Poroelastic model to relate seismic wave attenuation and dispersion to permeability anisotropy

Geophysics ◽  
2000 ◽  
Vol 65 (1) ◽  
pp. 202-210 ◽  
Author(s):  
Jorge O. Parra
Keyword(s):  
Seismic Waves ◽  
Velocity Dispersion ◽  
Wave Attenuation ◽  
Test Site ◽  
Compressional Wave ◽  
P Wave ◽  
Low Velocity ◽  
Stiffness Constant ◽  
Principal Axes ◽  
Permeability Anisotropy

A transversely isotropic model with a horizontal axis of symmetry, based on the Biot and squirt‐flow mechanisms, predicts seismic waves in poroelastic media. The model estimates velocity dispersion and attenuation of waves propagating in the frequency range of crosswell and high‐resolution reverse vertical seismic profiling (VSP) (250–1250 Hz) for vertical permeability values much greater than horizontal permeability parameters. The model assumes the principal axes of the stiffness constant tensor are aligned with the axes of the permeability and squirt‐flow tensors. In addition, the unified Biot and squirt‐flow mechanism (BISQ) model is adapted to simulate cracks in permeable media. Under these conditions, the model simulations demonstrate that the preferential direction of fluid flow in a reservoir containing fluid‐filled cracks can be determined by analyzing the phase velocity and attenuation of seismic waves propagating at different azimuth and incident angles. As a result, the fast compressional wave can be related to permeability anisotropy in a reservoir. The model results demonstrate that for a fast quasi-P-wave propagating perpendicular to fluid‐filled cracks, the attenuation is greater than when the wave propagates parallel to the plane of the crack. Theoretical predictions and velocity dispersion of inter‐well seismic waves in the Kankakee Limestone Formation at the Buckhorn test site (Illinois) demonstrate that the permeable rock matrix surrounding a low‐velocity heterogeneity contains vertical cracks.

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.

Simulation of thermoelastic waves based on the Lord-Shulman theory

Geophysics ◽  
2021 ◽  
Vol 86 (3) ◽  
pp. T155-T164
Author(s):  
Wanting Hou ◽  
Li-Yun Fu ◽  
José M. Carcione ◽  
Zhiwei Wang ◽  
Jia Wei
Keyword(s):  
Thermal Conductivity ◽  
Expansion Coefficient ◽  
Velocity Dispersion ◽  
Wave Attenuation ◽  
Splitting Method ◽  
Grazing Incidence ◽  
P Wave ◽  
Staggered Grid ◽  
Thermal Mode ◽  
P Waves

Thermoelasticity is important in seismic propagation due to the effects related to wave attenuation and velocity dispersion. We have applied a novel finite-difference (FD) solver of the Lord-Shulman thermoelasticity equations to compute synthetic seismograms that include the effects of the thermal properties (expansion coefficient, thermal conductivity, and specific heat) compared with the classic forward-modeling codes. We use a time splitting method because the presence of a slow quasistatic mode (the thermal mode) makes the differential equations stiff and unstable for explicit time-stepping methods. The spatial derivatives are computed with a rotated staggered-grid FD method, and an unsplit convolutional perfectly matched layer is used to absorb the waves at the boundaries, with an optimal performance at the grazing incidence. The stability condition of the modeling algorithm is examined. The numerical experiments illustrate the effects of the thermoelasticity properties on the attenuation of the fast P-wave (or E-wave) and the slow thermal P-wave (or T-wave). These propagation modes have characteristics similar to the fast and slow P-waves of poroelasticity, respectively. The thermal expansion coefficient has a significant effect on the velocity dispersion and attenuation of the elastic waves, and the thermal conductivity affects the relaxation time of the thermal diffusion process, with the T mode becoming wave-like at high thermal conductivities and high frequencies.

P-wave velocity profile at very shallow depths in sand dunes

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. U129-U137
Author(s):  
Sherif M. Hanafy ◽  
Ammar El-Husseiny ◽  
Mohammed Benaafi ◽  
Abdullatif Al-Shuhail ◽  
Jack Dvorkin
Keyword(s):  
Velocity Profile ◽  
Wave Velocity ◽  
Sand Dunes ◽  
Seismic Signal ◽  
Compressional Wave ◽  
Dominant Frequency ◽  
P Wave ◽  
Beach Sand ◽  
Low Velocity ◽  
Measured Velocity

We have addressed the problem of measuring the compressional wave velocity at a very shallow depth in unconsolidated dune sand. Because the overburden stress is very small at shallow depths, the respective velocity is small and the seismic signal is weak. This is why such data are scarce, in the lab and in the field. Our approach is to stage a high-resolution seismic experiment with a dense geophone line with spacing varying between 10 and 25 cm, allowing us to produce a velocity-depth relation in the upper 1 m interval. These results are combined with another survey in which the geophone spacing is 2 m and the dominant frequency is an order of magnitude lower than in the first survey. The latter results give us the velocity profile in the deeper interval between 1 and 7 m, down to the base of the dune. The velocity rapidly increases from about 48 m/s in the first few centimeters to 231 m/s at 1 m depth and then gradually increases to 425 m/s at 7 m depth. This is the first time when such a low velocity has been recorded at extremely shallow depths in sand in situ. The velocity profile thus generated is statistically fitted with a simple analytical equation. Our velocity values are higher than those published previously for beach sand. We find that using replacement or tomogram velocities instead of an accurately measured velocity profile may result in 23%–44% error in the static correction.

P-wave attenuation measurements from laboratory resonance and sonic waveform data

Geophysics ◽  
1989 ◽  
Vol 54 (1) ◽  
pp. 76-81 ◽  
Author(s):  
D. Goldberg ◽  
B. Zinszner
Keyword(s):  
Wave Attenuation ◽  
Compressional Wave ◽  
P Wave ◽  
Laboratory Measurements ◽  
Frequency Range ◽  
Waveform Data ◽  
Sonic Log ◽  
In Situ Conditions ◽  
The Mean

We computed compressional‐wave velocity [Formula: see text] and attenuation [Formula: see text] from sonic log waveforms recorded in a cored, 30 m thick, dolostone reservoir; using cores from the same reservoir, laboratory measurements of [Formula: see text] and [Formula: see text] were also obtained. We used a resonant bar technique to measure extensional and shear‐wave velocities and attenuations in the laboratory, so that the same frequency range as used in sonic logging (5–25 kHz) was studied. Having the same frequency range avoids frequency‐dependent differences between the laboratory and in‐situ measurements. Compressional‐wave attenuations at 0 MPa confining pressure, calculated on 30 samples, gave average [Formula: see text] values of 17. Experimental and geometrical errors were estimated to be about 5 percent. Measurements at elevated effective pressures up to 30 MPa on selected dolostone samples in a homogeneous interval showed mean [Formula: see text] and [Formula: see text] to be approximately equal and consistently greater than 125. At effective stress of 20 MPa and at room temperature, the mean [Formula: see text] over the dolostone interval was 87, a minimum estimate for the approximate in‐situ conditions. We computed compressional‐wave attenuation from sonic log waveforms in the 12.5–25 kHz frequency band using the slope of the spectral ratio of waveforms recorded 0.914 m and 1.524 m from the source. Average [Formula: see text] over the interval was 13.5, and the mean error between this value and the 95 percent confidence interval of the slope was 15.9 percent. The laboratory measurements of [Formula: see text] under elevated pressure conditions were more than five times greater than the mean in‐situ values. This comparison shows that additional extrinsic losses in the log‐derived measurement of [Formula: see text], such as scattering from fine layers and vugs or mode conversion to shear energy dissipating radially from the borehole, dominate the apparent attenuation.

Transmission and detection of guided seismic waves in attenuating media

Geophysics ◽  
1998 ◽  
Vol 63 (4) ◽  
pp. 1190-1199 ◽  
Author(s):  
Jorge O. Parra ◽  
Brian J. Zook ◽  
Pei‐Cheng Xu ◽  
Raymon L. Brown
Keyword(s):  
Seismic Waves ◽  
Guided Waves ◽  
Test Site ◽  
Guided Wave ◽  
Leaky Mode ◽  
Head Wave ◽  
British Petroleum ◽  
Low Velocity ◽  
Time Frequency ◽  
Shaly Sandstone

We can use guided seismic waves to map properties of reservoirs between wells, with the low‐velocity layers acting as waveguides. When guided waves are detected, they are an indication of the continuity of the bed examined. Guided waveforms are characterized by time‐frequency representations to study important physical properties of the beds acting as waveguides. We used full waveform seismic modeling in viscoelastic media to examine the required velocity contrasts and distances over which guided‐wave signals can be used. In one set of models, sandstones are the central waveguide lithology; in another set, shales. We applied these models, referred to here collectively as shaly sandstone waveguides, to a range of geological circumstances where either the sands or the shales represent the low‐velocity layers within a reservoir. To study the distances over which guided waves can be detected, we compared the amplitudes of the signals computed for the models, using a realistic source strength, to the signal levels determined from published borehole noise studies. In shaly sandstone waveguides, we find it is feasible to use particle velocity measurements to record guided waves above seismic noise levels in the frequency range of 60 to 800 Hz at well separations exceeding a distance of 800 m. However, pressure detectors such as hydrophones may only be useful up to distances of 400 m between wells. In addition to the issues of shaly sandstone waveguides and practical distances between wells, we present an application of guided waves using crosswell seismic data from the Gypsy test site in Oklahoma (a site originally established by British Petroleum). In this field example within a sandstone reservoir, we demonstrate the sensitivity of leaky mode amplitudes to source‐receiver location. Another telltale characteristic of continuity in the type of reservoir studied at the Gypsy test site, where there is a low shear velocity contrast between the host medium and the waveguide, is the head wave followed by the leaky mode.

scholarly journals Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks — A review

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A147-75A164 ◽  
Author(s):  
Tobias M. Müller ◽  
Boris Gurevich ◽  
Maxim Lebedev
Keyword(s):  
Fluid Flow ◽  
Velocity Dispersion ◽  
Wave Attenuation ◽  
Field Measurements ◽  
Theoretical Models ◽  
Seismic Attenuation ◽  
P Wave ◽  
Induced Flow ◽  
Wave Induced ◽  
Attenuation And Dispersion

One major cause of elastic wave attenuation in heterogeneous porous media is wave-induced flow of the pore fluid between heterogeneities of various scales. It is believed that for frequencies below [Formula: see text], the most important cause is the wave-induced flow between mesoscopic inhomogeneities, which are large compared with the typical individual pore size but small compared to the wavelength. Various laboratory experiments in some natural porous materials provide evidence for the presence of centimeter-scale mesoscopic heterogeneities. Laboratory and field measurements of seismic attenuation in fluid-saturated rocks provide indications of the role of the wave-induced flow. Signatures of wave-induced flow include the frequency and saturation dependence of P-wave attenuation and its associated velocity dispersion, frequency-dependent shear-wave splitting, and attenuation anisotropy. During the last four decades, numerous models for attenuation and velocity dispersion from wave-induced flow have been developed with varying degrees of rigor and complexity. These models can be categorized roughly into three groups ac-cording to their underlying theoretical framework. The first group of models is based on Biot’s theory of poroelasticity. The second group is based on elastodynamic theory where local fluid flow is incorporated through an additional hydrodynamic equation. Another group of models is derived using the theory of viscoelasticity. Though all models predict attenuation and velocity dispersion typical for a relaxation process, there exist differences that can be related to the type of disorder (periodic, random, space dimension) and to the way the local flow is incorporated. The differences manifest themselves in different asymptotic scaling laws for attenuation and in different expressions for characteristic frequencies. In recent years, some theoretical models of wave-induced fluid flow have been validated numerically, using finite-difference, finite-element, and reflectivity algorithms applied to Biot’s equations of poroelasticity. Application of theoretical models to real seismic data requires further studies using broadband laboratory and field measurements of attenuation and dispersion for different rocks as well as development of more robust methods for estimating dissipation attributes from field data.

scholarly journals Radar and Seismic Ice-Thickness Measurements Compared on Sub Polar Glaciers in Svalbard (Abstract)

1987 ◽  
Vol 9 ◽  
pp. 246 ◽  
Author(s):  
D.J. Drewry
Keyword(s):  
Seismic Waves ◽  
Seismic Energy ◽  
The Other ◽  
P Wave ◽  
Seismic Velocities ◽  
Radio Waves ◽  
Low Velocity ◽  
Factors Affecting ◽  
Radio Echo Sounding ◽  
Echo Sounding

A comparison has been made of 46 radar-determined ice thicknesses and those resulting from seismic sounding on Bakaninbreen, Skobreen, and Paulabreen in central Spitsbergen. Significant differences were recorded between the two techniques, with 50% of the comparisons exceeding 15 m. Systematic differences between the three glaciers were also observed: on Paulabreen the seismic ice depths are consistently deeper than those determined by radio echo- sounding, whilst the opposite is true on Skobreen. Instrumental errors from the radar (SPRI 60 MHz unit) and seismic equipment (ABEM Terraloc) are considered small or insignificant. Factors affecting the respective propagation velocities may be responsible for differences in mean thickness particularly in the case of seismic waves, although the changes are obtained from the first returns. One hypothesis to explain the differences on Paulabreen, and to a lesser degree on Bakaninbreen, is that these glaciers are underlain by a seismic low-velocity layer due to the presence of moraine or till. Unfortunately, equipment problems in the field prevented the digital logging of the seismic data and the analogue records are not of sufficient quality for detailed analyses to reveal the possible presence of a till horizon and its seismic velocities. However, observations at the snout of Paulabreen show considerable thicknesses of basal till. With a “P”-wave velocity in such a layer close to or less than that of ice acoustic returns would possibly come from the till–bedrock interface, whereas radar returns would be from the region of the ice–till boundary. For the seismic ice depths that are shallower than the radar soundings on Skobreen an alternative explanation is required. The valley occupied by the glacier is considerably narrower than in the case of the other two glaciers. According to one detailed radio echo-sounding cross-profile, the line of the combined seismic and radar sounding was displaced to one side of the centre and deepest part of the glacier. This would result in early seismic returns from the nearest facets of the valley side rather than the subjacent bed. The radio waves, however, undergo a focussing effect in the ice, giving rise to a considerably smaller footprint. The difference in slant length between the general area of the bed viewed by the radar and that returning seismic energy is approximately +15–20 m at the location of the cross-profile. This value is of the order of the differences between the two systems and could therefore account for the observed disparity here and at the other locations.

scholarly journals Radar and Seismic Ice-Thickness Measurements Compared on Sub Polar Glaciers in Svalbard (Abstract)

1987 ◽  
Vol 9 ◽  
pp. 246-246
Author(s):  
D.J. Drewry
Keyword(s):  
Seismic Waves ◽  
Seismic Energy ◽  
The Other ◽  
P Wave ◽  
Seismic Velocities ◽  
Radio Waves ◽  
Low Velocity ◽  
Factors Affecting ◽  
Radio Echo Sounding ◽  
Echo Sounding

A comparison has been made of 46 radar-determined ice thicknesses and those resulting from seismic sounding on Bakaninbreen, Skobreen, and Paulabreen in central Spitsbergen. Significant differences were recorded between the two techniques, with 50% of the comparisons exceeding 15 m. Systematic differences between the three glaciers were also observed: on Paulabreen the seismic ice depths are consistently deeper than those determined by radio echo- sounding, whilst the opposite is true on Skobreen.Instrumental errors from the radar (SPRI 60 MHz unit) and seismic equipment (ABEM Terraloc) are considered small or insignificant. Factors affecting the respective propagation velocities may be responsible for differences in mean thickness particularly in the case of seismic waves, although the changes are obtained from the first returns. One hypothesis to explain the differences on Paulabreen, and to a lesser degree on Bakaninbreen, is that these glaciers are underlain by a seismic low-velocity layer due to the presence of moraine or till. Unfortunately, equipment problems in the field prevented the digital logging of the seismic data and the analogue records are not of sufficient quality for detailed analyses to reveal the possible presence of a till horizon and its seismic velocities. However, observations at the snout of Paulabreen show considerable thicknesses of basal till. With a “P”-wave velocity in such a layer close to or less than that of ice acoustic returns would possibly come from the till–bedrock interface, whereas radar returns would be from the region of the ice–till boundary.For the seismic ice depths that are shallower than the radar soundings on Skobreen an alternative explanation is required. The valley occupied by the glacier is considerably narrower than in the case of the other two glaciers. According to one detailed radio echo-sounding cross-profile, the line of the combined seismic and radar sounding was displaced to one side of the centre and deepest part of the glacier. This would result in early seismic returns from the nearest facets of the valley side rather than the subjacent bed. The radio waves, however, undergo a focussing effect in the ice, giving rise to a considerably smaller footprint. The difference in slant length between the general area of the bed viewed by the radar and that returning seismic energy is approximately +15–20 m at the location of the cross-profile. This value is of the order of the differences between the two systems and could therefore account for the observed disparity here and at the other locations.

Estimation of fracture compliance based on group delays inferred from full-waveform sonic log data

2021 ◽  
Author(s):  
Zhenya Zhou ◽  
Eva Caspari ◽  
Nicolás D. Barbosa ◽  
Andrew Greenwood ◽  
Klaus Holliger
Keyword(s):  
Time Delay ◽  
Travel Time ◽  
Seismic Waves ◽  
Test Site ◽  
P Wave ◽  
Log Data ◽  
Full Waveform ◽  
Sonic Log ◽  
Wide Range ◽  
First Arrival Travel Times

<p>Fractures, which are ubiquitous in the Earth’s upper crust, have significant impacts on a wide range of human activities, and, hence, their adequate characterization is of wide interest and importance. Seismic methods have significant potential for effectively addressing this objective. When a seismic wave propagates across a fluid-filled fracture, its amplitude is diminished and its travel time is increased. Based on the linear slip theory, the associated amplitude decays and phase delays<strong> </strong>can be used to estimate the mechanical compliance of fractures.<strong> </strong>Full-waveform sonic (FWS) log data are particularly well-suited for this purpose. While the amplitudes of FWS data acquired during standard continuous logging runs (tool being moved uphole at a constant logging speed) can be somewhat unstable, the associated first-arrival travel times are generally quite robust. In this work, we exploit the relation between the time delay that seismic waves experience across fractures and relate them to the associated compliances. Specifically, we estimate fracture compliance from the differences in group time delay of the refracted P-wave between fractured and non-fractured sections along a borehole. Numerical simulations indicate that the proposed method provides reliable compliance estimates not only for individual fractures, but also for sets of multiple discrete fractures. This finding is corroborated by applying our approach to FWS log data acquired in the course of standard logging runs in the Bedretto Underground Laboratory (www.bedrettolab.ethz.ch). Our estimates are comparable to previously inferred compliance values in a closely comparable geological environment (Grimsel test site, www.grimsel.com). The latter were inferred under rather ideal conditions, involving the quasi-static acquisition of the FWS data as well as the combination of amplitude and travel time information for their interpretation. An interesting and important open question, which we plan to address in the following, concerns the influence of the heterogeneity of the host rock embedding the fractures on compliance estimation in general and on the proposed method in particular.</p>

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