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

Geophysics ◽  
1982 ◽  
Vol 47 (3) ◽  
pp. 323-335 ◽  
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.

scholarly journals Approaches for investigation of oriented cracks of reservoirs using multicomponent VSP

2021 ◽  
Vol 2092 (1) ◽  
pp. 012025
Author(s):  
S B Gorshkalev ◽  
W V Karsten ◽  
D M Vishnevsky ◽  
S V Yaskevich
Keyword(s):  
Elastic Constants ◽  
Seismic Waves ◽  
Arrival Time ◽  
Transversely Isotropic ◽  
Fractured Reservoir ◽  
Data Inversion ◽  
Full Wave ◽  
Displacement Vectors ◽  
Vsp Data ◽  
Anisotropic Layers

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.

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

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. C113-C126 ◽  
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.

ESTIMATION OF AERODYNAMIC FORCES AND MOMENTS DERIVATIVES WITH RESPECT TO THE ANGULAR VELOCITY COMPONENTS OF THE AIRCRAFT MODEL IN A WIDE RANGE OF ANGLES OF ATTACK

2018 ◽  
Vol 49 (1) ◽  
pp. 43-64
Author(s):  
Mikhail Alekseyevich Golovkin ◽  
Andrey Aleksandrovich Efremov ◽  
Miroslav Sergeevich Makhnev
Keyword(s):  
Angular Velocity ◽  
Aerodynamic Forces ◽  
Aircraft Model ◽  
Wide Range

The Elastic Characterization of Composite Based on Ultrasonic Waves

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.

Stacking-velocity tomography for tilted orthorhombic media

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. C171-C180 ◽  
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.

Normal moveout from dipping reflectors in anisotropic media

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 268-284 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Weak Anisotropy ◽  
Anisotropic Models ◽  
Transversely Isotropic Media ◽  
Wide Range ◽  
Isotropic Media ◽  
The Difference

Description of reflection moveout from dipping interfaces is important in developing seismic processing methods for anisotropic media, as well as in the inversion of reflection data. Here, I present a concise analytic expression for normal‐moveout (NMO) velocities valid for a wide range of homogeneous anisotropic models including transverse isotropy with a tilted in‐plane symmetry axis and symmetry planes in orthorhombic media. In transversely isotropic media, NMO velocity for quasi‐P‐waves may deviate substantially from the isotropic cosine‐of‐dip dependence used in conventional constant‐velocity dip‐moveout (DMO) algorithms. However, numerical studies of NMO velocities have revealed no apparent correlation between the conventional measures of anisotropy and errors in the cosine‐of‐dip DMO correction (“DMO errors”). The analytic treatment developed here shows that for transverse isotropy with a vertical symmetry axis, the magnitude of DMO errors is dependent primarily on the difference between Thomsen parameters ε and δ. For the most common case, ε − δ > 0, the cosine‐of‐dip–corrected moveout velocity remains significantly larger than the moveout velocity for a horizontal reflector. DMO errors at a dip of 45 degrees may exceed 20–25 percent, even for weak anisotropy. By comparing analytically derived NMO velocities with moveout velocities calculated on finite spreads, I analyze anisotropy‐induced deviations from hyperbolic moveout for dipping reflectors. For transversely isotropic media with a vertical velocity gradient and typical (positive) values of the difference ε − δ, inhomogeneity tends to reduce (sometimes significantly) the influence of anisotropy on the dip dependence of moveout velocity.

Estimating azimuth and slowness from three-component and array stations

1990 ◽  
Vol 80 (6B) ◽  
pp. 1987-1998 ◽  
Author(s):  
Anne Suteau-Henson
Keyword(s):  
Arrival Time ◽  
Dominant Frequency ◽  
Polarization Analysis ◽  
Vertical Array ◽  
Regional Network ◽  
Array Measurements ◽  
Short Period ◽  
Wide Range ◽  
P Type ◽  
Teleseismic Events

Abstract The capabilities of three-component (3-C) and array stations for estimating azimuth and slowness are compared for short-period P-type phases recorded at the NORESS array. For vertical array data, azimuth and slowness estimates are obtained from broadband frequency-wavenumber (f-k) analysis. For 3-C data, polarization analysis is performed. The data processing is automated, using arrival time and dominant frequency information from the NORESS Bulletin. Independent determinations of azimuth and/or slowness, obtained from locations in the NEIS or regional network bulletins, are used as reference estimates. Over 100 events are analyzed, both teleseismic and regional. They were selected from a variety of distances and azimuths, and cover a wide range of signal-to-noise ratios (SNR). The capability of 3-C stations for azimuth and slowness estimation critically depends on SNR. For SNR below a threshold of ∼2, the scatter in the estimates is very large for both parameters, and the slowness of teleseismic events tends to be overestimated. Also, the results are site-dependent within the NORESS array. The array measurements obtained with the broadband f-k method are not significantly affected by noise at the levels of SNR considered. For events with sufficient SNR, both methods compare well, and only a slightly better performance is observed with the f-k method.

scholarly journals The magnetorotational instability prefers three dimensions

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190622
Author(s):  
Jeffrey S. Oishi ◽  
Geoffrey M. Vasil ◽  
Morgan Baxter ◽  
Andrew Swan ◽  
Keaton J. Burns ◽  
...  
Keyword(s):  
Shear Rate ◽  
Angular Velocity ◽  
Laboratory Experiments ◽  
Three Dimensional ◽  
Linear Instability ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Magnetorotational Instability ◽  
Dynamo Action ◽  
Wide Range

The magnetorotational instability (MRI) occurs when a weak magnetic field destabilizes a rotating, electrically conducting fluid with inwardly increasing angular velocity. The MRI is essential to astrophysical disc theory where the shear is typically Keplerian. Internal shear layers in stars may also be MRI-unstable, and they take a wide range of profiles, including near-critical. We show that the fastest growing modes of an ideal magnetofluid are three-dimensional provided the shear rate, S , is near the two-dimensional onset value, S c . For a Keplerian shear, three-dimensional modes are unstable above S  ≈ 0.10 S c , and dominate the two-dimensional modes until S  ≈ 2.05 S c . These three-dimensional modes dominate for shear profiles relevant to stars and at magnetic Prandtl numbers relevant to liquid-metal laboratory experiments. Significant numbers of rapidly growing three-dimensional modes remainy well past 2.05 S c . These finding are significant in three ways. First, weakly nonlinear theory suggests that the MRI saturates by pushing the shear rate to its critical value. This can happen for systems, such as stars and laboratory experiments, that can rearrange their angular velocity profiles. Second, the non-normal character and large transient growth of MRI modes should be important whenever three-dimensionality exists. Finally, three-dimensional growth suggests direct dynamo action driven from the linear instability.

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