P-wave Reflection Coefficient Research Articles

Accurate P-wave reflection and transmission coefficients for non-welded interface incorporating elasto-plastic deformation

P-wave reflection and transmission coefficients for non-welded interface play crucial roles in broad practical engineering productions, involving fracture properties prediction and seismic inversion. However, the existing reflection coefficient equations for non-welded interface in elasto-plastic media are seldom studied, although the elasto-plastic deformation is frequently encountered in the Earth’s subsurface due to artificial and tectonic activities. In this study, we proposed the accurate reflection and transmission coefficients equation for a non-welded interface embedded in an elasto-plastic deformed medium based on the elasto-plastic acoustoelastic and linear-slip theory. In detail, this paper uses elasto-plastic acoustoelastic theory to derive the reflection and transmission coefficients equation. The reflection and transmission coefficients matrix are solved using the linear-slip theory as the boundary condition. Moreover, we use the hardening parameter and plastic deformation to represent the plastic properties of the rock, which is a function of stress and plastic deformation. Through Numerical analysis, the deformation caused by static stress has significantly changed the amplitude and the slope of the reflection and transmission coefficients amplitude. As the stress increases, the rock’s velocity becomes higher, and all reflection and transmission coefficients (i.e., RPP, RPS, TPP, TPS) abruptly change at the critical angle. Furthermore, with the increase in plastic deformation, the critical angle of the incident P-wave and the hardening parameter becomes larger than the unstressed state. The non-welded interface exhibits a low-pass frequency filter for reflected SV-waves and a high-pass frequency filter for reflected P-waves and transmitted P and SV waves. In addition, we can observe that static vertical stress can weaken the anomalous reflections caused by non-welded formations, but the effect is insignificant. On the other hand, the effect of fracture normal compliance to reflection and transmission is detailly investigated. When N<2.5*10-10(MPa-1), The non-welded interface is close to the welded interface, while N>2.5*10-5(MPa-1), the non-welded interface is close to the solid-air interface.

Rock physics and seismic reflectivity parameterization for amplitude-variation-with-angle inversion of low-maturity source rocks

Rock-physics inversion has been widely used in reservoir prediction. However, the prediction and evaluation of source rocks still predominantly rely on data-driven inversion methods. To directly incorporate the rock-physics relationship into the seismic inversion of source rocks, we first introduce a linearization approximation of the rock-physics model through the first-order approximation of the Taylor series. Model examples and well-logging tests substantiate the reliability of this linear approximation in establishing the connection between the elastic moduli and essential physical parameters (EPPs) of source rocks. Subsequently, we develop a novel equation for the P-wave reflection coefficient by combining the linear rock-physics relationship and Gray approximation. The newly developed reflectivity equation is a linear expression of differences in EPPs of source rocks. Model-simulating results demonstrate a favorable agreement between the novel P-wave reflectivity equation and the exact Zoeppritz equation until the incident angle reaches 60°. Furthermore, we explore the amplitude-variation-with-angle (AVA) effects of EPPs to validate their contributions meet the requirement of seismic inversion. Under the Bayesian scheme, we further develop an AVA inversion method, based on the novel P-wave reflectivity equation, to predict the EPPs of source rocks. Our AVA inversion method obtains satisfactory results under noise testing and demonstrates promising application potential in field examples. The predicted EPPs indicate a strong agreement with the actual well loggings. Comparative analysis against data-driven inversion results reveals that the EPPs predicted by our AVA inversion method possess enhanced rock-physics support and significance. Specifically, this study focuses on isotropic clay-rich source rocks with low maturity.

Monitoring the change in horizontal stress with multi-wave time-lapse seismic response based on nonlinear elasticity theory

Monitoring the change in horizontal stress from the geophysical data is a tough challenge, and it has a crucial impact on broad practical scenarios which involve reservoir exploration and development, carbon dioxide (CO2) injection and storage, shallow surface prospecting and deep-earth structure description. The change in in-situ stress induced by hydrocarbon production and localized tectonic movements causes the changes in rock mechanic properties (e.g. wave velocities, density and anisotropy) and further causes the changes in seismic amplitudes, phases and travel times. In this study, the nonlinear elasticity theory that regards the rock skeleton (solid phase) and pore fluid as an effective whole is used to characterize the effect of horizontal principal stress on rock overall elastic properties and the stress-dependent anisotropy parameters are therefore formulated. Then the approximate P-wave, SV-wave and SH-wave angle-dependent reflection coefficient equations for the horizontal-stress-induced anisotropic media are proposed. It is shown that, on the different reflectors, the stress-induced relative changes in reflectivities (i.e., relative difference) of elastic parameters (i.e., P- and S-wave velocities and density) are much less than the changes in contrasts of anisotropy parameters. Therefore, the effects of stress change on the reflectivities of three elastic parameters are reasonably neglected to further propose an AVO inversion approach incorporating P-, SH- and SV-wave information to estimate the change in horizontal principal stress from the corresponding time-lapse seismic data. Compared with the existing methods, our method eliminates the need for man-made rock-physical or fitting parameters, providing more stable predictive power. 1D test illustrates that the estimated result from time-lapse P-wave reflection data shows the most reasonable agreement with the real model, while the estimated result from SH-wave reflection data shows the largest bias. 2D test illustrates the feasibility of the proposed inversion method for estimating the change in horizontal stress from P-wave time-lapse seismic data.

Rock physics and seismic reflectivity parameterization and amplitude variation with offsets inversion in terms of total organic carbon indicator

Total organic carbon (TOC) prediction with elastic parameter inversions has been widely used in the identification and evaluation of source rocks. However, the elastic parameters used to predict TOC are not only determined by TOC but also depend on the other physical properties of source rocks. Besides, the TOC prediction with the elastic parameters inversion is an indirect method based on the statistical relationship obtained from well logs and experiment data. Therefore, we propose a rock physics model and define a TOC indicator mainly affected by TOC to predict TOC directly. The proposed rock physics model makes the equivalent elastic moduli of source rocks parameterized by the TOC indicator. Combining the equivalent elastic moduli of source rocks and Gray’s approximation leads to a novel linearized approximation of the P-wave reflection coefficient incorporating the TOC indicator. Model examples illustrate that the novel reflectivity approximation well agrees with the exact Zoeppritz equation until incident angles reach 40°. Convoluting the novel P-wave reflection approximation with seismic wavelets as the forward solver, an AVO inversion method based on the Bayesian theory is proposed to invert the TOC indicator with seismic data. The synthetic examples and field tests validate the feasibility and stability of the proposed AVO inversion approach. Using the inversion results of the TOC indicator, TOC is directly and accurately estimated in the target area.

Second-order approximate expressions of P- and SV-plane-wave reflection coefficients at the solid/solid media interface

To completely use large incident angle seismic data and improve the accuracy of amplitude-variation-with-offset inversion, especially for density information, we have derived second-order approximate expressions of the P- and SV-wave reflection coefficients at the solid/solid media interface. Vectors and Hessian matrices are used to describe the first- and second-order terms of the approximate expressions. The second-order approximations are then rewritten in a simple form. Furthermore, different pseudosecond-order approximations with different power series of the ray parameter p are derived based on the Taylor expansion of the second-order approximation of the P-wave reflection coefficient for the incident P wave (PP-wave reflection coefficient) according to the ray parameter p. By establishing four different single-phase medium models, we have verified that the accuracies of the second-order approximate expressions were remarkably higher than those of the first-order approximations. Furthermore, the pseudo p2 second-order approximation of the PP-wave reflection coefficient is highly consistent with the exact analytical expression.

Fluid discrimination incorporating amplitude variation with angle inversion and squirt flow of the fluid

Pre-stack seismic inversion is an important method for fluid identification and reservoir characterization in exploration geophysics. In this study, an effective fluid factor is initially established based on Biot poroelastic theory, and a pre-stack seismic inversion method based on Bayesian framework is used to implement the fluid identification. Compared with conventional elastic parameters, fluid factors are more sensitive to oil and gas. However, the coupling effect between rock porosity and fluid content is not considered in conventional fluid factors, which may lead to fuzzy fluid identification results. In addition, existing fluid factors do not adequately consider the physical mechanisms of fluid content, such as squirt flow between cracks and pores. Therefore, we propose a squirt fluid factor (SFF) that minimizes the fluid and pore mixing effects and takes into account the squirt flow. On this basis, a novel P-wave reflection coefficient equation is derived, and the squirt fluid factor is estimated by amplitude variation with offset (AVO) inversion method. The new reflection coefficient equation has sufficient accuracy and can be utilized to estimate the parameters. The effectiveness and superiority of the proposed method in fluid identification are verified by the synthetic and field examples.

Amplitude-variation-with-offset inversion using P- to S-wave velocity ratio and P-wave velocity

The estimation of P- to S-wave velocity ratio (PSR) in the subsurface has many applications in gas-bearing reservoir prospecting, lithology discrimination, and anomalous pore-pressure prediction. Conventionally, it is estimated with the P- and S-wave velocities/moduli/impedances that are directly obtained from prestack seismic data using the existing reflection coefficient equation (e.g., the Aki-Richards approximation). However, this indirect inversion method creates cumulative errors for the estimated PSR results. To eliminate cumulative errors, we first develop a novel generalized elastic impedance that has more explicit physical meaning compared to conventional elastic impedance. Then, we derive a linear P-wave reflection coefficient equation in terms of the PSR, P-wave velocity, and density under the assumption of weak contrast. Furthermore, a robust amplitude-variation-with-offset inversion method is constructed with the proposed reflection coefficient equation in the Bayesian framework. Cauchy and Gaussian probability distributions are used as the prior probability distribution of the model parameter and likelihood function, respectively, to predict the maximum posterior probability solution for PSR, P velocity, and density. Synthetic and field examples illustrate that the proposed direct inversion method performs with higher accuracy compared with the indirect method that inverts for the P- and S-wave velocities and also illustrate the feasibility of our method for inverting the three parameters even with strong noise. Our inverted results conform to the drilling results, which validate the robustness of the proposed direct inversion method.

Weak-anisotropy approximation of P-wave reflection coefficient in anisotropic media of arbitrary symmetry and tilt

Applicability of the approximate expression for the P-wave reflection coefficient at a weak-contrast reflector separating two weakly anisotropic half-spaces of arbitrary symmetry is extended to media of arbitrary symmetry and tilt. The reflection coefficient consists of the approximate P-wave reflection coefficient at a weak-contrast interface separating two reference isotropic half-spaces and a correction term due to anisotropy. Along an arbitrarily chosen profile, the “isotropic” term depends on the density and P- and S-wave contrasts, and the correction term depends linearly on the contrasts of four profile weak-anisotropy (WA) parameters specifying anisotropy along the profile. In addition, both terms depend on the polar angle of incidence. In each half-space, the four profile WA parameters can be expressed as a linear combination of 12 of 21 global WA parameters specifying anisotropy of the half-space. Coefficients of this linear combination are functions of the azimuth of the profile. WA parameters are a generalization of Thomsen parameters to arbitrary anisotropy and represent an alternative to 21 independent elements of the stiffness tensor. WA parameters can be used for the approximation of other related concepts such as the reflection moveout or the geometric spreading. Presented tests illustrate high accuracy and flexibility of the proposed formula for the P-wave reflection coefficient. They also show that very accurate results can be obtained for contrasts and anisotropy, which cannot be considered weak.

Influence of interface condition on reflection of elastic waves in fluid-saturated porous media

The characteristics of P-wave reflection coefficients can be dependent on the properties of the interface separating the two dissimilar poroelastic media. To evaluate the influence of the interface condition, we have developed a general theoretical formulation of seismic reflection and transmission of waves at arbitrary incidence angles in fluid-saturated porous media. The formulation is derived based on the quasistatic Biot’s theory and incorporates a more general boundary condition for fluid pressure. Simple analytic expressions are obtained for reflection and transmission coefficients at normal incidence. The equations incorporate an interfacial impedance that can be used to effectively characterize the interface condition. Based on the new formulation, we study the coupled effects of dynamic fluid flow and the interface condition on the reflection and transmission coefficients. Two pertinent reflection scenarios in exploration geophysics are considered in the numerical analysis, i.e., a gas-water contact and a free fluid overlying a gas-saturated medium. We examine the corresponding P-wave reflection coefficient resulting from different interface conditions such as imperfect hydraulic contact, capillary pressure, and open- and sealed-pore interfaces. Our results reveal that the interface condition can affect the frequency dependence and amplitude-versus-angle signatures of the reflection coefficient.

Estimation of Brittleness and Anisotropy Parameters in Transversely Isotropic Media With Vertical Axis of Symmetry

In the absence of fracture, the strata with horizontal interbedding structure can be approximately equivalent to transversely isotropic media with vertical axis of symmetry (VTI) in the sedimentary basin. Accurate estimation of Young’s modulus, Poisson’s ratio, and weak anisotropy (WA) parameters can provide basic information for further prediction of shale reservoir rock brittleness and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> stress. Based on the scattering theory and Born approximation, we derive the P-wave reflection coefficients involving Young’s modulus and Poisson’s ratio and WA parameters for an interface separating two elastic VTI media. Assuming in the case of shale, we modify this reflection coefficient to involve only three model parameters through a series of integration and simplification for stabler inversion. A Bayesian amplitude versus offset (AVO) inversion method is implemented to estimate the three attributes, which are then converted to calculate the brittleness-related and WA parameters. The numerical simulation results show that for AVO of III in the case of gas-bearing shale, the derived approximation has more accuracy than the Young’s modulus, Poisson’s ratio and density (YPD) equation, especially at large angle. Tests on synthetic and real seismic data verify that the established inversion strategy for VTI shale reservoirs is stable and accurate in the estimation of brittleness-related and WA parameters.

AVO Inversion in Orthotropic Media Based on SA-PSO

The seismic inversion of anisotropic media is a popular research direction. Orthotropic media closely approximate real strata, but their inversion remains difficult because of their many parameters and large variations. In this article, particle swarm optimization (PSO) and simulated annealing (SA) are combined to invert prestack amplitude variation with offset (AVO) data in orthotropic media. PSO is a stochastic algorithm that easily falls into local minima and has a poor global search ability. Integrating SA into PSO adds the probabilistic jump-out mechanism of SA, modifying the global optimization of PSO by adjusting the temperature. The hybrid SA-PSO algorithm can overcome premature phenomena, avoids easily falling into local minima, and fissures stronger global optimization. With the P-wave reflection coefficient formula, we establish an objective function for the anisotropic parameters of orthotropic media and use SA-PSO to invert prestack AVO data in orthotropic media. The inversion process is stable, and the inversion error is small. The proposed method is applied to the partial Marmousi2 model, and seven anisotropic parameters of orthotropic media are inverted. According to the relationships between anisotropic and fracture weakness parameters, profiles of the weakness parameters are obtained, and the fracture infill materials are predicted. The prediction results are consistent with the actual model, verifying the correctness of the method. The difference between the reservoir and surrounding rock is significant in the inversion profiles, benefiting reservoir identification. These results will provide a basis for reservoir identification and prediction and provide theoretical support for AVO inversion in anisotropic media.

Estimation of weak anisotropy parameters and fracture density of asymmetric fractures in monoclinic medium

Abstract One of the typical anisotropic media is the monoclinic anisotropy (MA) medium, which is formed by embedding two sets of non-orthogonal fracture sets into an isotropic or vertical transverse isotropic (VTI) background medium. Weak anisotropy (WA) parameters and fracture density provide important in situ stress and high-porosity zone information. Estimation of WA parameters and fracture density of MA medium by prestack seismic amplitude inversion is important for shale reservoir characterisation. We derive the expression of generalised WA parameters in a basic reflection coefficients formula of MA medium by incorporating a stiffness matrix of VTI background and disturbance compliance matrix of asymmetric fracture. We then re-express the P-wave reflection coefficients in terms of WA parameters and fracture compliance tensors. To achieve the direct inversion of fracture density, we rewrite the linearised expression of P-wave reflection coefficients related to WA parameters and fracture density. Finally, under the Bayesian framework, the WA parameters and fracture density are estimated by using the amplitude versus offset and azimuth (AVOA) inversion parameters. We use a Monte Carlo simulation to test the effect of uncertainties in the priori information about fracture property parameters. The application of synthetic seismic gathers show that the proposed inversion strategy is reliable within moderate noise. Compared with the results obtained by using inversion based on a rotationally invariant fracture, the test indicates that a fracture model with a simplified shape or wrong assumption will increase calculation error and reduce the inversion accuracy.

Seismic AVOA Inversion for Weak Anisotropy Parameters and Fracture Density in a Monoclinic Medium

In shale gas development, fracture density is an important lithologic parameter to properly characterize reservoir reconstruction, establish a fracturing scheme, and calculate porosity and permeability. The traditional methods usually assume that the fracture reservoir is one set of aligned vertical fractures, embedded in an isotropic background, and estimate some alternative parameters associated with fracture density. Thus, the low accuracy caused by this simplified model, and the intrinsic errors caused by the indirect substitution, affect the estimation of fracture density. In this paper, the fractured rock of monoclinic symmetry assumes two non-orthogonal vertical fracture sets, embedded in a transversely isotropic background. Firstly, assuming that the fracture radius, width, and orientation are known, a new form of P-wave reflection coefficient, in terms of weak anisotropy (WA) parameters and fracture density, was obtained by substituting the stiffness coefficients of vertical transverse isotropic (VTI) background, normal, and tangential fracture compliances. Then, a linear amplitude versus offset and azimuth (AVOA) inversion method, of WA parameters and fracture density, was constructed by using Bayesian theory. Tests on synthetic data showed that WA parameters, and fracture density, are stably estimated in the case of seismic data containing a moderate noise, which can provide a reliable tool in fracture prediction.

Inversion of differences in frequency components of azimuthal seismic data for indicators of oil-bearing fractured reservoirs based on an attenuative cracked model

Based on a model of attenuative cracked rock, we have derived a simplified and frequency-dependent stiffness matrix associated with (1) a rock volume containing aligned and partially saturated cracks and (2) a new indicator of oil-bearing fractured reservoirs, which is related to pressure relaxation in cracked rocks and influenced by fluid viscosity and saturation. Starting from the mathematical form of a perturbation in this stiffness matrix across a reflecting interface separating two attenuative cracked media, we set up a linearized P-wave to P-wave reflection coefficient as an azimuthally and frequency-dependent function of dry rock elastic properties, dry fracture weaknesses, and the new indicator. By varying this reflection coefficient with azimuthal angle, we derive a further expression referred to as the quasidifference in elastic impedance, or [Formula: see text], which is primarily affected by the dry fracture weaknesses and the new indicator. An inversion approach is established to use differences in frequency components of seismic amplitudes to estimate these weaknesses and the indicator based on the derived [Formula: see text]. In synthetic inversion tests, we determine that the approach produces interpretable parameter estimates in the presence of data with a moderate signal-to-noise ratio (S/N). Testing on a real data set suggests that reliable fracture weakness and indicator are generated by the approach; fractured and oil-bearing reservoirs are identified through a combination of the dry fracture weakness and the new indicator.

Direct inversion for sensitive elastic parameters of deep reservoirs

The deep reservoir is usually a type of tight reservoir with high pressure, high stress, low permeability and low porosity. The elastic parameters including Poisson’s ratio and Young’s modulus are important sensitive parameters to the tight reservoir, and the Gassmann fluid term is frequently used in the field of fluid identification as a highly sensitive fluid factor. Such parameters can be obtained by the common prestack seismic inversion method, but not directly. It must first invert for other elastic parameters and then convert them into the Poisson’s ratio, Young’s modulus and Gassmann fluid term by some formula. The errors will be accumulated in the conversion step, and the inversion results will have a large deviation. We propose a one-step inversion method to solve this problem. Firstly, a new form of P-wave reflection coefficient equation in terms of Poisson’s ratio, Young’s modulus and Gassmann fluid term is derived which can directly establish the functional relationship between the P-wave reflection coefficient and these elastic parameters. Considering seismic data of deep reservoir generally have a lower signal-to-noise ratio (S/N) and the partial angle stack gather has a higher S/N than single angle gather, we then derive a stack impedance equation which is suitable for the partial angle stack gather. By using three stacked impedance inversion data with different angle stack ranges, we can directly get the Poisson’s ratio, Young’s modulus and Gassmann fluid term simultaneously. Model and real data tests both prove that the one-step direct inversion method can reduce the cumulative errors effectively and has higher inversion accuracy.

Simultaneous seismic inversion to identify prospective areas in carbonate rocks of the southeastern part of the West Siberian Platform

This paper focuses on the description of a technology and results of identifying and mapping areas in Devonian carbonate rocks prospective for hydrocarbons and associated with increased fracture-cavern porosity in the southeastern part of the West Siberian Platform. The lack of wide-azimuthal seismic data and recording of only the vertical component in the study area did not allow the use of the direct indicators of fracture systems based either on azimuthal anisotropy of the amplitudes of pressure waves or on splitting converted waves into fast and slow. Instead, abnormally low values of the ratio of pressure-wave and shear-wave velocities derived by deterministic simultaneous pre-stack seismic inversion were used as an indirect indicator of increased fracturing. The choice of this seismic signature of fractures is substantiated by a brief review of publications on its successful use in the identification and delineation of highly fractured and cavernous zones in carbonate reservoirs. The behaviour of the indicator showed good agreement with well productivity in the study area and, therefore, made it possible to predict a number of perspective pay zones, presumably associated with in-creased fracturing. At the same time, however, well log estimates of the velocity ratio related to fractured reservoirs exhibited an opposite trend, which mismatched the facts observed in the study area and reported in the literature. This apparent discrepancy is explained by the impact of near-vertical natural macro-fracturing, which, due to different measurement scales, might substantially reduce seismic estimates while producing no impact on well log estimates. In order to describe this phenomenon quantitatively, the weak-anisotropy approximation of P-wave reflection coefficients at a horizontal boundary derived by Rüger for transversely isotropic media with a horizontal axis of symmetry was used. This equation was rewritten in terms of impedances and density and then was analyzed analytically. To express the impact of fractures in terms of fracture density, the simplest model of thin, isolated, penny-shaped fractures was used.

Prestack Stochastic Frequency-Dependent Velocity Inversion With Rock-Physics Constraints and Statistical Associated Hydrocarbon Attributes

Previous studies have demonstrated that P-wave velocity dispersion at seismic frequencies is often related to hydrocarbons, which results in frequency-dependent P-wave reflection coefficients. This effect is neglected in the conventional amplitude-versus-angle (AVA) inversion, or reduced in most AVA inversion involving seismic dispersion due to the linearization of either the forward modeling or the inversion objective function. As a consequence, there are times when nonnegligible error exists in the inverted dispersion-associated result, which is probably nonnegligible in some cases. In this letter, we adopt the propagator matrix forward modeling derived from the wave equation and the particle swarm optimization (PSO)-based inversion to solve the uncollapsed objective function to avoid any linearization operator at the cost of probably more computational complexity and inversion ill-posedness. To address the ill-posedness, in both the forward modeling and inversion, we introduce rock-physics constraints of frequency-independent S-wave velocity and limited variations of P-wave velocity with frequency. Furthermore, we statistically derive the average frequency-dependent P-wave velocity attribute, the P-wave velocity dispersion intensity attribute, and the characteristic frequency attribute corresponding to the maximum velocity dispersion gradient from multiple experimental inverted dispersive P-wave velocity results. These attributes can be directly applied to detect hydrocarbons. A synthetic data example and a real data example through a drilling well are used to demonstrate that PSO-based prestack stochastic inversion method with rock-physics constraints is effective, and that the statistical attributes derived from the multiple inverted dispersive P-wave velocities can be utilized to favorably indicate gas reservoirs.

Using ultrasonic wave reflection to monitor false set of cement paste

The standard mechanical penetration approach for monitoring cement paste stiffening (Vicat needle method, ASTM C191) does not distinguish responses associated with false set of cement paste caused by secondary gypsum formation. The objective of this research is to determine whether ultrasonic wave reflection, using a testing set up with high measurement sensitivity, could be used to monitor false set of cement paste. Penetration resistance, P-wave, and S-wave reflection coefficients were measured on cement pastes with water-to-cement ratio 0.5. The S-wave reflection coefficient showed a sharp and abrupt linear drop associated with secondary gypsum formation, thereby indicating that S-wave ultrasonic wave reflection can be used to monitor false set of cement pastes. False set could not be distinguished in penetration resistance or P-wave UWR test data.

Bayesian AVO inversion with consistent angle parameters

Amplitude versus offset (AVO) inversion has been extensively used in seismic exploration. Many different elastic parameters can be inverted by incorporating corresponding reflection coefficient approximations. Although efforts have been made to improve the accuracy of AVO inversions for years, there is still one problem that has long been ignored. In most methods, the angle in the approximation and the angle used in seismic angle gather extractions are not the same one. This inconsistency leads to inaccurate inversion results. In this paper, a Bayesian AVO inversion method with consistent angles is proposed to solve the problem and improve inversion accuracy. Firstly, a linearized P-wave reflection coefficient approximation with consistent angles is derived based on angle replacements. The equivalent form of the approximation in terms moduli and density is derived so that moduli can be inverted for reservoir characterization. Then, by convoluting it with seismic wavelets as the forward solver, a probabilistic prestack seismic inversion method with consistent angles is presented in a Bayesian scheme. The synthetic test proves that the accuracy of this method is higher than the traditional one. The real data example shows that the inversion result fits better with well log interpretation data, which verifies the feasibility of the proposed method.

The limits of narrow and wide-angle AVA inversions for high Vp/Vs ratios: An application to elastic seabed characterization

Since its introduction in the oil and gas industry, amplitude versus angle (AVA) inversion has become a standard tool in deep hydrocarbon exploration. However, with the intensification of offshore construction activity, applications of this method have been extended to evaluate the elastic properties of seabed sediments and of the shallowest part of the subsurface. These regions are often characterized by undercompacted sediments with very low S-wave velocities (Vs) and high P-wave velocity to S-wave velocity (Vp/Vs) ratios. However, the importance of the Vp/Vs ratio is usually underrated in AVA inversion. In this study, we analyse the limits of the AVA method in cases of high Vp/Vs ratios and the benefits introduced by wide-angle reflections in constraining the inversion results. A simplified seabed model that is characterized by a high Vp/Vs ratio is used to study the influence of the elastic and viscoelastic parameters on the P-wave reflection coefficients and to compute the error function of the AVA inversion. In addition, a synthetic AVA inversion is performed on this simplified model, which enables us to apply the sensitivity analysis tools to the inversion kernel. These theoretical analyses show that in the case of high Vp/Vs ratios, the Vs contrast at the reflecting interface plays a very minor role in determining the P-wave reflection coefficients and that the viscoelastic effects can be neglected when only pre-critical angles are considered in the inversion. In addition, wide-angle reflections are essential to reducing both the cross-talk between the inverted elastic parameters and the uncertainties in the Vp and density estimations, but they are not sufficient to better constrain the Vs estimation. As an application to field data, we derive the elastic properties of the seabed interface by applying AVA inversion to a 2D seismic dataset from a well-site survey acquisition. The limited water depth, the maximum available source-to-receiver offset, and the high frequency content of the data allow two different ranges of incidence angles to be considered: 0–30° and 0–60°. The results of the field data inversion confirm the conclusions from the theoretical analysis.