Seismic Reflection Coefficients Research Articles

Constraints on fracture connectivity from AVAz analysis

The analysis of seismic reflection amplitude variations with incidence angle and azimuth (AVAz) is a powerful tool for studying and characterizing fractured formations. There is evidence to suggest that wave-induced fluid pressure diffusion (FPD) within connected fractures can significantly affect the AVAz response. This, in turn, indicates that this seismic attribute may contain information on the connectivity degree of the fracture network, which represents a key hydraulic property of fractured formations. The assessment of the sensitivity of seismic reflectivity with respect to fracture connectivity accounting for FPD effects is so far limited to 2D models, which is mainly due to the complexity and the associated computational cost of modeling the effective properties of corresponding generically anisotropic 3D media. To overcome these issues, we employ a numerical upscaling procedure based on Biot’s theory of poroelasticity that allows us to obtain effective anisotropic representations of 3D fractured formations accounting for FPD effects. Using these effective properties, we then perform a plane-wave analysis to compute the reflection coefficients at the top of the corresponding fractured formation. The results of our numerical analyses extend previous 2D studies and demonstrate that seismic reflection coefficients are highly sensitive to the degree of connectivity of the fracture networks. The reflectivity responses of formations comprising connected and unconnected fractures show pronounced differences not only with respect to incidence angle, but also with respect to azimuth. Quite importantly, our results also demonstrate that crossplots of commonly used AVAz coefficients permit us to identify regions with higher or lower fracture connectivity.

Joint data-driven and physics-driven prestack amplitude-variation-with-angle elastic parameter inversion

Elastic parameters such as P-wave and S-wave velocity and density are of great significance for subsurface quantitative interpretation and reservoir prediction. Current prestack amplitude-variation-with-angle (AVA) inversion methods have been widely used in the industry to obtain subsurface elastic parameters. Conventional AVA inversion methods are theoretically based on a linearized amplitude-variation-with-offset model that formulates the relationship between prestack seismic reflection coefficients and the subsurface model of elastic parameters, which is called physical model-driven inversion. However, due to the linearized physical model, it is difficult to obtain high-accuracy and high-resolution inversion results using model-driven inversion when the incident angles are greater than 30°. In recent years, several neural network-based prestack AVA inversion methods, known as data-driven inversion, have been developed to address this issue. However, these methods typically require a large amount of labeled data for training networks, and there is no physical mechanism in the network training process. To solve this problem, a joint data-driven and physics-driven inversion of prestack AVA elastic parameters is proposed. Under the framework of semisupervised learning, a 2D convolutional neural network and a recurrent neural network are used to establish the mapping between several adjacent prestack AVA gathers and 1D elastic parameters in the time domain. The full Zoeppritz equation suitable for large incidence angles is used as a physical constraint for training the neural network. The loss functions of the network are constructed by combing well-log data and prestack AVA seismic data. This approach enables us to use fewer labeled data for training the network and increases the physical interpretability of the training process. To further improve the inversion results, the inverse distance weighted correlation coefficient of seismic data is applied to the loss function of seismic data and well-log data. Synthetic and field data examples demonstrate that the joint data-driven and physics-driven prestack AVA elastic parameter inversion improves accuracy and resolution compared with conventional model-driven inversion.

Nonlinear constitutive relation in acoustoelastic-orthotropic media and its wide azimuth seismic reflection coefficient characteristics for in-situ stress prediction

With the development of oil and gas exploration targets towards deep water and deep layer, change of subsurface rock physical properties caused by in-situ stress can no longer be ignored. Hence, it is of great significance to study the acoustoelasticity characteristics of rocks under complex subsurface stress environment. Based on acoustoelasticity theory and anisotropic analysis of rock under triaxial stress state, equivalent stiffness matrix of acoustoelastic-orthotropic media is established. According to the equivalent stiffness matrix, exact solution of reflection coefficient for stress-induced orthotropic media is derived. Through model experiments, reflection coefficient varies with incident and azimuth angle is analyzed. Based on the azimuthal characteristics of acoustoelastic medium reflection coefficient and in-situ stress prediction models, two in-situ stress characteristic parameters are proposed to describe in-situ stress distribution. Then, by numerical simulation, the law between azimuthal characteristics of acoustoelastic medium reflection coefficient and in-situ stress characteristic parameters is summarized. And an effective way to predict in-situ stress field that wide azimuth seismic data dependent is established. Finally, through actual wide azimuth seismic data in a field, the practicability of this in-situ stress prediction method rely on stress characteristic parameters is verified. The results illustrate that the prediction method of in-situ stress characteristic parameters can accurately describe the distribution of in-situ stress.

Direct inversion for the equivalent pore aspect ratio based on the theory of ellipsoid modelling

AbstractPore aspect ratio, together with porosity, is a structural parameter that represents the geometric property of rock reservoirs. We have adopted the theory of ellipsoid modelling in material mechanics to derive the dry rock modulus. Based on this derivation, the Gassmann equation, which is a constitutional equation for a fully saturated rock model, can be linearized in terms of the pore structure parameters and the elastic parameters. We have established a relationship between the seismic reflection coefficient and the pore structure parameters, where the equivalent pore aspect ratio and porosity are two key parameters. Based on this relationship, the equivalent pore aspect ratio can be inverted directly from seismic reflection data instead of being converted from the intermediate parameters of conventional seismic inversion. Therefore, seismic inversion is a simultaneous inversion in which seven parameters are inverted: the elastic moduli (matrix bulk modulus and shear modulus, fluid bulk modulus), the densities (matrix and fluid densities) and the pore structure parameters (the equivalent pore aspect ratio and porosity). We applied this direct inversion scheme to a carbonate reservoir to predict the fracture development zone with low porosity and low aspect ratio.

Can we use seismic reflection data to infer the interconnectivity of fracture networks?

Summary While variations of seismic reflection amplitudes with incidence angle (AVA) and azimuth have been widely used to provide information on geometric characteristics of fractures, this attribute has, as of yet, not been linked to fracture interconnectivity, which tends to govern the hydraulic property of the affected formation. This is due to limitations of the forward models considered to represent the corresponding seismic responses. Based on a poroelastic upscaling procedure and a subsequent plane-wave analysis, we show for the first time that seismic reflection coefficients are highly sensitive to fracture interconnectivity. Moreover, our results suggest that crossplots of commonly used AVA coefficients can be used to delineate regions of fractured formations with higher or lower fracture interconnectivity. This sensitivity is due to changes of the stiffening effect of the fluid contained within interconnected fractures in response to wave-induced fluid-pressure diffusion, a physical process that has not been previously accounted for in seismic reflection analyses.

A COMPUTER PROGAM FOR COMPUTING SISMIC WAVE REFLECTION AND TRANSMISSION COEFFICIENTS OF A SINGLE INTERFACE

Reflection and transmission properties of a single interface form the basic step in understanding and solving many problems of seismic waves propagation in multilayered media. The computational procedure of these coefficients is an essential element for numerical modeling or simulation purposes. A computer program for computing seismic wave reflection and transmission coefficients of a single interface has been effectively performed using the Gauss-Jordan elimination technique which is operated on a 4x 4 system of simultaneous linear equations with complex elements. The simultaneous equations have been ar ranged in matribx from. Elements of the matrix are obtained from the application of the boundary conditions to the solution of the seismic wave equations. The reflection and transmission coefficients for the compressional and shear waves constitute the unknowns of the simultaneous linear equations. Experiments using the program demonstrate the efficiency and the precislon of this procedure.

Density stability estimation method from pre-stack seismic data

As one of the most important elastic parameters in seismic exploration, density plays an important role in lithology identification and hydrocarbon indicator. Based on the approximate Zoeppritz equation, the density term is usually estimated using AVO/AVA (Amplitude variation with offset/incident angle) inversion. However, the small contribution of density to the reflection coefficient or the strong correlation with other parameters in the approximate equation renders the density estimation tough. By analyzing the contribution of density to reflection coefficient in different approximate equations, Aki-Richards is finally selected as the inversion equation, in which the density term has a higher contribution to the reflectivity. The conventional inversion approach is to invert several parameters simultaneously on the basis of approximate equation. The same convergence criterion is used for the estimation of the three parameters, but the density estimation error fails to converge to the minimum due to its small sensitivity, which makes density inversion unstable. Furthermore, the conventional inversion methods involve the inverse of large matrix, which also reduces the stability of density estimation. Therefore, a new form of Aki-Richards approximate reflection equation is derived on the assumption that the inverse of coefficient matrix exists. The reflectivity of elastic parameter is independently expressed as the weighted superposition of seismic reflection coefficients at different incident angles. Then utilizing well logging data and seismic reflection coefficient estimated by elastic impedance inversion as constraints, the inverse of coefficient matrix in inversion equation is estimated directly, which avoids inverse of large matrix and improves the precision of density estimation. In physical, the weighted coefficients directly reflect the contribution of elastic parameters reflectivity to seismic data. Finally, different experimental examples show that proposed method can stably estimate density term.

Geophysical constraints on the properties of a subglacial lake in northwest Greenland

Abstract. In this study, we report the results of an active-source seismology and ground-penetrating radar survey performed in northwestern Greenland at a site where the presence of a subglacial lake beneath the accumulation area has previously been proposed. Both seismic and radar results show a flat reflector approximately 830–845 m below the surface, with a seismic reflection coefficient of −0.43 ± 0.17, which is consistent with the acoustic impedance contrast between a layer of water and glacial ice. Additionally, in the seismic data we observe an intermittent lake bottom reflection arriving between 14–20 ms after the lake top reflection, corresponding to a lake depth of approximately 10–15 m. A strong coda following the lake top and lake bottom reflections is consistent with a package of lake bottom sediments although its thickness and material properties are uncertain. Finally, we use these results to conduct a first-order assessment of the lake origins using a one-dimensional thermal model and hydropotential modeling based on published surface and bed topography. Using these analyses, we narrow the lake origin hypotheses to either anomalously high geothermal flux or hypersalinity due to local ancient evaporite. Because the origins are still unclear, this site provides an intriguing opportunity for the first in situ sampling of a subglacial lake in Greenland, which could better constrain mechanisms of subglacial lake formation, evolution, and relative importance to glacial hydrology.

High-resolution fixed-point seismic inversion

Resolution improvement always presents as the crucial task in geologic inversion. Band-limited characteristics of seismic data and noise make seismic inversion complicated. Specifically, geologic inversion suffers from the deficiency of low- and high-frequency components. We have developed the fixed-point seismic inversion method to alleviate these issues. The problem of solving the objective function is transformed into the problem of finding the fixed point of the objective function. Concretely, a recursive formula between seismic signal and reflection coefficient is established, which is characterized by good convergence and verified by model examples. The error between the model value and the inverted value is reduced to approximately zero after a few iterations. The model examples show that in either case, that is, the seismic traces are noise-free or with a little noise, the model value can almost be duplicated. Even if the seismic trace is accompanied by moderate noise, optimal inverted results can still be obtained with our method. The initial model constraint is further introduced into the objective function to increase the low-frequency component of the inverted results by adding prior information into the target function. The singular value decomposition method is applied to the inversion framework, thus making a high improvement of antinoise ability. Finally, the synthetic models and seismic data are investigated following our method. The inverted results obtained from the fixed-point seismic inversion are compared with those obtained from the conventional seismic inversion, and it is found that the former has a higher resolution than the latter.

Applicability of a proposed groundwater level determination approach for the K‐NET in Japan

ABSTRACTThe evaluation of groundwater presence by means of seismic wave velocities is of great concern for many hydrological related engineering applications. This work introduces a simple basic procedure to accurately and systematically identify groundwater levels using P‐wave and S‐wave velocities. This procedure is defined as a seismic reflectivity parameter and based on the seismic reflection coefficients of P‐wave and S‐wave at the unsaturated/saturated interfaces (i.e., groundwater level). The present procedure is applied to 1045 K‐NET sites in Japan. Observed velocity structures, accompanied by their bulk densities and detailed lithology, for the upper 20 m depth are obtained from the National Research Institute for Earth Science and Disaster Prevention, Japan. Calculations are carried out considering three distinct lithological conditions – gravel, sand and clay–silt sediments – in order to evaluate the ability of this approach (seismic reflectivity parameter) to detect the groundwater level and assess its practical limitations. The increase of the seismic reflectivity parameter value varies substantially with Poisson's ratio, resembling the relationship between and Poisson's ratio in gravel, sand and clay–silt sediments. However, positive seismic reflectivity parameter values indicate groundwater presence, whereas negative seismic reflectivity parameter values indicate lithological variation. The seismic reflectivity parameter can also be used as a relative indicator for groundwater saturation levels. Fair comparisons are established between the seismic reflectivity parameter and the water seismic index technique. However, the seismic reflectivity parameter approach shows consistency with previous theoretical and experimental studies related to variations of and in saturated conditions, whereas the water seismic index shows inconsistency with these previous theoretical and experimental studies and an inability in determining saturation levels and detecting groundwater levels.

Seismic reflectivity and transmissivity parametrization with the effect of normal in situ stress

SUMMARY In situ stress has a significant effect on the properties of underground formations, including seismic wave velocity, porosity and permeability, and further affects seismic reflectivity and transmissivity. Research works on the effect of in situ stress are helpful to construct more precise seismic reflection and transmission coefficient equations. However, previous studies on seismic reflectivity equations did not take the effect of normal in situ stress into consideration. The mechanism of stress on seismic reflectivity and transmissivity is still ambiguous. In this study, we propose new explicit equations to help analyse the changes of seismic reflectivity and transmissivity under the effect of normal in situ stress. First, we deduce the Christoffel equation on the basis of solid acoustoelastic theory. Then, we utilize appropriate boundary conditions to formulate analytical equations of the reflectivity at the interface between two stressed formations, which can provide some new insights into the role of in situ stress. The shear wave birefringence will vanish because we assume that the wave propagates in the X–Z plane. Different rock models with different lithology and saturation are used to analyse the variation of seismic reflectivity and transmissivity with normal stress and incident angle at the interface. The main effect of normal stress on reflection and transmission coefficients is to change amplitude and critical incident angle. When the upper and lower layers are sandstones, the critical incident angle decreases with the increase of normal in situ stress, which is consistent with previous studies. In addition, the reflectivity equation can be degenerated to the Zoeppritz equation when the normal in situ stress vanishes, which further validates that the equation proposed is correct. Seismic reflectivity equations that couple the effect of stress can lay a foundation for direct prediction of in situ stress.

Seismic Reflection Coefficient Inversion Using Basis Pursuit Denoising in the Joint Time-Frequency Domain

Seismic reflection coefficient inversion in the joint time-frequency domain is a method for inverting reflection coefficients using time domain and frequency domain information simultaneously. It can effectively improve the time-frequency resolution of seismic data. However, existing research lacks an analysis of the factors that affect the resolution of inversion results. In this paper, we analyze the influence of parameters, such as the length of the time window, the size of the sliding step, the dominant frequency band, and the regularization factor of the objective function on inversion results. The SPGL1 algorithm for basis pursuit denoising was used to solve our proposed objective function. The applied geological model and experimental field results show that our method can obtain a high-resolution seismic reflection coefficient section, thus providing a potential avenue for high-resolution seismic data processing and seismic inversion, especially for thin reservoir inversion and prediction.

Seismic Anisotropy and Its Impact on Imaging the Shallow Alpine Fault: An Experimental and Modeling Perspective

AbstractThe transpressional Alpine Fault in New Zealand has created a thick shear zone with associated highly anisotropic rocks. Low seismic velocity zones and high seismic reflectivity are recorded in the Alpine Fault Zone, but no study has explored the underlying physical rock parameters of the shallow crust that control these observations. Protomylonites are the volumetrically dominant lithology of the fault zone. Here we combine experimental measurements of P‐wave speeds with numerical models of elastic wave anisotropy of protomylonite samples to explore how the fault zone can be seismically imaged. Numerical models that account for the porosity‐free real samples' fabric elastic tensors from electron backscatter diffraction (EBSD) are calculated by MTEX and a finite element model (FEM), while microfractures are modeled with differential effective medium (DEM) theory. At effective pressures representative of the Alpine Fault brittle zone, experimental wave speeds are lower than those predicted by MTEX/FEM. A possible DEM model suggests that a combination of random and aligned microfractures with aspect ratios increasing with pressure can explain the experimental wave speeds for pressures <70 MPa. Such microporosity in the form of foliation‐ and mica basal plane‐parallel microfractures and grain boundaries is validated with synchrotron X‐ray microtomography and transmission electron microscopy (TEM) images. Finally, by modeling anisotropy of seismic reflection coefficients with angle of incidence, we demonstrate that the high reflectivity and low‐velocity zone (LVZ) observed at the Alpine Fault can only be explained if this microporosity is accounted for throughout the brittle fault zone, even at depths of 7–10 km.

Elastic parameter inversion of a sand body based on the exact reflection coefficient

Prestack seismic inversion is an important technology for oil and gas exploration that can provide accurate lithology and pore fluid information on underground media. Prestack inversion is theoretically based on the Zoeppritz equations, which establish the relationship between the seismic reflection coefficients of different offsets and elastic parameter contrasts between the interface of two lithologies. However, these are fourth-order matrix equations with a complex form and are difficult to be directly applied to inversion. Approximate analytical solutions have been used to establish a linear relationship between the seismic reflection coefficients and elastic parameters. And the approximations are based on the assumptions of a small angle and weak contrast, they cannot be applied to layers of high contrast, such as gas-bearing sandstones and coal seams. In this paper, we present an accurate prestack seismic inversion method that can be applied to a wider range of geological models. First, we derive the partial derivatives of the exact reflection coefficients of PP waves based on the Zoeppritz equations with respect to the elastic parameters and establish the exact Jacobian and Hessian matrices. Then, we use the least-squares algorithm to construct objective functions for the simultaneous inversion of three elastic parameters: The P-wave velocity, S-wave velocity, and density. Examples show that our inversion method is more accurate for strata with strong reflection interfaces than the approximate prestack inversion methods and stable under noisy conditions. The inversion method was applied in channel sand depositions of the Lower Permian Shanxi and Shihezi Formation of the Ordos Basin, and it was efficient to identify the gas-bearing sand layers and determine the range of potentially favorable areas.

Analysis of wave dispersion and attenuation effects on seismic low-frequency reflections of a poroelastic layer

We investigated reflection dispersion characteristics of a poroelastic layer with patchy saturations in seismic low-frequency range. Frequency-dependent attenuation and dispersion of phase velocity were determined with varying fluid saturation, porosity, permeability and heterogeneity size, using analytical solutions of a generalised 1D White’s model proposed here, obtained by incorporating capillary forces into the patchy saturation model. Numerical predictions were employed in combinations with an approximation for the complex and frequency-dependent reflection coefficient from an attenuating thin layer embedded in a dissipative background medium, so as to give a deep insight into the impacts of velocity dispersion and tuning, as well as acoustic impedance contrast, on the seismic low-frequency reflections. Results from this study suggest that wave-induced fluid flow in poroelastic media might account for low-frequency reflection signature anomalies that are associated with fluid saturation in the pore space. We also observed that seismic reflection coefficients of a partially saturated layer can vary strongly versus frequencies, especially in low-frequency range where high attenuation and dispersion can take place due to fluid partial saturation. Analysis of the crossplots of the magnitude for reflection coefficients and dispersion showed that attenuation, dispersion and tuning are more sensitive to gas saturation, porosity, and heterogeneity size. Thus the crossplot provides a useful means for detecting changes in fluid saturation and rock properties.

Second-Order Approximation of the Seismic Reflection Coefficient in Thin Interbeds

As most of the lithostratigraphic reservoirs in China are thin interbeds, the study of seismic responses in thin interbeds is an integral part of lithologic reservoir exploration. However, at present, the research on seismic reflection coefficients of thin interbeds in exploration seismology is still weak, which leads to the lack of theoretical basis for the subsequent interpretation of amplitude variation with offset (AVO) related to thin interbed. To solve this problem, in this paper, we proposed second-order approximate equations of the seismic reflection coefficients in thin-bed and thin-interbed layers. Under the assumption of a small impedance contrast in layered media, we made a second-order approximation with a more evident physical meaning to the reflection coefficient calculation method proposed by Kennett. Then, based on the test of the single thin-layer theoretical model, it was confirmed that the second-order approximation equation of the PP-wave (reflected compressional wave) is accurate at incident angles less than 30°, and that of the PS-wave (converted shear wave) is accurate at wider incident angles. Finally, based on the single-thin-bed equations, the approximate equations of seismic reflection coefficients in thin interbeds were established, the validity of which was verified by the theoretical model. Our equations will be applicable to the calculation of PP- and PS-wave reflection coefficients in thin interbeds where internal multiples are difficult to suppress and transmission loss is hard to accurately compensate. This lays a theoretical foundation for improving the seismic prediction accuracy of lithologic reservoirs.

Accurate Jacobian Matrix Using the Exact Zoeppritz Equations and Effects on the Inversion of Reservoir Properties in Porous Media

The analysis of amplitude variation with offset (AVO) plays a significant role in fluid detection and lithology discrimination in hydrocarbon reservoirs. The Zoeppritz equations are part of the basic theory of AVO analysis which describes the relationship between seismic reflection and transmission coefficients and elastic rock properties (e.g., P- and S-wave velocities and density). Currently, most AVO inversion methods are based on approximations of the exact Zoeppritz equations, which not only limit the accuracy of AVO inversion, but also restrict its application to wide-angle seismic reflection data. In addition, the most difficult part of linear AVO inversion obtaining an accurate Jacobian matrix (partial derivatives of reflection coefficients with respect to inverted parameters). Based on our previous study on the accurate gradient calculation of seismic reflection coefficients for the inversion of rock properties, we further combine the exact Zoeppritz equations with Biot–Gassmann equations to compute the gradients of seismic reflection coefficients with solid density and reservoir properties (e.g., porosity, water/gas/oil saturations) in porous media. In this paper, the partial derivative expressions of the Zoeppritz matrix elements with respect to solid density and reservoir properties are simplified to simple algebraic equations, which are readily calculated. By comparing reflection coefficients and partial derivative curves with those obtained by classic Shuey and Aki–Richards approximations, we show that our proposed method can be used to accurately obtain reservoir properties in AVO inversion.

SWRT: A package for semi-analytical solutions of surface wave propagation, including mode conversion, across transversely aligned vertical discontinuities

Abstract. We present a suite of programs that implement decades-old algorithms for computation of seismic surface wave reflection and transmission coefficients at a welded contact between two laterally homogeneous quarter-spaces. For Love as well as Rayleigh waves, the algorithms are shown to be capable of modelling multiple mode conversions at a lateral discontinuity, which was not shown in the original publications or in the subsequent literature. Only normal incidence at a lateral boundary is considered so there is no Love–Rayleigh coupling, but incidence of any mode and coupling to any (other) mode can be handled. The code is written in Python and makes use of SciPy's Simpson's rule integrator and NumPy's linear algebra solver for its core functionality. Transmission-side results from this code are found to be in good agreement with those from finite-difference simulations. In today's research environment of extensive computing power, the coded algorithms are arguably redundant but SWRT can be used as a valuable testing tool for the ever evolving numerical solvers of seismic wave propagation. SWRT is available via GitHub (https://github.com/arjundatta23/SWRT.git).

A rapid and nondestructive method to determine normal and shear stiffness of a single rock joint based on 1D wave-propagation theory

Determination of joint stiffness, one of the most important mechanical properties of rock joints, is of great significance. However, joint stiffness is often difficult to complete and accurate determine because of the 3D nature of joints and limited budgets and visible exposure. Wave attenuation in a rock mass is mainly attributed to the presence of joints. Based on 1D plane-wave theory, a rapid and nondestructive method, namely, the rapid evaluation method, is proposed to calculate normal and shear stiffness of joints. The joint is viewed as a boundary condition modeled by the displacement discontinuity model. By solving wave equations with reasonable approximation, joint stiffness can be inversely solved, which is dependent on the seismic impedance, transmission or reflection coefficient, and dominant frequency of transmitted waves. Ultrasonic laboratory tests were carried out to record incident, reflected, and transmitted waveforms as input to the rapid evaluation method. It was found that the presence of joints played three major roles on wave propagation, i.e., velocity, amplitude, and dominant frequency decay. Compared with wave slowness, wave attenuation, on which the proposed rapid evaluation method is based, is more sensitive to the presence of joints. Uniaxial compression tests and direct shear tests were also carried out to directly measure the normal and shear stiffness of joints, respectively. A comparison was then made between joint stiffness obtained from the rapid evaluation method and from direct measurements. It was found that joint stiffness acquired from the rapid evaluation method agreed with the direct laboratory measurements. In addition, theoretical predictions of joint stiffness using different ultrasonic transducers are almost the same. Therefore, the applicability and reliability of this proposed method are verified.

Seismic reflection and transmission coefficients of a single layer sandwiched between two dissimilar poroelastic solids

The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is modeled as a porous solid with finite thickness. The propagation of waves is represented with potential functions. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. Due to the presence of viscosity in pore fluids, the reflected and transmitted waves are inhomogeneous in nature, i.e., with different directions of propagation and attenuation. The closed-form analytical expressions for reflection and transmission coefficients are derived theoretically for appropriate boundary conditions. These expressions are calculated as a non-singular system of linear algebraic equations and depend on the various parameters involved in this non-singular system. Hence, numerical examples are studied to determine the effects of various properties of the sandwich layer on reflection and transmission coefficients. The essential features of layer thickness, incident direction, wave frequency, liquid saturation and capillary pressure of the porous layer on reflection and transmission coefficients are depicted graphically and discussed. The analysis shows that reflection and transmission coefficients are strongly associated with incident direction and various properties of the porous layer.