VELOCITY ANISOTROPY MEASUREMENTS IN WELLS

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 900-916 ◽  
Author(s):  
D. M. Vander Stoep
Keyword(s):  
Seismic Waves ◽  
Layered Medium ◽  
Sedimentary Rocks ◽  
Transversely Isotropic ◽  
Anisotropy Factor ◽  
Propagation Time ◽  
Reflection Seismology ◽  
Simple Description ◽  
Velocity Anisotropy ◽  
The Difference

Sedimentary rocks are generally anisotropic to the propagation of seismic waves. Anisotropy can be defined as the difference between propagation time predicted by the simple theory of Snell’s Law and observed propagation time between two points in a layered medium that lie on a line oblique to the layers. This difference can be explained by the more complicated theory of wave propagation in transversely isotropic materials. In the zone about the vertical that is of interest in reflection seismology, the effect of anisotropy usually can be described geometrically by an anisotropy factor A. This simple description is not valid for propagation directions making large angles with the normal to the layers. The anisotropy factor as well as the vertical velocity can vary with depth. A method is given for determining the factor A as a function of depth from a continuous velocity log and a range of oblique shots into a well phone. The method is applied to two field examples. In one of the examples, it is shown by data obtained from the larger shooting distances that the simple A factor description is inadequate for higher angles of propagation direction.

Numerical modeling of seismic waves with a 3-D, anisotropic scalar-wave equation

1991 ◽  
Vol 81 (3) ◽  
pp. 769-780
Author(s):  
Zhengxin Dong ◽  
George A. McMechan
Keyword(s):  
Wave Equation ◽  
Seismic Waves ◽  
Layered Medium ◽  
Grid Point ◽  
Scalar Wave ◽  
Scalar Wave Equation ◽  
Velocity Anisotropy ◽  
Isotropic Media ◽  
Isotropic Structure ◽  
Stress Orientations

Abstract By systematically defining the orientation and amount of velocity anisotropy at every point in a computational grid, and modifying the scalar-wave equation to accommodate directionally dependent velocity coefficients, scalar waves may be numerically synthesized in heterogeneous anisotropic 3-D structure by finite-differencing. The use of an intermediate, local, rotated coordinate system associated with each grid point allows the anisotropy orientation to conform spatially with 3-D structure, stress orientations, or any other correlate of the anisotropy. Both travel times and amplitudes in anisotropic media may differ significantly from those in the corresponding isotropic media. Under some conditions, the seismic response of an anisotropic flat-layered medium is nearly identical to, and may be confused with, that of a symmetrical isotropic structure. In general, these alternate interpretations can be evaluated by obtaining independent data from different recording configurations.

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.

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

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 309-318 ◽  
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.

scholarly journals Linear traveltime perturbation interpolation: a novel method to compute 3-D traveltimes

2015 ◽  
Vol 203 (1) ◽  
pp. 548-552 ◽  
Author(s):  
Jianzhong Zhang ◽  
Junjie Shi ◽  
Lin-Ping Song ◽  
Hua-wei Zhou
Keyword(s):  
Seismic Waves ◽  
Homogeneous Medium ◽  
Cell Boundary ◽  
Routine Method ◽  
Bilinear Interpolation ◽  
Linear Distribution ◽  
Heterogeneous Model ◽  
Computational Errors ◽  
Novel Method ◽  
The Difference

Abstract The linear traveltime interpolation has been a routine method to compute first arrivals of seismic waves and trace rays in complex media. The method assumes that traveltimes follow a linear distribution on each boundary of cells. The linearity assumption of traveltimes facilitates the numerical implementation but its violation may result in large computational errors. In this paper, we propose a new way to mitigate the potential shortcoming hidden in the linear traveltime interpolation. We use the vertex traveltimes in a calculated cell to introduce an equivalent homogeneous medium that is specific to the cell boundary from a source. Therefore, we can decompose the traveltime at a point on the cell boundary into two parts: (1) a reference traveltime propagating in the equivalent homogeneous medium and (2) a perturbation traveltime that is defined as the difference between the original and reference traveltimes. We now treat that the traveltime perturbation is linear along each boundary of cells instead of the traveltime. With the new assumption, we carry out the bilinear interpolation over traveltime perturbation to complete traveltime computation in a 3-D heterogeneous model. The numerical experiments show that the new method, the linear traveltime perturbation interpolation, is able to achieve much higher accuracy than that based on the linear traveltime interpolation.

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

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. D161-D170 ◽  
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.

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.

Resilience in Adolescence, Disability, and Gender

2021 ◽  
pp. 105413732110406
Author(s):  
Shambel Molla Bizuneh
Keyword(s):  
Female Students ◽  
Female Adolescent ◽  
Female Adolescents ◽  
Deaf Students ◽  
Simple Description ◽  
Adolescent Students ◽  
Significant Difference ◽  
The Difference ◽  
And Gender ◽  
Data Collections

Introduction: Disabled adolescents are facing the adversity of life like social expectations, academic, and economic demands. Objective: This described deaf and female adolescents’ resilience with their respective counterparts using the Connor–Davidson Resilience Scale (CD-RISC-25). The resilience of disabled and female adolescents was not adequately addressed in the study province, Dangila, Amhara-Ethiopia. Methods: The study was conducted on 160 adolescent (80 deaf [40 female] and 80 hearing [40 female]) students who were selected based on multistage sampling. Quantitative and qualitative data collections were made through the questionnaire as well as interview. The study used mean, standard deviation, independent t-test and ANOA, and simple description for data analysis. Result: The results revealed that hearing adolescent students’ average resilience score was significantly greater than deaf students. It was also shown that female adolescent students’ level of average resilience score was found significantly less than their counterparts. Analysis of variance revealed that there was a significant difference in resilience score among deaf female, deaf male, hearing female, and hearing male adolescent students in which deaf female adolescent students resilience score was the lowest. Conclusion: The difference in resilience between deaf and hearing students signified deaf students’ capability to cope with stressors and academic demands was less than their counterparts, and the resilience of deaf female students was found the lowest among the groups. This calls for health and psychological professional and families to provide adequate support for deaf and female adolescents to develop resilience.

The Effect of Total Precipitation of Various Periods to Flow Regimes in Mountainous Catchments in Japan : Considering the Geological Characteristics of Catchments

2021 ◽  
Author(s):  
Yuka Muto ◽  
Takeyoshi Chibana ◽  
Masafumi Yamada
Keyword(s):  
Sedimentary Rocks ◽  
Correlation Coefficients ◽  
Flow Regimes ◽  
Rate Of Change ◽  
Total Precipitation ◽  
Lower Type ◽  
Geological Characteristics ◽  
Mountainous Catchments ◽  
Geological Conditions ◽  
The Difference

<p>In order to conduct an appropriate management in each catchment, it is important to understand how the difference in geological conditions affect the relationship between precipitation and flow regimes.</p><p>Considering the differences in geological characteristics of catchments, this study aims 1)to clarify the period for calculating the total precipitation that is most influential to several levels of daily flow respectively and 2)to clarify the contribution of the change in the total precipitation of ‘the most influential period’ to the change in flow.</p><p>In this study, 63 mountainous catchments (dam catchments) within the Japanese Archipelago were selected as target areas. First, the 63 catchments were divided into 4 groups according to their geological characteristics. Second, from the observed data of daily flow lasting 26 years (from 1993 to 2018), 6 types of daily flow which represent flow of different scales within a year (1, 10, 25, 50, 75, 95 percentiles of daily flow within a year) were searched. In each geological classification, correlation coefficients between each 6 type of flow and total precipitation of various periods (from 2 days to 365 days) were calculated. Finally, for each geological classification and each type of flow, single regression analyses were conducted, setting the rate of change in flow amount as the objective variable, and the rate of change in total precipitation amount of the appropriate period as the explanatory variable.</p><p>As a result, in the analysis of correlation coefficients, significant differences among different geological classifications were seen for lower type of flows but not for higher type of flows. For catchments of volcanic rocks in the Quaternary period, total precipitation of 365 days before the flow occurrence had the highest correlation coefficient with lower type of flows. On the other hand, for catchments of sedimentary rocks in the Mesozoic or Paleozoic era, the most influential period was approximately 45 days, which was the shortest.</p><p>Also, increasing trends in flow (i.e. the rate of change in flow > 1.0) during the target period were seen regardless of the geological classification or the type of flow. However, from the simple regression analysis, the significant effect of the change in precipitation to the change in flow was only seen for annual maximum flow of catchments of sedimentary rocks from the Mesozoic or Paleozoic era. Except this specific geological characteristic and flow type, there is a possibility that other conditions of the catchments (e.g. change in land use) have larger effect to the change in flow compared to the change in precipitation.</p><p>In the analyses mentioned above, the effect of snowfall is not considered. Therefore, in the presentation, the difference between snow covered regions and others are compared in addition.</p>

Enrichment of chalcophile elements in seawater accompanying the end-Cretaceous impact event

2020 ◽  
Vol 132 (9-10) ◽  
pp. 2055-2066
Author(s):  
Teruyuki Maruoka ◽  
Yoshiro Nishio ◽  
Tetsu Kogiso ◽  
Katsuhiko Suzuki ◽  
Takahito Osawa ◽  
...  
Keyword(s):  
Organic Matter ◽  
Iron Oxides ◽  
Sedimentary Rocks ◽  
Reductive Dissolution ◽  
X Ray ◽  
Asteroid Impact ◽  
Chalcophile Elements ◽  
The Difference ◽  
Impact Heating ◽  
Fe Ions

Abstract Chalcophile elements are enriched in the Cretaceous–Paleogene (KPg) boundary clays from Stevns Klint, Denmark. As the concentrations of Cu, Ag, and Pb among several chalcophile elements such as Cu, Zn, Ga, As, Ag, and Pb are correlated with those of Ir, we suggest that these elements were supplied to the oceans by processes related to the end-Cretaceous asteroid impact. Synchrotron X-ray fluorescence images revealed that Cu and Ag exist as trace elements in pyrite grains or as 1–10-µm-sized discrete phases specifically enriched in Cu or Ag. The difference in carrier phases might depend on the materials that transported these elements to the seafloor. Based on their affinities with Cu, Ag, and Ir, iron oxides/hydroxides and organic matter were identified as the potential carrier phases that supplied these elements to the seafloor. Chalcophile elements adsorbed on iron oxides/hydroxides might have been released during reductive dissolution of iron oxides/hydroxides and incorporated into the pyrite produced simultaneously with the reductive dissolution of iron oxides/hydroxides. Both iron oxides/hydroxides and chalcophile elements were possibly released from the KPg target rocks (i.e., sedimentary rocks and/or basement crystalline rocks) by impact heating. Elements with a high affinity to organic matter would have been released upon its degradation and then converted into discrete minerals because of the deficiency in Fe ions. As such discrete minerals include the elements that form acid soluble sulfides such as Cu, Ag, and Pb, enrichment of these elements might have been induced by the intense acid rain just after the end-Cretaceous asteroid impact.

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