Viscoelastic amplitude variation with offset equations with account taken of jumps in attenuation angle

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. N17-N29 ◽  
Author(s):  
Shahpoor Moradi ◽  
Kristopher A. Innanen
Keyword(s):  
Seismic Waves ◽  
Steam Injection ◽  
Seismic Wave Propagation ◽  
Type I ◽  
Amplitude Variation ◽  
Volume Scattering ◽  
Amplitude Variation With Offset ◽  
S Waves ◽  
Fluid Saturation ◽  
Special Cases

Anelastic properties of reservoir rocks are important and sensitive indicators of fluid saturation and viscosity changes due (for instance) to steam injection. The description of seismic waves propagating through viscoelastic continua is quite complex, involving a range of unique homogeneous and inhomogeneous modes. This is true even in the relatively simple theoretical environment of amplitude variation with offset (AVO) analysis. For instance, a complete treatment of the problem of linearizing the solutions of the low-loss viscoelastic Zoeppritz equations to obtain an extended Aki-Richards equations (one that is in accord with the appropriate complex Snell’s law) is lacking in the literature. Also missing is a clear analytical path allowing such forms to be reconciled with more general volume scattering pictures of viscoelastic seismic wave propagation. Our analysis, which provides these two missing elements, leads to approximate reflection and transmission coefficients for the P- and type-I S-waves. These involve additional, complex terms alongside those of the standard isotropic-elastic Aki-Richards equations. The extra terms were shown to have a significant influence on reflection strengths, particularly when the degree of inhomogeneity was high. The particular AVO forms we evaluated were finally shown to be special cases of potentials for volume scattering from viscoelastic inclusions.

Modelling the effects of diffusive-viscous waves in a 3-D fluid-saturated media using two numerical approaches

2020 ◽  
Vol 224 (2) ◽  
pp. 1443-1463
Author(s):  
Victor Mensah ◽  
Arturo Hidalgo
Keyword(s):  
Seismic Wave ◽  
Fourth Order ◽  
Seismic Waves ◽  
Time Discretization ◽  
Seismic Wave Propagation ◽  
Second Order ◽  
Finite Volume Scheme ◽  
Fluid Saturation ◽  
Runge Kutta ◽  
Saturated Medium

SUMMARY The accurate numerical modelling of 3-D seismic wave propagation is essential in understanding details to seismic wavefields which are, observed on regional and global scales on the Earth’s surface. The diffusive-viscous wave (DVW) equation was proposed to study the connection between fluid saturation and frequency dependence of reflections and to characterize the attenuation property of the seismic wave in a fluid-saturated medium. The attenuation of DVW is primarily described by the active attenuation parameters (AAP) in the equation. It is, therefore, imperative to acquire these parameters and to additionally specify the characteristics of the DVW. In this paper, quality factor, Q is used to obtain the AAP, and they are compared to those of the visco-acoustic wave. We further derive the 3-D numerical schemes based on a second order accurate finite-volume scheme with a second order Runge–Kutta approximation for the time discretization and a fourth order accurate finite-difference scheme with a fourth order Runge–Kutta approximation for the time discretization. We then simulate the propagation of seismic waves in a 3-D fluid-saturated medium based on the derived schemes. The numerical results indicate stronger attenuation when compared to the visco-acoustic case.

scholarly journals Ground Water Induced Changes in Velocities of P and S Waves (Vp and Vs) Measured Using Accurately Controlled Seismic Source

2020 ◽  
Author(s):  
Rina Suzuki ◽  
Koshun Yamaoka ◽  
Shuhei Tsuji ◽  
Toshiki Watanabe
Keyword(s):  
Ground Water ◽  
Seismic Waves ◽  
Crack Density ◽  
Seismic Source ◽  
Initial Response ◽  
Vibration Source ◽  
Water Mixture ◽  
S Waves ◽  
Fluid Saturation ◽  
Induced Changes

Abstract We analyzed the temporal variation in the travel times of both the P and S waves (Vp and Vs) for 14 months at Toyohashi (central Japan) with a continuously operating vibration source that could produce both P and S waves efficiently. The seismic waves produced by the source, which is named ACROSS (accurately-controlled routinely-operated signal system), were recorded by three nearby seismic stations, and the travel time variation at each station was calculated using the transfer function calculated from the recorded data. We observed the seasonal variations in the Vp and Vs for all the stations—which can be interpreted using the change in the fluid saturation and crack density of subsurface rocks—are consistent with the variation in the ground water level. The short-term responses to rainfall are observed at the nearest station; the interpretation of the changes in crack density and saturation is inconsistent with the ground water observation partly due the initial response to rainfall. This can be interpreted as an air-water mixture within pores or cracks on a fine scale.

Predicting the seismic implications of salt anisotropy using numerical simulations of halite deformation

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1272-1280 ◽  
Author(s):  
Daniel G. Raymer ◽  
Andréa Tommasi ◽  
J‐Michael Kendall
Keyword(s):  
Elastic Constants ◽  
Seismic Waves ◽  
Seismic Anisotropy ◽  
Numerical Models ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
The Past ◽  
Numerical Studies ◽  
Polycrystalline Aggregates ◽  
Ray Paths

In the past, the potential for seismic anisotropy in salt structures and its effect on their seismic imaging has received little attention. We consider the plausibility of salt anisotropy through linked numerical studies of salt deformation and its seismic consequences. Numerical models are used to predict lattice preferred orientations (LPOs) in halite polycrystalline aggregates subjected to axial extension and simple shear. The elastic constants for the deformed polycrystalline aggregate are then calculated. Simple models representing a salt sill and the stem of a diapir are created using these elastic constants. Ray tracing is used to investigate the effects of halite LPO on the propagation of seismic waves. The results suggest that salt anisotropy can cause significant traveltime effects and could lead to significant errors in seismic interpretation in salt environments if this anisotropy is ignored. We also investigate potential amplitude variation with offset and azimuth (AVOA) for the reflection from the top and bottom of an anisotropic salt sill. Ray paths with a shear‐wave leg within the salt display strong AVOA effects with a clear four‐fold symmetry.

Effects of transverse isotropy on P‐wave AVO for gas sands

Geophysics ◽  
1993 ◽  
Vol 58 (6) ◽  
pp. 883-888 ◽  
Author(s):  
Ki Young Kim ◽  
Keith H. Wrolstad ◽  
Fred Aminzadeh
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Velocity Anisotropy ◽  
Special Cases ◽  
Class 1 ◽  
Zero Offset ◽  
Ti Media

Velocity anisotropy should be taken into account when analyzing the amplitude variation with offset (AVO) response of gas sands encased in shales. The anisotropic effects on the AVO of gas sands in transversely isotropic (TI) media are reviewed. Reflection coefficients in TI media are computed using a planewave formula based on ray theory. We present results of modeling special cases of exploration interest having positive reflectivity, near‐zero reflectivity, and negative reflectivity. The AVO reflectivity in anisotropic media can be decomposed into two parts; one for isotropy and the other for anisotropy. Zero‐offset reflectivity and Poisson’s ratio contrast are the most significant parameters for the isotropic component while the δ difference (Δδ) between shale and gas sand is the most important factor for the anisotropic component. For typical values of Tl anisotropy in shale (positive δ and ε), both δ difference (Δδ) and ε difference (Δε) amplify AVO effects. For small angles of incidence, Δδ plays an important role in AVO while Δε dominates for large angles of incidence. For typical values of δ and ε, the effects of anisotropy in shale are: (1) a more rapid increase in AVO for Class 3 and Class 2 gas sands, (2) a more rapid decrease in AVO for Class 1 gas sands, and (3) a shift in the offset of polarity reversal for some Class 1 and Class 2 gas sands.

scholarly journals Ground water-induced changes in velocities of P and S waves (Vp and Vs) measured using an accurately controlled seismic source

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Rina Suzuki ◽  
Koshun Yamaoka ◽  
Shuhei Tsuji ◽  
Toshiki Watanabe
Keyword(s):  
Ground Water ◽  
Seismic Waves ◽  
Crack Density ◽  
Seismic Source ◽  
Initial Response ◽  
Temporal Variations ◽  
Vibration Source ◽  
Water Mixture ◽  
S Waves ◽  
Fluid Saturation

AbstractWe analyze temporal variations in the travel times of both P and S waves (Vp and Vs) for 14 months at Toyohashi (central Japan) with a continuously operating vibration source that could efficiently produce both P and S waves. Seismic waves produced by the source, which is called the accurately controlled routinely operated signal system (ACROSS), are recorded by three nearby seismic stations, and the travel time variation at each station is estimated using the transfer function calculated from the recorded data. Long-term variations in Vp and Vs are observed and can be interpreted by the change in fluid saturation and crack density of the subsurface rocks. The variation in fluid saturation and crack density are consistent with that in the groundwater level, which is measured at the station nearest to the ACROSS. Short-term responses to rainfalls are observed at the station nearest to the ACROSS system; the interpretation of the changes in crack density and saturation is inconsistent with the ground water observation, partly owing to the initial response to rainfall. This can be interpreted as an air–water mixture within pores or cracks on a fine scale.

The O’Doherty‐Anstey formula and localization of seismic waves

Geophysics ◽  
1993 ◽  
Vol 58 (5) ◽  
pp. 736-740 ◽  
Author(s):  
Serguei A. Shapiro ◽  
Holger Zien
Keyword(s):  
Multiple Scattering ◽  
Seismic Waves ◽  
Seismic Attenuation ◽  
Adequate Description ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Seismic Profiling ◽  
Seismic Amplitude ◽  
Vertical Seismic Profiling ◽  
Vsp Data

Angle (or offset) dependent effects of scattering in finely layered media can be observed and analyzed or must be compensated for in vertical seismic profiling data (VSP‐ data), crosshole observations, or seismic amplitude variation with offset (AVO) measurements. Moreover, the adequate description of multiple scattering is important for the study of seismic attenuation in sediments and for the design of inversion procedures.

Perturbation analysis of an explicit wavefield separation scheme for P‐ and S‐waves

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1972-1982 ◽  
Author(s):  
Remco Muijs ◽  
Klaus Holliger ◽  
Johan O. A. Robertsson
Keyword(s):  
Explicit Calculation ◽  
Angle Of Incidence ◽  
Separation Scheme ◽  
S Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
S Waves ◽  
Wave Separation ◽  
Small Phase ◽  
Wavefield Decomposition

Dense spatial recording patterns of three‐component (3C) receivers allow for direct wavefield decomposition through explicit calculation of divergence and curl of the recorded elastic wavefield. Since this approach is based upon the observation of small phase shifts, it requires highly accurate deployment of the receiver configurations. To study the feasibility of a recently proposed P/S‐wave separation scheme, we systematically assess the effects of position and orientation errors of one or several geophones within the recording pattern on technique performance. We find that realistic deployment errors can significantly affect estimates of the divergence and curl of particle velocity. The errors induced by mispositioned or misoriented geophones differ for each of the geophones that make up a pattern. Moreover, the inaccuracies vary with the angle of incidence, potentially affecting analysis procedures applied to the data at a later stage, such as amplitude variation with offset (AVO). Based on a relative L1‐criterion, the position of each receiver needs to be accurate within 10% of the length of the sides of the configuration to obtain meaningful divergence and curl estimates. Furthermore, the output is particularly sensitive to misorientations of geophones, requiring that the orientations of all geophones be accurate within 2°. These observations point to significant difficulties when applying this technique. To alleviate this problem, we present an approach to detect and compensate for such deployment‐related inaccuracies prior to explicit P/S‐wave separation. This strategy is based on a pyramid‐shaped receiver configuration and relies on minimizing the differences between the divergence and curl estimates calculated over the pyramid and each of the four subtetrahedra that comprise the pyramid.

Characterization of naturally fractured Arbuckle Group in the Wellington Field, Kansas, using S-wave amplitude variation with offset

2017 ◽  
Vol 5 (1) ◽  
pp. T49-T63 ◽  
Author(s):  
Menal Gupta ◽  
Kyle Spikes ◽  
Bob Hardage
Keyword(s):  
Wave Amplitude ◽  
Anisotropy Parameter ◽  
P Wave ◽  
Fracture Density ◽  
S Wave ◽  
Amplitude Variation ◽  
Fracture Characterization ◽  
Amplitude Variation With Offset ◽  
S Waves ◽  
Arbuckle Group

S-wave amplitude variation with offset (AVO) analysis is sensitive to the presence of fractures and can provide a high-resolution seismic-based fracture characterization as compared with traditionally used traveltime-based methods. To determine viable attributes for estimation of properties such as spatial density and fluid fill of fractures, S-wave AVO modeling and analysis is carried out in the Wellington Field, Kansas, where 9C-2D seismic data have been acquired. Analysis is performed on the Ordovician fractured-carbonate interval called the Arbuckle Group, which is being considered for [Formula: see text] sequestration. AVO modeling of the Arbuckle interval indicates that differences in AVO intercepts of different S-wave polarizations can estimate S-wave anisotropy parameter [Formula: see text], which gives an estimate of fracture density. In addition, modeling suggests that AVO gradients of [Formula: see text] and [Formula: see text] waves can be used to derive a seismic attribute to discriminate fluid fill in fractures, provided good-quality S-wave gathers are available. The intercept anisotropy (IA) attribute obtained from AVO intercepts of S-waves provides fracture density estimates within the Arbuckle Group. These estimates are consistent with the field-wide, low-frequency observations from seismic velocities and spatially limited, high-frequency estimates obtained from drill cores and sonic and borehole-image logs. The IA attribute highlights possible high-permeability zones in the Upper and Lower Arbuckle suitable for [Formula: see text] injection. The Middle Arbuckle indicates low fracture density, potentially acting as a baffle to vertical flow and providing a seal for the Lower Arbuckle. The gradient anisotropy attribute obtained from the AVO gradient of S-waves suggests that most fractures in the Arbuckle are brine saturated. This attribute has a potential application in monitoring the movement of a [Formula: see text] plume in the Arbuckle Group when time-lapse data become available. These results demonstrate that S-wave AVO attributes can supplement the P-wave derived subsurface properties and significantly reduce uncertainties in subsurface fracture characterization.

One Size Fits All?

Methodology ◽  
2012 ◽  
Vol 8 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Manuel C. Voelkle ◽  
Patrick E. McKnight
Keyword(s):  
Repeated Measures ◽  
Structural Equation ◽  
Type I Error ◽  
Equation Modeling ◽  
Type I ◽  
Finite Sample ◽  
Traditional Methods ◽  
Repeated Measures Anova ◽  
Special Cases ◽  
Latent Curve

The use of latent curve models (LCMs) has increased almost exponentially during the last decade. Oftentimes, researchers regard LCM as a “new” method to analyze change with little attention paid to the fact that the technique was originally introduced as an “alternative to standard repeated measures ANOVA and first-order auto-regressive methods” (Meredith & Tisak, 1990, p. 107). In the first part of the paper, this close relationship is reviewed, and it is demonstrated how “traditional” methods, such as the repeated measures ANOVA, and MANOVA, can be formulated as LCMs. Given that latent curve modeling is essentially a large-sample technique, compared to “traditional” finite-sample approaches, the second part of the paper addresses the question to what degree the more flexible LCMs can actually replace some of the older tests by means of a Monte-Carlo simulation. In addition, a structural equation modeling alternative to Mauchly’s (1940) test of sphericity is explored. Although “traditional” methods may be expressed as special cases of more general LCMs, we found the equivalence holds only asymptotically. For practical purposes, however, no approach always outperformed the other alternatives in terms of power and type I error, so the best method to be used depends on the situation. We provide detailed recommendations of when to use which method.

Fracture mapping using seismic amplitude variation with offset and azimuth analysis at the Weyburn CO2 storage site

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. B295-B306 ◽  
Author(s):  
Alexander Duxbury ◽  
Don White ◽  
Claire Samson ◽  
Stephen A. Hall ◽  
James Wookey ◽  
...  
Keyword(s):  
Cross Sections ◽  
Co2 Storage ◽  
Horizontal Stress ◽  
Storage Site ◽  
Fracture Zones ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Seal Integrity ◽  
Cap Rock ◽  
Weyburn Field

Cap rock integrity is an essential characteristic of any reservoir to be used for long-term [Formula: see text] storage. Seismic AVOA (amplitude variation with offset and azimuth) techniques have been applied to map HTI anisotropy near the cap rock of the Weyburn field in southeast Saskatchewan, Canada, with the purpose of identifying potential fracture zones that may compromise seal integrity. This analysis, supported by modeling, observes the top of the regional seal (Watrous Formation) to have low levels of HTI anisotropy, whereas the reservoir cap rock (composite Midale Evaporite and Ratcliffe Beds) contains isolated areas of high intensity anisotropy, which may be fracture-related. Properties of the fracture fill and hydraulic conductivity within the inferred fracture zones are not constrained using this technique. The predominant orientations of the observed anisotropy are parallel and normal to the direction of maximum horizontal stress (northeast–southwest) and agree closely with previous fracture studies on core samples from the reservoir. Anisotropy anomalies are observed to correlate spatially with salt dissolution structures in the cap rock and overlying horizons as interpreted from 3D seismic cross sections.

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