Seismic anisotropy in sedimentary rocks, part 1: A single‐plug laboratory method

Geophysics ◽  
2002 ◽  
Vol 67 (5) ◽  
pp. 1415-1422 ◽  
Author(s):  
Zhijing Wang
Keyword(s):  
Seismic Anisotropy ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Cylindrical Sample ◽  
Laboratory Method ◽  
Piezoelectric Transducers ◽  
Low Permeability ◽  
Seismic Velocities ◽  
Fluid Displacement ◽  
Fluid Saturation

A single‐plug method for measuring seismic velocities and transverse isotropy in rocks has been rigorously validated and laboratory tested. The method requires only one sample to measure the velocities needed to derive the five independent elastic constants for transversely isotropic materials. In this method, piezoelectric transducers are fitted to the top, bottom, and sides of the cylindrical sample. Laboratory velocity and anisotropy can be measured as functions of pressure, temperature, fluid saturation, and fluid displacement. Because this method uses a horizontal core plug that has much higher permeability than a vertical core plug, it is especially suitable for low‐permeability shale measurements. It reduces the sample preparation and velocity measurement time by more than two‐thirds.

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.

Wrinkling of a Fiber-Reinforced Membrane

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
E. Shmoylova ◽  
A. Dorfmann
Keyword(s):  
Boundary Conditions ◽  
Energy Function ◽  
Mechanical Response ◽  
Transverse Isotropy ◽  
Base Material ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Incompressible Material ◽  
Fiber Reinforced ◽  
Relaxed Energy

In this paper we investigate the response of fiber-reinforced cylindrical membranes subject to axisymmetric deformations. The membrane is considered as an incompressible material, and the phenomenon of wrinkling is taken into account by means of the relaxed energy function. Two cases are considered: transversely isotropic membranes, characterized by one family of fibers oriented in one direction, and orthotropic membranes, characterized by two family of fibers oriented in orthogonal directions. The strain-energy function is considered as the sum of two terms: The first term is associated with the isotropic properties of the base material, and the second term is used to introduce transverse isotropy or orthotropy in the mechanical response. We determine the mechanical response of the membrane as a function of fiber orientations for given boundary conditions. The objective is to find possible fiber orientations that make the membrane as stiff as possible for the given boundary conditions. Specifically, it is shown that for transversely isotropic membranes a unique fiber orientation exists, which does not affect the mechanical response, i.e., the overall behavior is identical to a nonreinforced membrane.

Transverse isotropy of the upper mantle in the vicinity of Pacific fracture zones

1969 ◽  
Vol 59 (1) ◽  
pp. 59-72
Author(s):  
Robert S. Crosson ◽  
Nikolas I. Christensen
Keyword(s):  
Upper Mantle ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Seismic Wave Propagation ◽  
Fracture Zones ◽  
Mantle Material ◽  
Transversely Isotropic Media ◽  
Horizontal Symmetry ◽  
Isotropic Media

Abstract Several recent investigations suggest that portions of the Earth's upper mantle behave anisotropically to seismic wave propagation. Since several types of anisotropy can produce azimuthal variations in Pn velocities, it is of particular geophysical interest to provide a framework for the recognition of the form or forms of anisotropy most likely to be manifest in the upper mantle. In this paper upper mantle material is assumed to possess the elastic properties of transversely isotropic media. Equations are presented which relate azimuthal variations in Pn velocities to the direction and angle of tilt of the symmetry axis of a transversely isotropic upper mantle. It is shown that the velocity data of Raitt and Shor taken near the Mendocino and Molokai fracture zones can be adequately explained by the assumption of transverse isotropy with a nearly horizontal symmetry axis.

Reflection moveout approximations for P-waves in a moderately anisotropic homogeneous tilted transverse isotropy layer

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. C175-C185 ◽  
Author(s):  
Ivan Pšenčík ◽  
Véronique Farra
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Weak Anisotropy ◽  
P Waves ◽  
3D Space ◽  
Axis Of Symmetry ◽  
Relative Errors ◽  
Symmetry Tests ◽  
Ti Media

We have developed approximate nonhyperbolic P-wave moveout formulas applicable to weakly or moderately anisotropic media of arbitrary anisotropy symmetry and orientation. Instead of the commonly used Taylor expansion of the square of the reflection traveltime in terms of the square of the offset, we expand the square of the reflection traveltime in terms of weak-anisotropy (WA) parameters. No acoustic approximation is used. We specify the formulas designed for anisotropy of arbitrary symmetry for the transversely isotropic (TI) media with the axis of symmetry oriented arbitrarily in the 3D space. Resulting formulas depend on three P-wave WA parameters specifying the TI symmetry and two angles specifying the orientation of the axis of symmetry. Tests of the accuracy of the more accurate of the approximate formulas indicate that maximum relative errors do not exceed 0.3% or 2.5% for weak or moderate P-wave anisotropy, respectively.

scholarly journals Correlation of core and downhole seismic velocities in high-pressure metamorphic rocks: A case study for the COSC-1 borehole, Sweden

2020 ◽  
Author(s):  
Felix Kästner ◽  
Simona Pierdominici ◽  
Judith Elger ◽  
Christian Berndt ◽  
Alba Zappone ◽  
...  
Keyword(s):  
Seismic Anisotropy ◽  
Seismic Velocity ◽  
Metamorphic Rocks ◽  
Seismic Velocities ◽  
Mafic Rocks ◽  
Seismic Properties ◽  
The Core ◽  
Nappe Complex ◽  
Thrust Zone ◽  
Mountain Belts

<p>Deeply rooted thrust zones are key features of tectonic processes and the evolution of mountain belts. Exhumed and deeply-eroded orogens like the Scandinavian Caledonides allow to study such systems from the surface. Previous seismic investigations of the Seve Nappe Complex have shown indications for a strong but discontinuous reflectivity of this thrust zone, which is only poorly understood. The correlation of seismic properties measured on borehole cores with surface seismic data can help to constrain the origin of this reflectivity. In this study, we compare seismic velocities measured on cores to in situ velocities measured in the borehole. The core and downhole velocities deviate by up to 2 km/s. However, velocities of mafic rocks are generally in close agreement. Seismic anisotropy increases from about 5 to 26 % at depth, indicating a transition from gneissic to schistose foliation. Differences in the core and downhole velocities are most likely the result of microcracks due to depressurization of the cores. Thus, seismic velocity can help to identify mafic rocks on different scales whereas the velocity signature of other lithologies is obscured in core-derived velocities. Metamorphic foliation on the other hand has a clear expression in seismic anisotropy. To further constrain the effects of mineral composition, microstructure and deformation on the measured seismic anisotropy, we conducted additional microscopic investigations on selected core samples. These analyses using electron-based microscopy and X-ray powder diffractometry indicate that the anisotropy is strongest for mica schists followed by amphibole-rich units. This also emphasizes that seismic velocity and anisotropy are of complementary importance to better distinguish the present lithological units. Our results will aid in the evaluation of core-derived seismic properties of high-grade metamorphic rocks at the COSC-1 borehole and elsewhere.</p>

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.

Results of the downhole microseismic monitoring at a pilot hydraulic fracturing site in Poland — Part 1: Event location and stimulation performance

2018 ◽  
Vol 6 (3) ◽  
pp. SH39-SH48 ◽  
Author(s):  
Wojciech Gajek ◽  
Jacek Trojanowski ◽  
Michał Malinowski ◽  
Marek Jarosiński ◽  
Marko Riedel
Keyword(s):  
Hydraulic Fracturing ◽  
Seismic Anisotropy ◽  
Transverse Isotropy ◽  
Velocity Model ◽  
Microseismic Monitoring ◽  
Baltic Basin ◽  
Hydraulic Stimulation ◽  
Lower Paleozoic ◽  
Event Location ◽  
Microseismic Events

A precise velocity model is necessary to obtain reliable locations of microseismic events, which provide information about the effectiveness of the hydraulic stimulation. Seismic anisotropy plays an important role in microseismic event location by imposing the dependency between wave velocities and its propagation direction. Building an anisotropic velocity model that accounts for that effect allows for more accurate location of microseismic events. We have used downhole microseismic records from a pilot hydraulic fracturing experiment in Lower-Paleozoic shale gas play in the Baltic Basin, Northern Poland, to obtain accurate microseismic events locations. We have developed a workflow for a vertical transverse isotropy velocity model construction when facing a challenging absence of horizontally polarized S-waves in perforation shot data, which carry information about Thomsen’s [Formula: see text] parameter and provide valuable constraints for locating microseismic events. We extract effective [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text] for each layer from the P- and SV-wave arrivals of perforation shots, whereas the unresolved [Formula: see text] is retrieved afterward from the SH-SV-wave delay time of selected microseismic events. An inverted velocity model provides more reliable location of microseismic events, which then becomes an essential input for evaluating the hydraulic stimulation job effectiveness in the geomechanical context. We evaluate the influence of the preexisting fracture sets and obliquity between the borehole trajectory and principal horizontal stress direction on the hydraulic treatment performance. The fracturing fluid migrates to previously fractured zones, while the growth of the microseismic volume in consecutive stages is caused by increased penetration of the above-lying lithologic formations.

scholarly journals Topology optimization for transversely isotropic materials with high-cycle fatigue as a constraint

2020 ◽  
Vol 63 (1) ◽  
pp. 161-172
Author(s):  
Shyam Suresh ◽  
Stefan B. Lindström ◽  
Carl-Johan Thore ◽  
Anders Klarbring
Keyword(s):  
Topology Optimization ◽  
Fatigue Damage ◽  
High Cycle Fatigue ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Back Stress ◽  
Optimization Method ◽  
Fatigue Properties ◽  
Cycle Fatigue ◽  
Time Model

AbstractWe propose a topology optimization method for design of transversely isotropic elastic continua subject to high-cycle fatigue. The method is applicable to design of additive manufactured components, where transverse isotropy is often manifested in the form of a lower Young’s modulus but a higher fatigue strength in the build direction. The fatigue constraint is based on a continuous-time model in the form of ordinary differential equations governing the time evolution of fatigue damage at each point in the design domain. Such evolution occurs when the stress state lies outside a so-called endurance surface that moves in stress space depending on the current stress and a back-stress tensor. Pointwise bounds on the fatigue damage are approximated using a smooth aggregation function, and the fatigue sensitivities are determined by the adjoint method. Several problems where the objective is to minimize mass are solved numerically. The problems involve non-periodic proportional and non-proportional load histories. Two alloy steels, AISI-SAE 4340 and 34CrMo6, are treated and the respective as well as the combined impact of transversely isotropic elastic and fatigue properties on the design are compared.

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