Robust AVO inversion for the fluid factor and shear modulus

Seismic estimation of the fluid factor and shear modulus plays an important role in reservoir fluid identification and characterization. Various amplitude variation with offset inversion methods have been used to estimate these two parameters, which generally based on approximate formulations of the Zoeppritz equations. However, the accuracy of these methods is limited because the forward modeling ability of approximate equations is incorrect under the conditions of strong impedance contrast and large incidence angles. Therefore, to improve the estimation accuracy, we use the Zoeppritz equations to directly invert for the fluid factor and shear modulus. Based on poroelasticity theory, we derive the Zoeppritz equations in a new form containing the fluid factor, shear modulus, density and dry-rock velocity ratio squared. The objective function is then constructed using these equations in a Bayesian framework with the addition of a differentiable Laplace distribution blockiness constraint term to the prior model to enhance fluid boundaries. Finally, the nonlinear objective function is solved by combining the Taylor expansion and the iterative reweighed least-squares algorithm. Numerical experiments indicate that the inversion accuracy of the proposed method may heavily depends on the parameter of the dry-rock velocity ratio square that is assumed static. However, tests on synthetic and field data show that the proposed method can estimate the fluid factor and shear modulus with satisfactory accuracy in the case of choosing a reasonable static value of this parameter. In addition, we demonstrate that the accuracy of this method is higher than that of the linearized formulation.

An Adaptive Stratified Joint PP and PS AVA Inversion Using Accurate Jacobian Matrix

Amplitude variation with incidence angle (AVA) analysis is an essential tool for discriminating lithology in the hydrocarbon reservoirs. Compared with the traditional AVA inversion using only P-wave information, joint AVA inversion using PP and PS seismic data provides better estimation of rock properties (e.g., density, P- and S-wave velocities). At present, the most used AVA inversions depend on the approximations of Zoeppritz equations (e.g., Shuey and Aki-Richards approximations), which are not suitable for formations with strong contrast interfaces and seismic data with large incidence angles. Based on the previous derivation of accurate Jacobian matrix, we find that the sign of each partial derivative of reflection coefficient with respect to P-, S-wave velocities and density changes across the interface, represents good indicator for the reflection interfaces. Accordingly, we propose an adaptive stratified joint PP and PS AVA inversion using the accurate Jacobian matrix that can automatically obtain the layer information and can be further used as a constraint in the inversion of in-layer rock properties (density, P- and S-wave velocities). Due to the use of the exact Zoeppritz equations and accurate Jacobian matrix, this proposed inversion method is more accurate than traditional AVA inversion methods, has higher computational efficiency and can be applied to seismic wide-angle reflection data or seismic data acquired for formations with strong contrast interfaces. The model study shows that this proposed inversion method works better than the classical Shuey and Aki-Richards approximations at estimating reflection interfaces and in-layer rock properties. It also works well in handling a part of the complex Marmousi 2 model and real seismic data.

Nonlinear AVA Inversion Based on a Novel Quadratic Approximation for Fluid Discrimination

Fluid discrimination plays an important role in reservoir exploration and development. At present, the fluid factors used for fluid discrimination are estimated by linear AVA inversion methods based on the linear approximations of the Zoeppritz equations. However, the Zoeppritz equations show that the relationship between prestack AVA reflection coefficients and reservoir parameters is highly nonlinear. Therefore, inversion methods based on linear approximations will seriously influence the nonuniqueness and uncertainty of inversion results. In this paper, a nonlinear inversion based on the quadratic approximation is carried out to reduce the nonuniqueness and uncertainty of fluid factor. Firstly, in order to directly invert the fluid factor, a novel quadratic approximation in terms of the fluid factor ( ρ f ), shear modulus, and density on both sides of the reflection interface is derived based on poroelasticity theory. Then, a nonlinear inversion objective function is constructed using the novel quadratic approximation in a Bayesian framework, and the Gauss-Newton method is adopted to minimize this objective function. The synthetic data example shows that the new method can obtain reasonable fluid factor inversion results even in low SNR (signal-to-noise ratio) case. Finally, the proposed method is also applied to field data which shows that it can effectively discriminate reservoir fluids.

P-Wave Reflection Approximation of a Thin Bed and Its Application

“Thin-bed” reservoirs have become important targets of seismic exploration and exploitation. However, traditional amplitude versus offset/amplitude versus angle (AVO/AVA) technologies, for example, those based on Zoeppritz equations and their approximations for a single interface, are not sufficiently accurate for thin-bed stratigraphy. Analytic solutions of thin-bed reflectivity may become practical for thin-bed AVO analysis and inversion. Therefore, a linear analytic approximation of thin-bed P-wave reflectivity is developed under small-incidence and thin-bed assumptions. Numerical simulations show that the amplitude approximation errors are usually smaller than 10% for incidence angles less than 20 degrees, and the thin-bed thicknesses are less than one-tenth of the P-wave wavelength. Based on the least-squares approach, the inversion strategy is proposed using the approximate formula. A synthetic data test shows that the proposed inversion method can produce more accurate thin-bed properties than that based on the Zoeppritz equations, which reveals the potential of the inversion method based on the linear analytic approximate formula in the fine characterization of thin reservoirs.

Hamiltonian Monte Carlo algorithms for target- and interval-oriented amplitude versus angle inversions

A reliable assessment of the posterior uncertainties is a crucial aspect of any amplitude versus angle (AVA) inversion due to the severe ill-conditioning of this inverse problem. To accomplish this task, numerical Markov chain Monte Carlo algorithms are usually used when the forward operator is nonlinear. The downside of these algorithms is the considerable number of samples needed to attain stable posterior estimations especially in high-dimensional spaces. To overcome this issue, we assessed the suitability of Hamiltonian Monte Carlo (HMC) algorithm for nonlinear target- and interval-oriented AVA inversions for the estimation of elastic properties and associated uncertainties from prestack seismic data. The target-oriented approach inverts the AVA responses of the target reflection by adopting the nonlinear Zoeppritz equations, whereas the interval-oriented method inverts the seismic amplitudes along a time interval using a 1D convolutional forward model still based on the Zoeppritz equations. HMC uses an artificial Hamiltonian system in which a model is viewed as a particle moving along a trajectory in an extended space. In this context, the inclusion of the derivative information of the misfit function makes possible long-distance moves with a high probability of acceptance from the current position toward a new independent model. In our application, we adopt a simple Gaussian a priori distribution that allows for an analytical inclusion of geostatistical constraints into the inversion framework, and we also develop a strategy that replaces the numerical computation of the Jacobian with a matrix operator analytically derived from a linearization of the Zoeppritz equations. Synthetic and field data inversions demonstrate that the HMC is a very promising approach for Bayesian AVA inversion that guarantees an efficient sampling of the model space and retrieves reliable estimations and accurate uncertainty quantifications with an affordable computational cost.

Amplitude variation with offset inversion using acoustic-elastic local solver

Conventional amplitude variation with offset (AVO) inversion analysis uses the Zoeppritz equations, which are based on a plane-wave approximation. However, because real seismic data are created by point sources, wave reflections are better modeled by spherical waves than by plane waves. Indeed, spherical reflection coefficients deviate from planar reflection coefficients near the critical and postcritical angles, which implies that the Zoeppritz equations are not applicable for angles close to critical reflection in AVO analysis. Elastic finite-difference simulations provide a solution to the limitations of the Zoeppritz approximation because they can handle near- and postcritical reflections. We have used a coupled acoustic-elastic local solver that approximates the wavefield with high accuracy within a locally perturbed elastic subdomain of the acoustic full domain. Using this acoustic-elastic local solver, the local wavefield generation and inversion are much faster than performing a full-domain elastic inversion. We use this technique to model wavefields and to demonstrate that the amplitude from within the local domain can be used as a constraint in the inversion to recover elastic material properties. Then, we focus on understanding how much the amplitude and phase contribute to the reconstruction accuracy of the elastic material parameters ([Formula: see text], [Formula: see text], and [Formula: see text]). Our results suggest that the combination of amplitude and phase in the inversion helps with the convergence. Finally, we analyze elastic parameter trade-offs in AVO inversion, from which we find that to recover accurate P-wave velocities we should invert for [Formula: see text] and [Formula: see text] simultaneously with fixed density.

A new look at polarity information in D" reflections

<p>Polarities of seismic reflection of P and S-waves at the discontinuity at the top of  D" are usually assumed to indicate the sign of the velocity contrast across the D" reflector. For reflections in paleo-subduction regions the S-wave reflections off D" (SdS) are the same as ScS and S, indicating a positive velocity contrast at the reflector. In recent years, an opposite polarity of PdP waves (P-reflection at the D" discontinuity) has been observed in some regions, partly dependent on travel direction, partly dependent on distance. This would indicate a velocity reduction in P-waves where a velocity increase is detected in S-waves. This phenomenon can be explained with the presence of post-perovskite below the top of D", but azimuthal dependence of PdP polarities can be better explained with anisotropy. Here we re-analyse PdP and SdS wave polarities and, when modelling the polarities and amplitudes using Zoeppritz equations, we find that a ratio of dVs/dVp= R of larger than 3 reverses polarities of P-waves in the absence of anisotropy, i.e. we find a polarity of PdP that would point to a velocity decrease while modelling a velocity increase. The S-polarity stays the same as S and ScS and does not change even with large R. Values of R up to 4.1 have been reported recently, so these cases do exist in the lower mantle. Using a set of 1 million models with varying minerals and processes across the boundary, we carry out a statistical analysis (Linear Discriminant Analysis, LDA) and find that there is a marked difference in mantle mineralogy to explain R values larger and smaller than 3, respectively. The regime of cases with R-value larger than 3 is mostly due to an increase in MgO and post-perovskite across the discontinuity. In regions where high R is observed, alternate explanations of lowermost mantle composition versus anisotropy can then be tested by measuring polarities in different azimuths.</p>