropy analysis in the τ -p domain

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. A53-A57 ◽  
Author(s):  
Samik Sil ◽  
Mrinal K. Sen
Keyword(s):  
Critical Angle ◽  
Seismic Anisotropy ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
Seismic Line ◽  
Full Wave ◽  
Current Implementation ◽  
Approximation Errors ◽  
Anisotropy Parameters ◽  
Axis Of Symmetry

Seismic critical-angle reflectometry is a relatively new field for estimating seismic anisotropy parameters. The theory relates changes in the critical angle with azimuth of the seismic line to the principal axis and anisotropy parameters. Current implementation of the critical-angle reflectometry process has certain shortcomings in that the critical angle is determined from critical offset and the process is vulnerable to different approximation errors. Seismic critical-angle analysis in the plane-wave [Formula: see text] domain can handle these issues and has the potential to become an independent tool for estimating anisotropy parameters. The theory of seismic critical-angle reflectometry is modified to make it suitable for [Formula: see text] domain analysis. Then using full-wave synthetic seismograms at three different azimuths for a transversely isotropic medium with a horizontal axis of symmetry (HTI), the effectiveness of anisotropy parameter estimation is demonstrated.

Simplified anisotropy parameters for transversely isotropic sedimentary rocks

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1933-1935 ◽  
Author(s):  
Colin M. Sayers
Keyword(s):  
Elastic Constants ◽  
Sedimentary Rocks ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
P Wave ◽  
Time Migration ◽  
Vsp Data ◽  
Walkaway Vsp ◽  
Anisotropy Parameters ◽  
The Difference

Sedimentary rocks frequently possess an anisotropic structure resulting, for example, from fine scale layering, the presence of oriented microcracks or fractures, or the preferred orientation of nonspherical grains or anisotropic minerals. For many rocks the anisotropy may be described, to a good approximation, as being transversely isotropic. The purpose of this note is to present simplified anisotropy parameters for these rocks that are valid when the P‐wave normal moveout (NMO) and vertical velocities differ by less than 25%. This condition appears reasonable since depths calculated from P‐wave stacking velocities are often within 10% of actual depths (Winterstein, 1986). It is found that when this condition is satisfied the elastic constants [Formula: see text] and [Formula: see text] affect the P‐wave NMO velocity and anellipticity only through the combination [Formula: see text], a combination of elastic constants that can be determined using walkaway VSP data (Miller et al., 1993). The anellipticity quantifies the deviation of the P‐phase slowness from an ellipse and also determines the difference between the vertical and NMO velocities for SV‐waves. Helbig (1983) has shown that a time‐migrated section for which elliptical anisotropy has been taken into account is identical to one that has been determined under the assumption of isotropy. The anellipticity is therefore the important anisotropy parameter for anisotropic time migration. The results given are of interest for anisotropic velocity analysis, time migration, and time‐to‐depth conversion.

Layer-induced seismic anisotropy from full-wave sonic logs: Theory, application, and validation

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. D183-D190 ◽  
Author(s):  
Christopher L. Liner ◽  
Tong W. Fei
Keyword(s):  
Data Processing ◽  
Seismic Data ◽  
Seismic Anisotropy ◽  
Seismic Data Processing ◽  
Dominant Wavelength ◽  
Depth Migration ◽  
Full Wave ◽  
Theory Application ◽  
Anisotropy Parameters ◽  
Intrinsic Anisotropy

Thin isotropic elastic layering in the earth is one cause of seismic VTI anisotropy, along with intrinsic anisotropy and fractures. An important issue related to the routine use of VTI seismic data processing is the estimation of the necessary parameters. The full set of layer-induced VTI anisotropy parameters can be computed from full-wave sonic and density log data using Backus averaging. Intrinsic anisotropy can be incorporated if it is known from laboratory analysis. The isotropic layering method is applied to six wells in eastern Saudi Arabia, and the estimated anisotropy parameters are persistent across distances of many kilometers. This leads to the possibility of parameter estimation at sparse well locations for use in seismic data processing. Validation is demonstrated by direct numerical simulation of elastic wavefields in original and Backus-averaged earth models with various window lengths. We observe precise equivalence of the full wavefield when the averaging length is less than or equal to one-third of the minimum dominant wavelength. First arrival information, used in depth migration, is preserved with much longer averaging windows, up to twice the minimum dominant wavelength.

Seismic traveltime inversion for transverse isotropy

Geophysics ◽  
1990 ◽  
Vol 55 (2) ◽  
pp. 192-200 ◽  
Author(s):  
B. S. Byun ◽  
D. Corrigan
Keyword(s):  
Field Experiments ◽  
Seismic Anisotropy ◽  
Transverse Isotropy ◽  
Quantitative Measure ◽  
Transversely Isotropic ◽  
Velocity Anisotropy ◽  
Additional Information ◽  
Stiffness Coefficients ◽  
Anisotropy Parameters ◽  
Low Degrees

Quantitative measurements of seismic anisotropy can provide a valuable clue to the lithology and degree of stratification in sedimentary rocks with hydrocarbon potential. We present a practical technique for obtaining anisotropy parameters (i.e., five stiffness coefficients A, C, F, L, and M) from seismic traveltime measurements for horizontally layered, transversely isotropic media. The technique is based on the construction of ray‐velocity surfaces in terms of five measurement parameters. An iterative model‐based optimization scheme is then used to invert the traveltime parameters for the five stiffness coefficients in a layer‐stripping mode. Both model and field experiments are performed to demonstrate the feasibility of the method. The model experiment shows that inversion errors (especially in stiffness coefficients A, F, and M) increase with increasing number of layers. Despite these errors, the proposed method does provide a quantitative measure of velocity anisotropy as additional information that cannot be obtained readily from conventional methods. A field VSP data example shows the correlation between the anisotropy parameters and lithology: Chalk and shale exhibited high degrees of anisotropy, and sands showed low degrees of anisotropy.

Reverse time migration in tilted transversely isotropic media

2020 ◽  
Vol 38 (2) ◽  
Author(s):  
Razec Cezar Sampaio Pinto da Silva Torres ◽  
Leandro Di Bartolo
Keyword(s):  
Seismic Anisotropy ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Computer Clusters ◽  
Time Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Tti Media

ABSTRACT. Reverse time migration (RTM) is one of the most powerful methods used to generate images of the subsurface. The RTM was proposed in the early 1980s, but only recently it has been routinely used in exploratory projects involving complex geology – Brazilian pre-salt, for example. Because the method uses the two-way wave equation, RTM is able to correctly image any kind of geological environment (simple or complex), including those with anisotropy. On the other hand, RTM is computationally expensive and requires the use of computer clusters. This paper proposes to investigate the influence of anisotropy on seismic imaging through the application of RTM for tilted transversely isotropic (TTI) media in pre-stack synthetic data. This work presents in detail how to implement RTM for TTI media, addressing the main issues and specific details, e.g., the computational resources required. A couple of simple models results are presented, including the application to a BP TTI 2007 benchmark model.Keywords: finite differences, wave numerical modeling, seismic anisotropy. Migração reversa no tempo em meios transversalmente isotrópicos inclinadosRESUMO. A migração reversa no tempo (RTM) é um dos mais poderosos métodos utilizados para gerar imagens da subsuperfície. A RTM foi proposta no início da década de 80, mas apenas recentemente tem sido rotineiramente utilizada em projetos exploratórios envolvendo geologia complexa, em especial no pré-sal brasileiro. Por ser um método que utiliza a equação completa da onda, qualquer configuração do meio geológico pode ser corretamente tratada, em especial na presença de anisotropia. Por outro lado, a RTM é dispendiosa computacionalmente e requer o uso de clusters de computadores por parte da indústria. Este artigo apresenta em detalhes uma implementação da RTM para meios transversalmente isotrópicos inclinados (TTI), abordando as principais dificuldades na sua implementação, além dos recursos computacionais exigidos. O algoritmo desenvolvido é aplicado a casos simples e a um benchmark padrão, conhecido como BP TTI 2007.Palavras-chave: diferenças finitas, modelagem numérica de ondas, anisotropia sísmica.

scholarly journals Estimation of the anisotropy parameters of transversely isotropic shales with a tilted symmetry axis

2012 ◽  
Vol 190 (2) ◽  
pp. 1197-1203 ◽  
Author(s):  
Dariush Nadri ◽  
Joël Sarout ◽  
Andrej Bóna ◽  
David Dewhurst
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Anisotropy Parameters

scholarly journals A new traveltime approximation for TI media

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. C37-C42 ◽  
Author(s):  
Alexey Stovas ◽  
Tariq Alkhalifah
Keyword(s):  
Power Series ◽  
Eikonal Equation ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
Efficient Tool ◽  
Trade Off ◽  
Background Medium ◽  
The Common ◽  
Anisotropy Parameters ◽  
Ti Media

In a transversely isotropic (TI) medium, the trade-off between inhomogeneity and anisotropy can dramatically reduce our capability to estimate anisotropy parameters. By expanding the TI eikonal equation in power series in terms of the aneliptic parameter [Formula: see text], we derive an efficient tool to estimate (scan) for [Formula: see text] in a generally inhomogeneous, elliptically anisotropic background medium. For a homogeneous-tilted transversely isotropic medium, we obtain an analytic nonhyperbolic moveout equation that is accurate for large offsets. In the common case where we do not have well information and it is necessary to resolve the vertical velocity, the background medium can be assumed isotropic, and the traveltime equations becomes simpler. In all cases, the accuracy of this new TI traveltime equation exceeds previously published formulations and demonstrates how [Formula: see text] is better resolved at small offsets when the tilt is large.

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