Zhaoyun Zong

Elastic impedance variation with angle inversion for elastic parameters

Elastic impedance (EI) and amplitude variation with offset or angle (AVO/AVA) inversion are two cardinal methods to estimate elastic parameters underground with reflection seismic data. Conventional EI inversion as a kind of pre-stack and post-stack joint inversion method has been widely applied in the industry because of its high efficiency and high stability of wavelet extraction; however, the robustness of extracting elastic parameters in conventional EI inversion is still controversial. The robustness of three-term AVO inversion has improved a lot; however, it is still challenging to extract reasonable space variant wavelets for each offset or incident angle. In this paper, a robust three-parameter estimation method, named elastic impedance variation with angle (EVA) inversion, is proposed in the Bayesian framework, which can estimate elastic parameters directly from EI. This method supposes that the parameters to be inverted are Cauchy distributed and it is implemented based on a normalized EI equation in a logarithmic domain which can reduce the nonlinearity of inversion. Application of a covariance matrix to decorrelate the parameters and constraint of well log curves introduced in an objective function enhances the robustness of EVA inversion. A model test shows that the proposed EVA inversion method enables one to estimate reasonable elastic parameters with extremely smooth initial models and moderate Gaussian noise. A real data example shows that the inverted P-wave velocity, S-wave velocity and density are identical to well log interpretation results, which shows the validity of the proposed method.

Improving seismic interpretation: a high-contrast approximation to the reflection coefficient of a plane longitudinal wave

Linearized approximations of reflection and transmission coefficients set a foundation for amplitude versus offset (AVO) analysis and inversion in exploration geophysics. However, the weak properties contrast hypothesis of those linearized approximate equations leads to big errors when the two media across the interface vary dramatically. To extend the application of AVO analysis and inversion to high contrast between the properties of the two layers, we derive a novel nonlinearized high-contrast approximation of the PP-wave reflection coefficient, which establishes the direct relationship between PP-wave reflection coefficient and P-wave velocities, S-wave velocities and densities across the interface. (A PP wave is a reflected compressional wave from an incident compressional wave (P-wave).) This novel approximation is derived from the exact reflection coefficient equation with Taylor expansion for the incident angle. Model tests demonstrate that, compared with the reflection coefficients of the linearized approximations, the reflection coefficients of the novel nonlinearized approximate equation agree with those of the exact PP equation better for a high contrast interface with a moderate incident angle. Furthermore, we introduce a nonlinear direct inversion method utilizing the novel reflection coefficient equation as forward solver, to implement the direct inversion for the six parameters including P-wave velocities, S-wave velocities, and densities in the upper and lower layers across the interface. This nonlinear inversion algorithm is able to estimate the inverse of the nonlinear function in terms of model parameters directly rather than in a conventional optimization way. Three examples verified the feasibility and suitability of this novel approximation for a high contrast interface, and we still could estimate the six parameters across the interface reasonably when the parameters in both media across the interface vary about 50%.

Geofluid Discrimination Incorporating Poroelasticity and Seismic Reflection Inversion

Geofluid discrimination plays an important role in the fields of hydrogeology, geothermics, and exploration geophysics. A geofluid discrimination approach incorporating linearized poroelasticity theory and pre-stack seismic reflection inversion with Bayesian inference is proposed in this study to identify the types of geofluid underground. Upon the review of the development of different geofluid indicators, the fluid modulus is defined as the geofluid indicator mainly affected by the fluid contained in reservoirs. A novel linearized P-wave reflectivity equation coupling the fluid modulus is derived to avoid the complicated nonlinear relationship between the fluid modulus and seismic data. Model examples illustrate the accuracy of the proposed linearized P-wave reflectivity equation comparing to the exact P-wave reflectivity equation even at moderate incident angle, which satisfies the requirements of the parameter estimations with P-wave pre-stack seismic data. Convoluting this linearized P-wave reflectivity equation with seismic wavelets as the forward solver, a pragmatic pre-stack Bayesian seismic inversion method is presented to estimate the fluid modulus directly. Cauchy and Gaussian probability distributions are utilized for prior information of the model parameters and the likelihood function, respectively, to enhance the inversion resolution. The preconditioned conjugate gradient method is coupled in the optimization of the objective function to weaken the strong degree of correlation among the four model parameters and enhance the stability of those parameter estimations simultaneously. The synthetic examples demonstrate the feasibility and stability of the proposed novel seismic coefficient equation and inversion approach. The real data set illustrates the efficiency and success of the proposed approach in differentiating the geofluid filled reservoirs.

Direct inversion for a fluid factor and its application in heterogeneous reservoirs

ABSTRACT Prestack seismic inversion plays an important role in estimating elastic parameters that are sensitive to reservoirs and fluid underground. In this paper, a simultaneous inversion method named FMR‐AVA (Fluid Factor, Mu (Shear modulus), Rho (Density)‐Amplitude Variation with Angle) is proposed based on partial angle stack seismic gathers. This method can be used for direct inversion for the fluid factor, shear modulus and density of heterogeneous reservoirs. Firstly, an FMR approximation equation of a reflection coefficient is derived based on poroelasticity with P‐ and S‐wave moduli. Secondly, a stable simultaneous AVA inversion approach is presented in a Bayesian scheme. This approach has little dependence on initial models. Furthermore, it can be applied in heterogeneous reservoirs whose initial models for inversion are not easy to establish. Finally, a model test shows the superiority of this FMR‐AVA inversion method in stability and independence of initial models. We obtain a reasonable fluid factor, shear modulus and density even with smooth initial models and moderate Gaussian noise. A real data case example shows that the inverted fluid factor, shear modulus and density fit nicely with well log interpretation results, which verifies the effectiveness of the proposed method.

Pre-stack basis pursuit seismic inversion for brittleness of shale

Brittleness of rock plays a significant role in exploration and development of shale gas reservoirs. Young’s modulus and Poisson’s ratio are the key parameters for evaluating the rock brittleness in shale gas exploration because their combination relationship can quantitatively characterize the rock brittleness. The high-value anomaly of Young’s modulus and the low-value anomaly of Poisson’s ratio represent high brittleness of shale. The technique of pre-stack amplitude variation with angle inversion allows geoscientists to estimate Young’s modulus and Poisson’s ratio from seismic data. A model constrained basis pursuit inversion method is proposed for stably estimating Young’s modulus and Poisson’s ratio. Test results of synthetic gather data show that Young’s modulus and Poisson’s ratio can be estimated reasonably. With the novel method, the inverted Young’s modulus and Poisson’s ratio of real field data focus the layer boundaries better, which is helpful for us to evaluate the brittleness of shale gas reservoirs. The results of brittleness evaluation show a good agreement with the results of well interpretation.

Seismic wave scattering inversion for fluid factor of heterogeneous media

Elastic wave inverse scattering theory plays an important role in parameters estimation of heterogeneous media. Combining inverse scattering theory, perturbation theory and stationary phase approximation, we derive the P-wave seismic scattering coefficient equation in terms of fluid factor, shear modulus and density of background homogeneous media and perturbation media. With this equation as forward solver, a pre-stack seismic Bayesian inversion method is proposed to estimate the fluid factor of heterogeneous media. In this method, Cauchy distribution is utilized to the ratios of fluid factors, shear moduli and densities of perturbation media and background homogeneous media, respectively. Gaussian distribution is utilized to the likelihood function. The introduction of constraints from initial smooth models enhances the stability of the estimation of model parameters. Model test and real data example demonstrate that the proposed method is able to estimate the fluid factor of heterogeneous media from pre-stack seismic data directly and reasonably.

AVO inversion based on inverse operator estimation in trust region

Amplitude variation with offset (AVO) inversion is widely utilized in exploration geophysics, especially for reservoir prediction and fluid identification. Inverse operator estimation in the trust region algorithm is applied for solving AVO inversion problems in which optimization and inversion directly are integrated. The L1 norm constraint is considered on the basis of reasonable initial model in order to improve effciency and stability during the AVO inversion process. In this study, high-order Zoeppritz approximation is utilized to establish the inversion objective function in which variation of with time is taken into consideration. A model test indicates that the algorithm has a relatively higher stability and accuracy than the damp least-squares algorithm. Seismic data inversion is feasible and inversion values of three parameters () maintain good consistency with logging curves.

Joint AVO inversion in the time and frequency domain with Bayesian interference

Amplitude variations with offset or incident angle (AVO/AVA) inversion are typically combined with statistical methods, such as Bayesian inference or deterministic inversion. We propose a joint elastic inversion method in the time and frequency domain based on Bayesian inversion theory to improve the resolution of the estimated P- and S-wave velocities and density. We initially construct the objective function using Bayesian inference by combining seismic data in the time and frequency domain. We use Cauchy and Gaussian probability distribution density functions to obtain the prior information for the model parameters and the likelihood function, respectively. We estimate the elastic parameters by solving the initial objective function with added model constraints to improve the inversion robustness. The results of the synthetic data suggest that the frequency spectra of the estimated parameters are wider than those obtained with conventional elastic inversion in the time domain. In addition, the proposed inversion approach offers stronger antinoising compared to the inversion approach in the frequency domain. Furthermore, results from synthetic examples with added Gaussian noise demonstrate the robustness of the proposed approach. From the real data, we infer that more model parameter details can be reproduced with the proposed joint elastic inversion.

Resolution enhancement of robust Bayesian pre-stack inversion in the frequency domain

AVO/AVA (amplitude variation with an offset or angle) inversion is one of the most practical and useful approaches to estimating model parameters. So far, publications on AVO inversion in the Fourier domain have been quite limited in view of its poor stability and sensitivity to noise compared with time-domain inversion. For the resolution and stability of AVO inversion in the Fourier domain, a novel robust Bayesian pre-stack AVO inversion based on the mixed domain formulation of stationary convolution is proposed which could solve the instability and achieve superior resolution. The Fourier operator will be integrated into the objective equation and it avoids the Fourier inverse transform in our inversion process. Furthermore, the background constraints of model parameters are taken into consideration to improve the stability and reliability of inversion which could compensate for the low-frequency components of seismic signals. Besides, the different frequency components of seismic signals can realize decoupling automatically. This will help us to solve the inverse problem by means of multi-component successive iterations and the convergence precision of the inverse problem could be improved. So, superior resolution compared with the conventional time-domain pre-stack inversion could be achieved easily. Synthetic tests illustrate that the proposed method could achieve high-resolution results with a high degree of agreement with the theoretical model and verify the quality of anti-noise. Finally, applications on a field data case demonstrate that the proposed method could obtain stable inversion results of elastic parameters from pre-stack seismic data in conformity with the real logging data.

Reliability enhancement of mixed-domain seismic inversion with bounding constraints

ABSTRACT Seismic inversion works as one of pragmatic and effective approaches to estimate the subsurface parameters. One robust Bayesian sparse inversion method incorporating the mixed-domain convolution with model bounding constraints is proposed in this study. The time-domain response and partial frequency components are utilized in mixed-domain seismic inversion to improve the resolution and stability of seismic inversion. First, the objective updated function is yielded with Bayesian inference in joint time and frequency domain. And, the sparse constraint is incorporated into the objective function to improve robustness of inversion algorithm. Conventional seismic inversion methods always don’t focus on the lower and upper bounding constraints on subsurface model parameters, due to which unrealistic predicted results may arise. To get rid of the problem, the bounding constraints on P-wave impedance elaborated by logarithmic or inverse hyperbolic tangent formulas is introduced in mixed-domain seismic inversion as it renders to reduce the unrealistic parameters and enhance the reliability of prediction effectively. In addition, the synthetic examples demonstrate the effectiveness and robustness of the proposed inversion algorithm. Finally, one field case is studied carefully and the estimated parameters with bounding constraints at the borehole-side location can preserve a high degree of agreements with real logging data to verify the practicability of the bounding-constraining mixed-domain Bayesian inversion.