Linear Slip Theory Research Articles

Azimuthal Attenuation Elastic Impedance Inversion for Fluid and Fracture Characterization Based on Modified Linear-Slip Theory

The seismic attenuation should be considered while accounting for the effect of anisotropy on the seismic wave propagating through a saturated fractured porous medium. Based on the modified linear-slip theory and anisotropic Gassmann’s equation, we derive an analytical expression for a linearized PP-wave reflection coefficient and an azimuthal attenuation elastic impedance (AAEI) equation in terms of fluid/porosity term, shear modulus, density, dry normal and tangential fracture weaknesses, and compressional (P-wave) and shear (S-wave) attenuation parameters in a weak-attenuation isotropic background rock containing one single set of vertical aligned fractures. We then propose an AAEI inversion method to characterize the characteristics of fluids and fractures using two kinds of constrained regularizations in such a fractured porous medium. The proposed approach is finally confirmed by both the synthetic and real data sets acquired over a saturated fractured porous reservoir.

Low-frequency layer-induced kinematic parameters in transversely isotropic media and orthorhombic media

SUMMARY We develop a method to compute frequency-dependent kinematic parameters for an effective orthorhombic (ORT) medium. In order to investigate the influence of fracture weaknesses on the kinematic parameters, the effective ORT medium is composed based on the linear slip theory and derived by applying the limited Baker–Campbell–Hausdorff series. The frequency-dependent kinematic parameters including vertical velocity, two normal moveout velocities defined in vertical symmetry planes, and three anelliptic parameters (two of them are defined in vertical symmetry plane and one parameter is the cross-term one). We also investigate the influence of volume fraction, frequency, velocity ratio and fracture weaknesses on the effective kinematic parameters.

Anisotropic azimuthal surface‐wave inversion for a vertically fractured and transverse isotropy medium: Theory and examples from a controlled field experiment

ABSTRACTFractures in elastic media add compliance to a rock in the direction normal to the fracture strike. Therefore, elastic wave velocities in a fractured rock will vary as a function of the energy propagation direction relative to the orientation of the aligned fracture set. Anisotropic Thomson–Haskell matrix Rayleigh‐wave equations for a vertically transverse isotropic media can be used to model surface‐wave dispersion along the principal axes of a vertically fractured and transversely isotropic medium. Furthermore, a workflow combining first‐break analysis and azimuthal anisotropic Rayleigh‐wave inversion can be used to estimate P‐wave and S‐wave velocities, Thomsen's ε, and Thomsen's δ along the principal axes of the orthorhombic symmetry. In this work, linear slip theory is used to map our inversion results to the equivalent vertically fractured and transversely isotropic medium coefficients. We carried out this inversion on a synthetic example and a field example. The synthetic data example results show that joint estimation of S‐wave velocities with Thomsen's parameters ε and δ along normal and parallel to the vertical fracture set is reliable and, when mapped to the corresponding vertically fractured and transversely isotropic medium, provides insight into the fracture compliances. When the inversion was carried out on the field data, results indicated that the fractured rock is more compliant in the azimuth normal to the visible fracture set orientation and that the in situ normal fracture compliance to tangential fracture compliance ratio is less than half, which implies some cementation may have occurred along the fractures. Such an observation has significant implications when modelling the transport properties of the rock and its strength. Both synthetic and field examples show the potential of azimuthal anisotropic Rayleigh‐wave inversion as the method can be further expanded to a more general case where the vertical fracture set orientation is not known a priori.

Estimation of Fracture Compliance From Attenuation and Velocity Analysis of Full‐Waveform Sonic Log Data

AbstractIn fractured rocks, the amplitudes of propagating seismic waves decay due to various mechanisms, such as geometrical spreading, solid friction, displacement of pore fluid relative to the solid frame, and transmission losses due to energy conversion to reflected and transmitted waves at the fracture interfaces. In this work, we characterize the mechanical properties of individual fractures from P wave velocity changes and transmission losses inferred from static full‐waveform sonic log data. The methodology is validated using synthetic full‐waveform sonic logs and applied to data acquired in a borehole penetrating multiple fractures embedded in a granodioritic rock. To extract the transmission losses from attenuation estimates, we remove the contributions associated with other loss mechanisms. The geometrical spreading correction is inferred from a joint analysis of numerical simulations that emulate the borehole environment and the redundancy of attenuation contributions other than geometrical spreading in multiple acquisitions with different source‐receiver spacing configurations. The intrinsic background attenuation is estimated from measurements acquired in the intact zones. In the fractured zones, the variations with respect to the background attenuation are attributed to transmission losses. Once we have estimated the transmission losses associated with a given fracture, we compute the transmission coefficient, which, on the basis of the linear slip theory, can then be related to the mechanical normal compliance of the fracture. Our results indicate that the estimated mechanical normal compliance ranges from 1 × 10−13 to 1 × 10−12 m/Pa, which, for the size of the considered fractures, is consistent with the experimental evidence available.

Seismic anisotropy of a fractured rock during CO2 injection: a feasibility study

Fluid substitution plays the key role in reservoir characterization, leading to enhance understanding of the influence of fluids on seismic parameters. In general, fluid substitution tool assumes that the Earth is as an isotropic medium, which may not represent the practical field situation. Nevertheless, anisotropic fluid substitution provides important insights into the processes that control the anisotropic seismic response of a fractured rock when subjected to CO2 injection for enhanced oil recovery and its geological sequestration. Here, we examine the influence of fluid substitution in a porous yet fractured reservoir for quantitative interpretation of seismic data. This investigation involves anisotropic Gassmann’s equation and linear slip theory for fluid substitution in a transversely isotropic media with a horizontal axis of symmetry (HTI). We present a synthetic case by conceptualizing a double-layered half-space model with upper layer as shale and bottom layer as HTI sandstone, representing an Indian mature reservoir. The effects of variation in background porosity and fracture weaknesses on anisotropic (Thomsen’s) parameters, acoustic parameters including amplitude variation with angle have also been discussed. We observe that brine and oil sands to be associated with the highest elastic moduli, while CO2 sands exhibit contrasting trend. It is noteworthy that CO2 is more sensitive to fracture weakness when compared to the other reservoir fluids such as hydrocarbons and brines, as P-wave moduli (as much as 37.1%) and velocity (as high as 12.2%) reduces significantly with the increase in fracture weakness. Further, Gassmann’s assumption is validated as we noticed unchanged values in shear-wave moduli and shear-wave splitting parameter (γ) for various fluid types.

Estimation of fracture weaknesses and integrated attenuation factors from azimuthal variations in seismic amplitudes

Seismic wave propagation in fractured reservoirs exhibits anisotropy and attenuation, which are in turn related to fracture properties (e.g., fracture density) and fluid parameters (e.g., moduli and viscosity). Based on the linear slip theory, stiffness parameters can be determined for fractured and dissipative rocks, from which integrated attenuation factors involving host-rock intrinsic attenuation and fracture-induced attenuation emerge. Using a simplified mathematical form for these stiffness parameters, a linearized mathematical relationship directly relating the reflection coefficient to fracture weaknesses and integrated attenuation factors is available. A two-step inversion approach, involving (1) an iterative damped least-squares algorithm to predict P- and S-wave moduli using seismic angle gathers along the fracture orientation azimuth and (2) an iterative inversion method to estimate fracture weaknesses and integrated attenuation factors from azimuthal amplitude differences, is examined. The objective function for the second step is constructed based on a Bayesian framework. Synthetic testing confirms that fracture weaknesses and integrated attenuation factors are stably determined from seismic amplitudes exhibiting a moderate signal-to-noise ratio. The approach is applied to a field data set from a fractured carbonate reservoir. We observe that geologically reasonable results of fracture weaknesses and integrated attenuation factors are obtained. We conclude that this estimation procedure provides a reliable tool in fracture prediction and inverted attenuation factors appear as additional proofs to identify fluid type in fractured reservoirs.

Experimental verification of spatially varying fracture-compliance estimates obtained from amplitude variation with offset inversion coupled with linear slip theory

The elastic compliance of a fracture can be spatially varying, reflecting the variation of microscale properties of the fracture, e.g., aperture, contact asperities, and fracture infill. Characterizing the spatial heterogeneity of a fracture is crucial in explaining the apparent frequency dependence of fracture compliance and in addressing the spatially varying mechanical and hydraulic properties of the fractured medium. Apparent frequency dependence of the estimated fracture compliance is caused when the used seismic wavelength is very large compared to the scale of heterogeneity. We perform ultrasonic laboratory experiments, and characterize the spatially varying compliance along a fluid-filled fracture. We simulate a horizontal fracture, and introduce heterogeneous fluid distribution along the fracture. We perform amplitude variation with offset (AVO) inversion of the P-P reflections, in which we obtain the theoretical angle-dependent reflection responses by considering the linear-slip model. The estimated compliance distribution clearly separates the dry region from the wet region of the fracture. The effective bulk modulus of the fluid is estimated using the derived values of the compliance. We find that the obtained bulk modulus is well-explained by the presence of minute quantity of air bubbles in the water. We also find new evidence of the existence of scattered waves generated at the boundary representing a sharp change in fracture compliance. The estimated boundary between the dry and the wet regions of the fracture, which is detected by AVO inversion, is slightly shifted compared with the actual location. This is possibly due to the interference of the scattered waves that are generated at the boundary. The linear-slip model can represent thin structures in rocks in a wide range of scale. Therefore, our methodology, results, and discussion will be useful in developing new applications for assessing laterally varying mechanical and hydraulic properties of thin nonwelded discontinuities, e.g., fractures, joints, and faults.

Seismic dispersion and attenuation in saturated porous rocks with aligned fractures of finite thickness: Theory and numerical simulations — Part 2: Frequency-dependent anisotropy

Numerous theoretical models have been proposed for computing seismic wave dispersion and attenuation in rocks with aligned fractures due to wave-induced fluid flow between the fractures and the embedding background. However, all these models rely on certain assumptions, for example, infinitesimal fracture thickness or dilute fracture concentration, which rarely hold in real reservoirs and, thus, limit their applicability. To alleviate this issue, theoretical models for periodically or randomly spaced planar fractures and penny-shaped cracks were recently extended by the authors to the case of finite fracture thickness for P-waves propagating perpendicular to the fracture plane. Theoretical predictions under low and relatively high fracture density were then assessed by comparing with corresponding numerical simulations. However, the case of arbitrary incidence angles as well as the behaviors of S-waves remained unexplored. In this work, we therefore extended the prediction results to the full stiffness matrix through two theoretical approaches. The first approach uses an interpolation between the low- and high-frequency limits using a relaxation function obtained from the normal-incidence solution. The second approach is based on the linear slip theory with a frequency-dependent fracture compliance. Both derivations rely on the fact that all the stiffness coefficients are controlled by the same relaxation function. With the full stiffness matrix, anisotropic seismic properties can then be studied. P- and S-wave velocities and attenuations at different frequencies and incidence angles and also corresponding anisotropy parameters are calculated for one synthetic 2D rock sample. The results indicate that the predictions provided by the two theoretical approaches are in good agreement with each other and also indicate a good agreement with the corresponding numerical simulations. The extended theoretical models presented in this work are easy to apply and computationally much cheaper than numerical simulations and, hence, can be used in the seismic characterization of fractured reservoirs.

3D-printed rock models: Elastic properties and the effects of penny-shaped inclusions with fluid substitution

3D printing techniques (additive manufacturing) using different materials and structures provide opportunities to understand porous or fractured materials and fluid effects on their elastic properties. We used a 3D printer (Stratasys Dimension SST 768) to print one “solid” cube model and another with penny-shaped inclusions. The 3D printing process builds materials, layer by layer, producing a slight “bedding” plane, somewhat similar to a sedimentary process. We used ultrasonic transducers (500 kHz) to measure the P- and S-wave velocities. The input printing material was thermoplastic with a density of [Formula: see text], P-wave velocity of [Formula: see text], and S-wave velocity of [Formula: see text]. The solid cube had a porosity of approximately 6% and a density of [Formula: see text]. Its P-wave velocity was [Formula: see text] in the bedding direction and [Formula: see text] normal to bedding. We observed S-wave splitting with fast and slow velocities of 879 and [Formula: see text], respectively. Quality factors for P- and S-waves were estimated using the spectral-ratio method with [Formula: see text] ranging from 15 to 17 and [Formula: see text] from 24 to 27. By introducing penny-shaped inclusions along the bedding direction in a 3D printed cube, we created a more porous volume with density of [Formula: see text] and porosity of 24%. The inclusions significantly decreased the P-wave velocity to 1706 and [Formula: see text] parallel and normal to the bedding plane. The fast and slow S-wave velocities also decreased to 812 and [Formula: see text]. A fluid substitution experiment, performed with water, increased (20%–46%) P-wave velocities and decreased (9%–10%) S-wave velocities. Theoretical predictions using Schoenberg’s linear-slip theory and Hudson’s penny-shaped theory were calculated, and we found that both theories matched the measurements closely (within 5%). The 3D printed material has interesting and definable properties and is an exciting new material for understanding wave propagation, rock properties, and fluid effects.

Using elastic nonlinear modulation of sound by sound to detect fracture orientation in reservoir rocks

Cracks play a key role in our ability to produce oil and gas or monitor water resources, from microscale cracks that enable permeability in tight formations to larger faults and fractures that compartmentalize reservoirs. Our ability to sense and understand cracks is thus of key importance. We explore the role that cracks play in the nonlinear interaction of propagating waves using an elastic version of modulation of sound by sound. We present a laboratory experiment in which a strong S-wave slightly changes the velocity of a lower amplitude P-wave, and use a rock sample with aligned fractures to demonstrate that this signal is strongly dependent on fracture orientation. We build on the linear slip theory to show that the propagating S-wave is indeed able to open the cracks that the P-wave velocity will be most sensitive to. This gives firm, direct evidence that cracks are a controlling factor in the nonlinear elastic properties of rocks, and opens up the possibility of using such signals to remotely map fracture orientations.

Scattering of SH-wave for a non-welded contact fluid saturated natural fracture

Closed-form time-domain formulas have been obtained for reflected and transmitted coefficients of SH-wave across a saturated fracture. SH-wave incident upon a fluid filling saturated fracture at arbitrary angle containing the scattering attenuation and wave-induced fluid flow attenuation mechanism. The fracture linear slip theory is introduced under the saturated condition and the dynamic shear compliance is expressed by the viscous fluid mechanics. A finite jump displacement and velocity across a fracture is expressed as a function of wave frequency and geometrical parameters of fracture. The frequency-dependent wave reflection and transmission in wave equations are given by the discontinuity boundary conditions. Coupling relationship between scattering and intrinsic attenuation can be explained partially based on our model.

Interpreting azimuthal Fourier coefficients for anisotropic and fracture parameters

Amplitude variation with offset and azimuth (AVOAz) analysis can be separated into two separate parts: amplitude variation with offset (AVO) analysis and amplitude variation with azimuth (AVAz) analysis. Useful information about fractures and anisotropy can be obtained just by examining the AVAz. The AVAz can be described as a sum of sinusoids of different periodicities, each characterized by its magnitude and phase. This sum is mathematically equivalent to a Fourier series, and hence the coefficients describing the AVAz response are azimuthal Fourier coefficients (FCs). This FC parameterization is purely descriptive. The aim of this paper is to help the interpreter understand what these coefficients mean in terms of anisotropic and fracture parameters for the case of P-wave reflectivity using a linearized approximation. The FC representation is valid for general anisotropy. However, to gain insight into the significance of FCs, more restrictive assumptions about the anisotropy or facture system must be assumed. In the case of transverse isotropic media with a horizontal axis of symmetry, the P-wave reflectivity linearized approximation may be rewritten in terms of azimuthal FCs with the magnitude and phase of the different FCs corresponding to traditional AVAz attributes. Linear slip theory is used to show that the FCs can be interpreted similarly for the cases of a single set of parallel vertical fractures in isotropic media and in transverse isotropic media with a vertical axis of symmetry (VTI). The magnitude of the FCs depends on the fracture weakness parameters and the background media. For the case of vertical fractures in a VTI background, the AVOAz inverse problem is underdetermined, so extra information must be incorporated to determine how the weights are modified due to this background anisotropy. We evaluated this on a 3D data set from northwest Louisiana for which the main target was the Haynesville shale.

Including poroelastic effects in the linear slip theory

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.

Fluid substitution effects on seismic anisotropy

AbstractWe derive equations for HTI and orthorhombic symmetries to analyze fluid substitution effects in porous fractured media. The derivations are based on the anisotropic Gassmann equation and linear slip theory. We assess the influence of fluid substitution (gas, brine, and oil) on elastic moduli, velocities, anisotropy, and azimuthal amplitude variations. We find that in the direction normal to fractures, P‐wave moduli increase as much as 56% and P‐wave velocity increases up to 19% for gas‐to‐brine substitution. For the direction parallel to fractures, P‐wave velocity remains almost constant when porosity is low (5%) but can increase up to 4% if porosity is high (25%). Since P‐waves in two different directions have different sensitivities to fluids and fractures, the Thomsen's parameters (defined for HTI and orthorhombic symmetries), ϵ and δ, are sensitive to fluid types and fractures. We also found that δ is sensitive to porosity for liquid saturation but insensitive to porosity for the case of gas saturation. Gassmann assumes (and as has been observed) that shear modulus does not depend on fluids. And we observe no changes in shear‐wave splitting (γ) for different fluids. The azimuthal amplitude variation is dependent on fluid types, fractures, and porosity. We observe up to 12% increase in azimuthal amplitude variation for low porosity gas sands after brine saturation and 6% decrease for high porosity gas sands. We find that the percentage changes in gas‐to‐oil substitution are about half that of the gas‐to‐brine case. The equations we have derived provide a useful tool to quantitatively evaluate the effects of fluid substitution on seismic anisotropy.

Amplitude Variation with Offsets and Azimuths Simultaneous Inversion for Elastic and Fracture Parameters

Azimuthal elastic inversion or AVO/AVA analysis has proven to be effective for fracture description and stress evaluation in unconventional resource plays. Fracture weakness including normal and tangential weakness from linear slip theory bridge the seismic data and fracturing parameters as intermediate parameters. However, the stability of the azimuthal elastic inversion methods available for anisotropic parameters or fracture parameters in field data remains challenging. This study explores a practical azimuthal simultaneous elastic inversion method in heterogeneous medium for fracture weakness estimation. Taking the heterogeneity and anisotropy of fracture media into consideration, and based on perturbation theory and stable phase approximation, the fracture medium can be considered as the superimposition of background medium and perturbation medium, and then the seismic scattering coefficient of fracture media can be derived. This equation establishes the relationship between seismic data and fracture weakness together with elastic parameters like P-wave and S-wave moduli and weaknesses. With this equation, a heterogeneous inversion method is proposed. This method implements the estimation of P-wave and S-wave moduli and fracture weaknesses simultaneously, and the constraint from initial model and multi-iterations enhances the stability of this method. In this approach, the parameters of the perturbation medium are initially estimated, and then they can be superposed to the parameters of the known background medium as the renewal parameters of the background medium in next iteration. We can yield the final estimation of the parameters in heterogeneous medium after several iterations when the last two estimated results are similar. Model test and field data examples verify the feasibility and potential of the proposed approach.

Seismic attenuation and velocity dispersion in fractured rocks: The role played by fracture contact areas

ABSTRACTThe presence of fractures in fluid‐saturated porous rocks is usually associated with strong seismic P‐wave attenuation and velocity dispersion. This energy dissipation can be caused by oscillatory wave‐induced fluid pressure diffusion between the fractures and the host rock, an intrinsic attenuation mechanism generally referred to as wave‐induced fluid flow. Geological observations suggest that fracture surfaces are highly irregular at the millimetre and sub‐millimetre scale, which finds its expression in geometrical and mechanical complexities of the contact area between the fracture faces. It is well known that contact areas strongly affect the overall mechanical fracture properties. However, existing models for seismic attenuation and velocity dispersion in fractured rocks neglect this complexity. In this work, we explore the effects of fracture contact areas on seismic P‐wave attenuation and velocity dispersion using oscillatory relaxation simulations based on quasi‐static poroelastic equations. We verify that the geometrical and mechanical details of fracture contact areas have a strong impact on seismic signatures. In addition, our numerical approach allows us to quantify the vertical solid displacement jump across fractures, the key quantity in the linear slip theory. We find that the displacement jump is strongly affected by the geometrical details of the fracture contact area and, due to the oscillatory fluid pressure diffusion process, is complex‐valued and frequency‐dependent. By using laboratory measurements of stress‐induced changes in the fracture contact area, we relate seismic attenuation and dispersion to the effective stress. The corresponding results do indeed indicate that seismic attenuation and phase velocity may constitute useful attributes to constrain the effective stress. Alternatively, knowledge of the effective stress may help to identify the regions in which wave induced fluid flow is expected to be the dominant attenuation mechanism.

Wet Fault or Dry Fault? A Laboratory Approach to Remotely Monitor the Hydro-Mechanical State of a Discontinuity Using Controlled-Source Seismics

Stress variation and fluid migration occur in deformation zones, which are expected to affect seismic waves reflected off or propagating across such structures. We developed a basic experimental approach to monitor the mechanical coupling with respect to seismic coupling across a single discontinuity between a granite sample in contact with a steel platen. Piezoceramics located on the platen were used to both generate and record the P and S wave fields reflected off the discontinuity at normal incidence. This way, normal (B n ) and tangential (B t ) compliances were calculated using Schoenberg’s linear slip theory (Schoenberg, J Acoust Soc Am 68:1516–1521, 1980) when the roughness, the effective pressure (P eff, up to 200 MPa), and the nature of the filling (gas or water) vary. We observe that increasing the effective pressure decreases B n and B t , which is interpreted as the effect of the closure of the voids at the interface, permitting more seismic energy to be transmitted across the interface. Values of B n are significantly higher than those of B t at low P eff (<60–80 MPa) in dry conditions, and significantly drop under water-saturated conditions. The water filling the voids therefore helps to transmit the seismic energy of compressional waves across the interface. These results show that the assumption B n ≈ B t commonly found in some theoretical approaches does not always stand. The ratio B n /B t actually reflects the type of saturating fluids and the effective pressure, in agreement with other experimental studies. However, we illustrate that only the relative variations of this ratio seem to be relevant, not its absolute value as suggested in previous studies. Consequently, the use of B n against B t plots may allow effective pressure variation and the nature of the pore fluid to be inferred. In this respect, this experimental approach at sample scale helps to pave the way for remotely monitoring in the field the hydro-mechanical state of deformation zones, such as seismogenic faults, fractured reservoirs, or lava conduits.

Anisotropy of Seismic Attenuation in Fractured Media: Theory and Ultrasonic Experiment

This is a study on anisotropy of seismic attenuation in a transversely isotropic (TI) model, which is a long-wavelength equivalent of an isotropic medium with embedded parallel fractures. The model is based on Schoenberg's linear-slip theory. Attenuation is introduced by means of a complex-valued stiffness matrix, which includes complex-valued normal and tangential weaknesses. To study the peculiarities of seismic attenuation versus wave-propagation direction in TI media, numerical modeling was performed. The model- input data were the complex-valued weaknesses found from the laboratory ultrasonic expe- riment made with a Plexiglas plate-stack model, oil-saturated (wet) and air-filled (dry). The laboratory experiment and the numerical modeling have shown that in the vicinity of the symmetry axis, in the wet model, P-wave attenuation is close to S-wave attenuation, while in the dry model, P-wave attenuation is much greater than S-wave attenuation. Moreover, the fluid fill affects the P-wave attenuation pattern. In the dry (air-saturated) model, the attenua- tion pattern in the vicinity of the symmetry axis exhibits steeper slope and curvature than in the wet (oil-saturated) model. To define the slope or the curvature, a QVO gradient was introduced, which was found to be proportional to the symmetry-axis QS/QP-ratio, which explains the differences between dry and wet models. Thus, depending on the QS/QP-ratio, the QVO gradient can serve as an indicator of the type of fluid in fractures, because the QVO gradient is greater in gas-saturated than in liquid-saturated rocks. The analysis of P-wave attenuation anisotropy in seismic reflection and vertical seismic profiling data can be useful in seismic exploration for distinguishing gas from water in fractures.

Seismic reflection coefficients of faults at low frequencies: a model study

ABSTRACTWe use linear slip theory to evaluate seismic reflections at non‐welded interfaces, such as faults or fractures, sandwiched between general anisotropic media and show that at low frequencies the real parts of the reflection coefficients can be approximated by the responses of equivalent welded interfaces, whereas the imaginary parts can be related directly to the interface compliances. The imaginary parts of low frequency seismic reflection coefficients at fault zones can be used to estimate the interface compliances, which can be related to fault properties upon using a fault model. At normal incidence the expressions uncouple and the complex‐valued P‐wave reflection coefficient can be related linearly to the normal compliance. As the normal compliance is highly sensitive to the infill of the interface, it can be used for gas/fluid identification in the fault plane. Alternatively, the tangential compliance of a fault can be estimated from the complex‐valued S‐wave reflection coefficient. The tangential compliance can provide information on the crack density in a fault zone. Coupling compliances can be identified and quantified by the observation of PS conversion at normal incidence, with a comparable linear relationship.

The scaling of fracture compliance

Abstract The seismic visibility of fractures depends on the magnitude of their normal and shear compliance and how these quantities vary with the scale of the fracture and depth of burial. Reliable estimates of fracture compliance as a function of confining pressure, in the range 10 -13 –10 -14 m Pa -1 , have been obtained from laboratory measurements on core samples. The possibility of fractal scaling of fracture parameters has been proposed, in which case fracture compliance might be expected to increase with the scale of the fracture. Laboratory and field estimates of fracture compliance are presented covering a range of fracture sizes. Compliance is shown to increase with the scale of the fractures. Results obtained are broadly consistent with the magnitudes predicted from linear slip theory, in which the displacement discontinuity across a partially sealed interface is linearly related to the traction on the interface.