Guochen Wu

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.

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.

Estimation of Layer Quality Factors From Pre-stack Seismic Data

Summary Pre-stack seismic data have a more detailed stratigraphic information than the post-stack seismic data. Some fine stratigraphic features in the post-stack seismic data is not visible. Based on this, this paper puts forward the modified spectral ratio method of earth layer absorption parameters extraction based on pre-stack data by using spectrum decomposition technology, by which we could adequately consider changes of seismic waves affected by earth layer absorption in time-frequency domain, also avoid the average effect of the absorption coefficient of the usual calculation, making earth layer absorption parameters extraction more accurately and more applicable. Meanwhile, it will be better to make appropriate preprocessing to improve the noise ratio of seismic data before the work, and the processing of return-to-zero is done to achieve absorption parameters at zero offset so as to realize the inherent attenuation study of layer media truly. The result shows that the method of extracting attenuation parameters discussed in this paper are feasible and effective.

Robust AVO inversion for elastic modulus and its application in fluid factor calculation

Fluid factor based on Biot-Gassmann equation plays an important role in reservoir fluid discrimination. We present a method to calculate fluid factor without density information and only with elastic modulus (P-wave and Swave modulus) inverted by nonlinear AVO inversion based on a novel zoeppritz approximation equation. A practical and robust nonlinear AVO inversion technique is developed in Bayesian framework. The objective is to obtain the maximum a posteriori (MAP) solution for Pwave modulus, S-wave modulus and density. Gaussian and Cauchy distributions are explored for the likelihood and a priori probability distributions. The optimization problem results in weak nonlinear solutions, and the introduction of low frequency constraint and statistic probability information to the objective function enables the inversion more stable and less sensitive to initial model. Tests on synthetic data show that all the parameters can be estimated perfectly when no noise exists, and the estimated P-wave and S-wave modulus still be reasonable when the S/N ratio is as low as 1:2, even with rather smooth initial model parameters. However, the estimated density gives much bias just when the S/N ratio is 2:1 while utilizing the same constraint for all parameters. The inversion method has also been tested on a real data set. The inverted results show good agreement with well logs except the uncertain density information, and the fluid factor calculated from the inverted P-wave and S-wave modulus also show good agreement with drilling result.