Approaches for investigation of oriented cracks of reservoirs using multicomponent VSP

Abstract The paper analyses the VSP data inversion in order to determine elastic constants of a transversely isotropic medium with a horizontal axis of symmetry of an infinite order (HTI), simulating an oriented fractured reservoir. Acquisition system of VSP is characterized by the absence of sub-horizontal directions of propagation of seismic waves. In this regard, it was necessary to determine the accuracy with which the elastic constants of the anisotropic layer are restored. The seismograms of the full wave field were selected as the initial data, calculated synthetically for the model of the medium containing azimuthally anisotropic layers. A complex of compressional and shear waves propagating from a source and recorded in the well. In such layers, the shear wave incident on the roof of the HTI layer splits into two waves that propagate at different velocities and have a mutually orthogonal displacement vectors. The processing task was to select waves S 1 and S 2 and build their arrival time curves. These arrival time curves were used in the inversion. The inversion was solved in the form of minimizing the functional of the mean square residual. Elastic constants, determined by inversion, almost exactly coincided with the model ones. The results obtained show the validity of the chosen approach for solving the inverse problem.

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Interpretation of synthetic common‐depth‐point gathers for a single anisotropic layer

Geophysics ◽

10.1190/1.1441338 ◽

1982 ◽

Vol 47 (3) ◽

pp. 323-335 ◽

Cited By ~ 15

Author(s):

Stuart Crampin ◽

Barbara J. Radovich

Keyword(s):

Angular Velocity ◽

Elastic Constants ◽

Arrival Time ◽

Transversely Isotropic ◽

Orthorhombic Symmetry ◽

Isotropic Layer ◽

Anisotropic Layer ◽

Wide Range ◽

Velocity Variations ◽

Anisotropic Layers

Analysis of synthetic traveltime gathers shows that anisotropy may have a large enough effect on P, SH, and SV propagation to alter significantly the interpretation of the subsurface below the anisotropic layers. Consequently, if anisotropy exists below a seismic line, it is important to estimate the anisotropic parameters correctly. We discuss the effects of anisotropy on seismic waves and present a method for estimating the elastic constants of a transversely isotropic layer from P and SH arrival‐time gathers. The technique may be extended to more general anisotropic symmetries by analyzing gathers from several azimuths. To illustrate the possible effect of anisotropy on exploration surveys, P, SH, and SV velocity variations are calculated for several types of anisotropic sedimentary fabrics. Alignments due to bedding, shale lithology, and dry parallel cracks may have similar velocity variations. Fabrics with other configurations of cracks may still possess overall transversely isotropic symmetry, but they have a wide range of angular velocity variations with different polarities and periodicities. Synthetic gather curves are generated for a range of models with an anisotropic layer over an isotropic substrate. They show departures from hyperbolas, and erroneous depth determinations, that depend upon the elastic constants of the anisotropic layer. The elastic constants of the anisotropic layers are estimated from the synthetic gather curves by means of approximate equations for the angular velocity variations, which are linear in the elastic constants. Formulas are developed which relate tangents to the gather curves directly in terms of the elastic constants. These are tested for single‐layer transversely isotropic models and allow the five elastic constants to be estimated by drawing three tangents to P and SH synthetic arrival‐time gathers in [Formula: see text] space. Comparisons of estimated with original elastic constants are good for a number of different types of transversely isotropic fabrics. Gathers are also calculated at two azimuths in an anisotropic layer with orthorhombic symmetry and are analyzed with some success.

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Upscaling in orthorhombic media: Behavior of elastic parameters in heterogeneous fractured earth

Geophysics ◽

10.1190/geo2015-0392.1 ◽

2016 ◽

Vol 81 (3) ◽

pp. C113-C126 ◽

Cited By ~ 12

Author(s):

Yuriy Ivanov ◽

Alexey Stovas

Keyword(s):

Seismic Waves ◽

Homogeneous Medium ◽

Transversely Isotropic ◽

Processing Parameters ◽

P Wave ◽

Orthorhombic Symmetry ◽

Weak Anisotropy ◽

Fluid Saturation ◽

Fractured Medium ◽

Anisotropic Layers

A stack of horizontal homogeneous elastic arbitrary anisotropic layers in welded contact in the long-wavelength limit is equivalent to an elastic anisotropic homogeneous medium. Such a medium is characterized by an effective average description adhering to previously derived closed-form formalism. We have used this formalism to study three different inhomogeneous orthorhombic (ORT) models that could represent real geologic scenarios. We have determined that a stack of thin orthorhombic layers with arbitrary azimuths of vertical symmetry planes can be approximated by an effective orthorhombic medium. The most suitable approach for this is to minimize the misfit between the effective anisotropic medium, monoclinic in that case, and the desirable orthorhombic medium. The second model is an interbedding of VTI (transversely isotropic with a vertical symmetry axis) layers with the same layers containing vertical fractures (shales are intrinsically anisotropic and often fractured). We have derived a weak-anisotropy approximation for important P-wave processing parameters as a function of the relative amount of the fractured lithology. To accurately characterize fractures, inversion for the fracture parameters should use a priori information on the relative amount of a fractured medium. However, we have determined that the cracks’ fluid saturation can be estimated without prior knowledge of the relative amount of the fractured layer. We have used field well-log data to demonstrate how fractures can be included in the interval of interest during upscaling. Finally, the third model that we have considered is a useful representation of tilted orthorhombic medium in the case of two-way propagation of seismic waves through it. We have derived a weak anisotropy approximation for traveltime parameters of the reflected P-wave that propagates through a stack of thin beds of tilted orthorhombic symmetry. The tilt of symmetry planes in an orthorhombic medium significantly affects the kinematics of the reflected P-wave and should be properly accounted for to avoid mispositioning of geologic structures in seismic imaging.

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Seismic anisotropy in the upper 500 m of the Southern Sydney Basin

Geophysics ◽

10.1190/1.1444696 ◽

1999 ◽

Vol 64 (6) ◽

pp. 1901-1911 ◽

Cited By ~ 4

Author(s):

Milovan Urosević ◽

Christopher Juhlin

Keyword(s):

Elastic Constants ◽

Seismic Anisotropy ◽

Full Range ◽

Transversely Isotropic ◽

Real Data ◽

Vertical Axis ◽

P Wave ◽

Small Range ◽

P Waves ◽

Vsp Data

An analysis of seismic anisotropy at a BHP mining site in the Southern Sydney Basin by combined use of crosshole and vertical seismic profiling (VSP) data is presented. The upper 250 m in this area is highly heterogeneous and has a major impact on the analysis of P-wave traveltimes. It is shown that using P-wave information solely would not, at least in this case, lead to any reasonable estimate of the elastic constants, in particular C13, even if the measurements contained a full range of incident angles. However, if the measurements of SV-waves are available, even over a small range of incident angles, then C13 is determined more accurately. P-wave velocities measured in the vertical and horizontal directions show that anisotropy is present in the area. Additional measurements, along different incident angles, indicate that the rock down to 500 m depth is predominantly transversely isotropic (TI) with a vertical axis of symmetry. The P-wave anisotropy can be approximated as elliptical. Using the elastic constants estimated from the data analyses, synthetic seismograms for heterogeneous TI media were generated. Comparison of the seismic modeling with real crosshole data shows that it is necessary to include both fault zones and gas accumulations in the model to qualitatively match the real data. By using SV-waves in the multioffset VSP data, reflectors are mapped more accurately than by using P-waves, even under the assumption of isotropy and in the presence of heterogeneity. Mapping of converted P-SV waves by a straight ray approach also produced better results than the corresponding isotropic P-wave mapping. Inclusion of elliptical anisotropy into Kirchhoff migration resulted in better P-wave images than using an isotopic migration code. We conclude that both P-wave VSP multioffset mapping and tomographic inversion methods need to account for anisotropy to be accurate in this area, while SV-waves may be handled using isotropic codes. The same is true for crosshole and surface seismic data.

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Simplified anisotropy parameters for transversely isotropic sedimentary rocks

Geophysics ◽

10.1190/1.1443925 ◽

1995 ◽

Vol 60 (6) ◽

pp. 1933-1935 ◽

Cited By ~ 15

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.

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The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms: Theory and application

Geophysics ◽

10.1190/1.1444132 ◽

1997 ◽

Vol 62 (1) ◽

pp. 309-318 ◽

Cited By ~ 47

Author(s):

Jorge O. Parra

Keyword(s):

Wave Equation ◽

Fluid Flow ◽

Analytical Solution ◽

Seismic Waves ◽

Transversely Isotropic ◽

P Wave ◽

Fluid Properties ◽

Permeability Anisotropy ◽

Attenuation And Dispersion ◽

Maximum Permeability

The transversely isotropic poroelastic wave equation can be formulated to include the Biot and the squirt‐flow mechanisms to yield a new analytical solution in terms of the elements of the squirt‐flow tensor. The new model gives estimates of the vertical and the horizontal permeabilities, as well as other measurable rock and fluid properties. In particular, the model estimates phase velocity and attenuation of waves traveling at different angles of incidence with respect to the principal axis of anisotropy. The attenuation and dispersion of the fast quasi P‐wave and the quasi SV‐wave are related to the vertical and the horizontal permeabilities. Modeling suggests that the attenuation of both the quasi P‐wave and quasi SV‐wave depend on the direction of permeability. For frequencies from 500 to 4500 Hz, the quasi P‐wave attenuation will be of maximum permeability. To test the theory, interwell seismic waveforms, well logs, and hydraulic conductivity measurements (recorded in the fluvial Gypsy sandstone reservoir, Oklahoma) provide the material and fluid property parameters. For example, the analysis of petrophysical data suggests that the vertical permeability (1 md) is affected by the presence of mudstone and siltstone bodies, which are barriers to vertical fluid movement, and the horizontal permeability (1640 md) is controlled by cross‐bedded and planar‐laminated sandstones. The theoretical dispersion curves based on measurable rock and fluid properties, and the phase velocity curve obtained from seismic signatures, give the ingredients to evaluate the model. Theoretical predictions show the influence of the permeability anisotropy on the dispersion of seismic waves. These dispersion values derived from interwell seismic signatures are consistent with the theoretical model and with the direction of propagation of the seismic waves that travel parallel to the maximum permeability. This analysis with the new analytical solution is the first step toward a quantitative evaluation of the preferential directions of fluid flow in reservoir formation containing hydrocarbons. The results of the present work may lead to the development of algorithms to extract the permeability anisotropy from attenuation and dispersion data (derived from sonic logs and crosswell seismics) to map the fluid flow distribution in a reservoir.

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The Elastic Characterization of Composite Based on Ultrasonic Waves

10.1115/pvp2021-62015 ◽

2021 ◽

Author(s):

Y. H. Park ◽

J. Dana

Keyword(s):

Composite Materials ◽

Fatigue Failure ◽

Elastic Constants ◽

Material Properties ◽

Weight Ratio ◽

Transversely Isotropic ◽

Ultrasonic Waves ◽

Material Strength ◽

Isotropic Composite

Abstract Anisotropic composite materials have been extensively utilized in mechanical, automotive, aerospace and other engineering areas due to high strength-to-weight ratio, superb corrosion resistance, and exceptional thermal performance. As the use of composite materials increases, determination of material properties, mechanical analysis and failure of the structure become important for the design of composite structure. In particular, the fatigue failure is important to ensure that structures can survive in harsh environmental conditions. Despite technical advances, fatigue failure and the monitoring and prediction of component life remain major problems. In general, cyclic loadings cause the accumulation of micro-damage in the structure and material properties degrade as the number of loading cycles increases. Repeated subfailure loading cycles cause eventual fatigue failure as the material strength and stiffness fall below the applied stress level. Hence, the stiffness degradation measurement can be a good indication for damage evaluation. The elastic characterization of composite material using mechanical testing, however, is complex, destructive, and not all the elastic constants can be determined. In this work, an in-situ method to non-destructively determine the elastic constants will be studied based on the time of flight measurement of ultrasonic waves. This method will be validated on an isotropic metal sheet and a transversely isotropic composite plate.

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Stacking-velocity tomography for tilted orthorhombic media

Geophysics ◽

10.1190/geo2018-0300.1 ◽

2019 ◽

Vol 84 (3) ◽

pp. C171-C180 ◽

Cited By ~ 1

Author(s):

Qifan Liu ◽

Ilya Tsvankin

Keyword(s):

Parameter Estimation ◽

Subsurface Layer ◽

Synthetic Data ◽

Transversely Isotropic ◽

P Waves ◽

Additional Information ◽

Reflection Data ◽

Anisotropic Layers ◽

Zero Offset ◽

Velocity Tomography

Tilted orthorhombic (TOR) models are typical for dipping anisotropic layers, such as fractured shales, and can also be due to nonhydrostatic stress fields. Velocity analysis for TOR media, however, is complicated by the large number of independent parameters. Using multicomponent wide-azimuth reflection data, we develop stacking-velocity tomography to estimate the interval parameters of TOR media composed of homogeneous layers separated by plane dipping interfaces. The normal-moveout (NMO) ellipses, zero-offset traveltimes, and reflection time slopes of P-waves and split S-waves ([Formula: see text] and [Formula: see text]) are used to invert for the interval TOR parameters including the orientation of the symmetry planes. We show that the inversion can be facilitated by assuming that the reflector coincides with one of the symmetry planes, which is a common geologic constraint often employed for tilted transversely isotropic media. This constraint makes the inversion for a single TOR layer feasible even when the initial model is purely isotropic. If the dip plane is also aligned with one of the symmetry planes, we show that the inverse problem for [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-waves can be solved analytically. When only [Formula: see text]-wave data are available, parameter estimation requires combining NMO ellipses from a horizontal and dipping interface. Because of the increase in the number of independent measurements for layered TOR media, constraining the reflector orientation is required only for the subsurface layer. However, the inversion results generally deteriorate with depth because of error accumulation. Using tests on synthetic data, we demonstrate that additional information such as knowledge of the vertical velocities (which may be available from check shots or well logs) and the constraint on the reflector orientation can significantly improve the accuracy and stability of interval parameter estimation.

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Anisotropic geometrical-spreading correction for wide-azimuth P-wave reflections

Geophysics ◽

10.1190/1.2335615 ◽

2006 ◽

Vol 71 (5) ◽

pp. D161-D170 ◽

Cited By ~ 29

Author(s):

Xiaoxia Xu ◽

Ilya Tsvankin

Keyword(s):

Transversely Isotropic ◽

Azimuthal Anisotropy ◽

P Wave ◽

Fractured Reservoir ◽

Geometrical Spreading ◽

Spreading Factor ◽

Velocity Anisotropy ◽

Reflection Data ◽

Fitting Procedure ◽

Avo Attributes

Compensation for geometrical spreading along a raypath is one of the key steps in AVO (amplitude-variation-with-offset) analysis, in particular, for wide-azimuth surveys. Here, we propose an efficient methodology to correct long-spread, wide-azimuth reflection data for geometrical spreading in stratified azimuthally anisotropic media. The P-wave geometrical-spreading factor is expressed through the reflection traveltime described by a nonhyperbolic moveout equation that has the same form as in VTI (transversely isotropic with a vertical symmetry axis) media. The adapted VTI equation is parameterized by the normal-moveout (NMO) ellipse and the azimuthally varying anellipticity parameter [Formula: see text]. To estimate the moveout parameters, we apply a 3D nonhyperbolic semblance algorithm of Vasconcelos and Tsvankin that operates simultaneously with traces at all offsets andazimuths. The estimated moveout parameters are used as the input in our geometrical-spreading computation. Numerical tests for models composed of orthorhombic layers with strong, depth-varying velocity anisotropy confirm the high accuracy of our travetime-fitting procedure and, therefore, of the geometrical-spreading correction. Because our algorithm is based entirely on the kinematics of reflection arrivals, it can be incorporated readily into the processing flow of azimuthal AVO analysis. In combination with the nonhyperbolic moveout inversion, we apply our method to wide-azimuth P-wave data collected at the Weyburn field in Canada. The geometrical-spreading factor for the reflection from the top of the fractured reservoir is clearly influenced by azimuthal anisotropy in the overburden, which should cause distortions in the azimuthal AVO attributes. This case study confirms that the azimuthal variation of the geometrical-spreading factor often is comparable to or exceeds that of the reflection coefficient.

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