Seismic attenuation and velocity dispersion in heterogeneous partially saturated porous rocks

Numerical simulations of seismic wave propagation in fractured media are often performed in the framework of the linear slip theory (LST). Therein, fractures are represented as interfaces and their mechanical properties are characterized through a compliance matrix. This theory has been extended to account for energy dissipation due to viscous friction within fluid-filled fractures by using complex-valued frequency-dependent compliances. This is, however, not fully adequate for fractured porous rocks in which wave-induced fluid flow (WIFF) between fractures and host rock constitutes a predominant seismic attenuation mechanism. In this letter, we develop an approach to incorporate WIFF effects directly into the LST for a 1D system via a complex-valued, frequency-dependent fracture compliance. The methodology is validated for a medium permeated by regularly distributed planar fractures, for which an analytical expression for the complex-valued normal compliance is determined in the framework of quasistatic poroelasticity. There is good agreement between synthetic seismograms generated using the proposed recipe and those obtained from comprehensive, but computationally demanding, poroelastic simulations.

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Fracture Related Cross-Over Frequencies of Seismic Attenuation in Porous Rocks

68th EAGE Conference and Exhibition incorporating SPE EUROPEC 2006 ◽

10.3997/2214-4609.201402330 ◽

2006 ◽

Author(s):

M. Brajanovski ◽

T. M. Mueller ◽

B. Gurevich ◽

M. Brajanovski

Keyword(s):

Seismic Attenuation ◽

Porous Rocks

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A dynamic elastic model for squirt-flow effect and its application on fluid-viscosity-associated velocity dispersion in reservoir sandstones

Geophysics ◽

10.1190/geo2019-0312.1 ◽

2020 ◽

Vol 85 (4) ◽

pp. MR201-MR212

Author(s):

Zhi-Qiang Yang ◽

Tao He ◽

Chang-Chun Zou

Keyword(s):

Velocity Dispersion ◽

Pore Space ◽

Pore Fluid ◽

Quantitative Prediction ◽

Elastic Model ◽

Fluid Viscosity ◽

Porous Rocks ◽

S Wave ◽

Flow Effect ◽

Reservoir Sandstones

Velocity dispersion is a common phenomenon for fluid-charged porous rocks and carries important information on the pore structure and fluid in reservoir rocks. Previous ultrasonic experiments had measured more significant non-Biot velocity dispersion on saturated reservoir sandstones with increasing pore-fluid viscosity. Although wave-induced local squirt-flow effect could in theory cause most of the non-Biot velocity dispersion, its quantitative prediction remains a challenge. Several popular models were tested to predict the measured velocities under undrained conditions, but they either underestimated the squirt-flow effect or failed to simultaneously satisfy P- and S-wave velocity dispersions (especially for higher viscosity fluids). Based on the classic double-porosity theory that pore space is comprised of mainly stiff/Biot’s porosity and minor compliant porosity, an effective “wet frame” was hypothesized to account for the squirt-flow effect, whose compliant pores are filled with a hypothesized fluid with dynamic modulus. A new dynamic elastic model was then introduced by extending Biot theory to include the squirt-flow effect, after replacing the dry-frame bulk/shear moduli with their wet-frame counterparts. In addition to yielding better velocity predictions for P- and S-wave measurements of different fluid viscosities, the new model is also more applicable because its two key tuning parameters (i.e., the effective aspect ratio and porosity of compliant pores) at in situ reservoir pressure could be constrained with laboratory velocity measurements associated with pore-fluid viscosities.

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Velocity-attenuation model from check-shot drift trends in North Sea well data

Geophysics ◽

10.1190/geo2019-0419.1 ◽

2020 ◽

Vol 85 (2) ◽

pp. D65-D74 ◽

Cited By ~ 1

Author(s):

Andrew J. Carter ◽

Veronica A. Torres Caceres ◽

Kenneth Duffaut ◽

Alexey Stovas

Keyword(s):

North Sea ◽

Velocity Dispersion ◽

Seismic Attenuation ◽

P Wave ◽

Linear Wave ◽

Velocity Models ◽

Velocity Attenuation ◽

Attenuation Models ◽

Well Data ◽

Attenuation Values

Seismic attenuation distorts phase and narrows bandwidth in seismic surveys. It is also an exploration attribute, as, for example, gas or overpressure, may create attenuation anomalies. Compensating attenuation in imaging requires accurate models. Detailed attenuation models may be obtained using full-waveform inversion (FWI) or attenuation tomography, but their accuracy benefits from reliable starting models and/or constraints. Seismic attenuation and velocity dispersion are necessarily linked for causal linear wave propagation such that higher frequencies travel faster than lower frequencies in an attenuative medium. In publicly released well data from the Norwegian North Sea, we have observed systematic positive linear trends in check-shot drift when comparing (lower frequency) time-depth curves with (higher frequency) integrated sonic transit times. We observe velocity dispersion consistent with layers having constant seismic attenuation. Adapting a previously published method, and assuming an attenuation-dispersion relationship, we use drift gradients, measured over thick stratigraphic units, to estimate interval P-wave attenuation and tentatively interpret its variation in terms of porosity and fluid mobility. Reflectivity modeling predicts a very low attenuation contribution from peg-leg multiples. We use the attenuation values to develop a simple regional relationship between P-wave velocity and attenuation. Observed low drift gradients in some shallower units lead to an arch-shaped model that predicts low attenuation at both low and high velocities. The attenuation estimates were broadly comparable with published effective attenuation values obtained independently nearby. This general methodology for quickly deriving a regional velocity-attenuation relationship could be used anywhere that coincident velocity models are available at seismic and sonic frequencies. Such relationships can be used for fast derivation (from velocities) of starting attenuation models for FWI or tomography, constraining or linking velocity and attenuation in inversion, deriving models for attenuation compensation in time processing, or deriving background trends in screening for attenuation anomalies in exploration.

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Effective thermal conductivity of partially saturated porous rocks

International Journal of Solids and Structures ◽

10.1016/j.ijsolstr.2006.05.023 ◽

2007 ◽

Vol 44 (3-4) ◽

pp. 811-833 ◽

Cited By ~ 61

Author(s):

C. Gruescu ◽

A. Giraud ◽

F. Homand ◽

D. Kondo ◽

D.P. Do

Keyword(s):

Thermal Conductivity ◽

Effective Thermal Conductivity ◽

Porous Rocks ◽

Partially Saturated

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Contact line friction and surface tension effects on seismic attenuation and effective bulk moduli in rock with a partially saturated crack

Geophysical Prospecting ◽

10.1111/1365-2478.12653 ◽

2018 ◽

Vol 67 (4) ◽

pp. 913-934 ◽

Cited By ~ 2

Author(s):

Alexander Y. Rozhko ◽

Andreas Bauer

Keyword(s):

Surface Tension ◽

Contact Line ◽

Seismic Attenuation ◽

Partially Saturated ◽

Contact Line Friction

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Impact of fluid saturation on the reflection coefficient of a poroelastic layer

Geophysics ◽

10.1190/1.3553002 ◽

2011 ◽

Vol 76 (2) ◽

pp. N1-N12 ◽

Cited By ~ 36

Author(s):

Beatriz Quintal ◽

Stefan M. Schmalholz ◽

Yuri Y. Podladchikov

Keyword(s):

Fluid Flow ◽

Reflection Coefficient ◽

Analytical Solution ◽

Quality Factor ◽

Velocity Dispersion ◽

Normal Incidence ◽

Sand Layer ◽

Partially Saturated ◽

Fluid Saturation ◽

Wave Induced

The impact of changes in saturation on the frequency-dependent reflection coefficient of a partially saturated layer was studied. Seismic attenuation and velocity dispersion in partially saturated (i.e., patchy saturated) poroelastic media were accounted for by using the analytical solution of the 1D White’s model for wave-induced fluid flow. White’s solution was applied in combination with an analytical solution for the normal-incidence reflection coefficient of an attenuating layer embedded in an elastic or attenuating background medium to investigate the effects of attenuation, velocity dispersion, and tuning on the reflection coefficient. Approximations for the frequency-dependent quality factor, its minimum value, and the frequency at which the minimum value of the quality factor occurs were derived. The approximations are valid for any two alternating sets of petrophysical parameters. An approximation for the normal-incidence reflection coefficient of an attenuating thin (compared to the wavelength) layer was also derived. This approximation gives insight into the influence of contrasts in acoustic impedance and/or attenuation on the reflectivity of a thin layer. Laboratory data for reflections from a water-saturated sand layer and from a dry sand layer were further fit with petrophysical parameters for unconsolidated sand partially saturated with water and air. The results showed that wave-induced fluid flow can explain low-frequency reflection anomalies, which are related to fluid saturation and can be observed in seismic field data. The results further indicate that reflection coefficients of partially saturated layers (e.g., hydrocarbon reservoirs) can vary significantly with frequency, especially at low seismic frequencies where partial saturation may often cause high attenuation.

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