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With the development of 5D (3D + offset + azimuth) seismic technology, the stable acquisition of anisotropy information from wide-azimuth seismic data has become a key scientific problem in the seismic inversion of fractured reservoirs. The amplitude variation with incidence and azimuth (AVAZ) inversion method using wide-azimuth seismic data is an effective way to predict the anisotropic information of the subsurface medium. However, the conventional AVAZ inversion method suffers from too many parameters to be estimated, large variation in contribution, and inversion instability. Therefore, an AVAZ inversion method with coherence-attribute constraints is developed to solve the problem of unstable inversion of anisotropic parameters. First, we use seismic coherence attributes to build a fracture-probability-distribution model containing anisotropic information of the subsurface medium, which can be used to simulate large-scale subsurface fractures and faults. Then, it is added to the objective function as an anisotropic information constraint to improve the reliability and stability of the anisotropic inversion. Furthermore, an AVAZ inversion method in a Bayesian framework is implemented by using wide-azimuth seismic data. Gaussian distribution and a smoothing background model are added to the objective function to improve the reasonableness and stability of the inversion. In addition, we develop a stepwise optimization inversion method for isotropic and anisotropic parameters, prioritizing the inversion of parameters that contribute significantly to the reflection coefficient, and then using the results of the previous inversion as the initial values for the next inversion step to achieve multiparameter inversion. This method can reduce the number of the estimated parameters and thus improve the stability of the inversion of the anisotropic parameters. Field data examples indicate that this method produces suitable inversion results even at moderate levels of noise. Therefore, we can conclude that the proposed method has good applicability and stability in predicting the anisotropy parameters of fractured shale reservoirs.

Undercompaction and hydrocarbon generation are the main factors affecting pore pressure. The current seismic pore-pressure prediction (PPP) method is to obtain the overpressure trend by estimating the normal compaction trend (NCT) to predict the physical parameters during normal compaction and comparing the measured parameters. However, selecting a single parameter to indicate overpressure may cause insufficient consideration of factors, such as hydrocarbon generation. Because hydrocarbon generation requires specific temperature and other conditions, pore pressure is divided into two parts: undercompaction in the early stage and hydrocarbon generation after reaching the hydrocarbon generation threshold. A rock-physical model is established for estimating the NCT before hydrocarbon generation to modify the bulk modulus of the model and calculate the pressure generated by undercompaction; the pressure generated by hydrocarbon generation is added to obtain the final pore pressure. In the shale gas work area in the Sichuan Basin, the prediction results are more in line with the actual situation, and the petrophysical analysis indicates that the ratio of free hydrocarbon content and kerogen to water is the influencing factor indicating pore pressure. The practicality of the PPP formula considering hydrocarbon generation in oil and gas sweet spots is illustrated through an example in the research area.

Identification and prediction of high-quality source rocks is the key to obtaining new resources in the exploration area of Cenozoic basins in offshore China. We research the seismic response and distribution of hydrocarbon source rocks using seismic data, well curves, lithologic interpretation, and geochemical analysis. The target is the source rock development zone of the W Formation in a survey of the South China Sea. The results show that the seismic response of thick layer source rocks differ from surrounding rocks in the seismic profile (strong reflections with opposite polarity at the top and bottom and messy or chaotic reflections inside). Seismic reflections of interlayer source rocks have the characteristics of low frequency and continuous strong amplitude. The dominant frequency and maximum amplitude decrease as the number of mudstone layers increases. Through seismic petrophysical analysis, we have obtained three sensitive parameters of source rock in this survey: clay content, P-wave impedance, and elastic impedance. Different classification methods can realize the classification and prediction of hydrocarbon source rocks, among which the Kernel Fisher discriminant analysis method is the best. The prediction results are consistent with the geological background, geochemical information, and well curves.

The estimation of physical and anisotropic parameters is of great importance for the characterization of fractured reservoirs. Vertical fractures developing in a laterally isotropic (VTI) setting are equivalent to orthotropic anisotropic (OA) media common in stratified fractured shale reservoirs. To obtain independent anisotropic and physical information, a novel reflection coefficient approximation containing physical and anisotropic parameters is derived to improve the stability of the inversion for orthotropic media. To simplify the equation for the reflection coefficient, an approximate rock physics model is constructed using the approximate theory of rock modulus. The estimated parameters are reduced from nine to six. The accuracy analysis reveals that the new reflection coefficient is appropriate and suitable for inversion. In addition, a stepwise Bayesian amplitude versus angle and azimuth (AVAZ) inversion method with smooth background constraints is developed to estimate the anisotropic and physical parameters from the azimuthal seismic data. The smooth background constraint improves the robustness of the inversion. And the stepwise inversion strategy solves the problem that the contribution of the fracture parameter to the reflection coefficient is smaller than the other parameters. Synthetic cases show that the proposed stepwise Bayesian AVAZ inversion method is feasible in estimating the anisotropic parameters for OA media even when the signal-to-noise ratio is 2. The field cases show that the proposed inversion method has good stability and robustness in predicting shale reservoirs with vertical or near-vertical fractures.

Lithology discrimination plays an important role in characterizing deep-hydrocarbon reservoirs, particularly for tight sandstones with special petrophysical properties. Stable prediction of lithological-sensitive parameters for deep tight sandstones is a significant challenge. In this paper, a direct inversion method of elastic impedance is developed to estimate lithological-sensitive parameters from pre-stack seismic data to improve the stability of the inversion. Elastic and physical parameter models extracted from actual wells are used to analyze the influence of petrophysical parameters on amplitude variation with offset characteristics. Cross-plots and sensitivity analysis of elastic parameters illustrate that the elastic-sensitive parameter Poisson impedance (PI) can distinguish gas-bearing sandstone and abnormal limestone in deep tight-sandstone reservoirs. In addition, a pragmatic elastic impedance direct inversion under the framework of Bayesian theory is implemented for the lithology indicator PI from pre-stack seismic data. And the Cauchy regularization and low-frequency regularization constraints are used to construct the objective function for improving the robustness of inversion. Field data examples show that the inversion results are in good agreement with the well logging interpretation results, and validate the feasibility and stability of the proposed method in the estimation of inverted parameters. Finally, we can conclude that this method has great application potential in the lithology discrimination of deep tight-sandstone reservoirs.

Joint inversion of seismic amplitude and frequency information for fluid discrimination works as a popular approach for reservoir fluid identification. However, ignorance of the factor caused by fluid flow and the viscosity of oil and gas in current frequency-dependent inversion approaches leads to the inaccuracy of oil and gas prediction. Therefore, based on squirt flow and viscoelastic theory, a new frequency-dependent viscoelastic squirt-flow fluid factor is established, which is compared with other conventional fluid factors to verify its advantages in fluid detection. In addition, a new linearized reflectivity equation related to frequency-dependent viscoelastic squirt-flow fluid factor is derived. Finally, to verify the feasibility of the new fluid factor in predicting oil/gas, a frequency-dependent elastic impedance inversion method is introduced. Synthetic data and field data examples find that frequency-dependent viscoelastic squirt-flow fluid factor can eliminate the interference of “false bright spots” in conventional fluid factors inversion and has a higher vertical resolution, which demonstrated the effectiveness and stability of our method in fluid prediction.

Geofluid identification from seismic data are crucial for understanding reservoir characteristics. However, fluid indicators based on elastic parameter combinations show strong ambiguity in terms of geofluid identification. Although the effective pore-fluid bulk modulus proves to be the superior fluid indicator in geofluid discrimination, it is limited to empirical models such as the critical porosity model. The consolidation parameter model can evaluate the consolidation and compaction of sediments and is widely used due to its better applicability. Therefore, a novel fluid indicator considering consolidation parameter is proposed and a boundary-constrained inversion strategy for geofluid identification is developed. First, the novel fluid indicator is defined based on the poroelasticity theory. Then, the linearized AVA (amplitude variation with angle) approximation equation related to the new fluid indicator is derived to directly link seismic data and properties of pore-filling materials. The model analysis verifies the accuracy of the derived approximation equation at moderate incident angles, which can be used for parameter prediction by pre-stack seismic inversion. Furthermore, the contribution of each attribute of the novel equation to the reflectivity is analyzed to validate the feasibility of new fluid indicator inversion. Finally, a boundary-constrained AVA pre-stack inversion method is presented to enhance the robustness of the inversion results of the model parameter. The reliability of the improved method is proved by accurate inversion results of synthetic seismic records. After determining the consolidation parameter using well-log data combined with BGT (Biot–Gassmann Theory), the field data further demonstrated that the proposed approach is accurate and effective.

Young’s modulus and Poisson ratio are essential parameters for rock brittleness evaluation. At present, prestack inversions of these parameters mostly adopt linear approximation, whereas the nonlinear inversion methods that are based on the exact Zoeppritz equation are seldomly conducted. Nevertheless, in the case of large incident angles and high-impedance contrast, the nonlinear equation has higher accuracy than the linear approximation. It is more in line with the nature of geophysical inversion problems, and it describes the variation of formations’ elastic parameters better than the linear approximation does. Therefore, based on the exact solution of the Zoeppritz equation, we have parameterized and derived a new nonlinear reflection coefficient equation using nonlinear Young’s modulus, Poisson ratio, and density (YPD) as variables. Subsequently, by combining the inverse operator algorithm with the YPD equation, we develop a new nonlinear amplitude-variation-with-offset inversion scheme. This approach can robustly extract Young’s modulus and Poisson ratio from seismic data and identify shale-gas sweet spot locations within the reservoir, as well as predict reservoir fluid properties. We have tested the accuracy and applicability of this approach with synthetic and real data examples.

The delineation of shale oil sweet spots is a crucial step in the exploration of shale oil reservoirs. A single attribute such as total organic carbon (TOC) is conventionally used to evaluate the sweet spots of shale oil. This study proposes a probabilistic Fisher discriminant approach for estimating shale oil sweet spots, in which the probabilistic method and Gaussian mixture model are incorporated. Statistical features of shale oil facies are obtained based on the well log interpretation of the samples. Several key parameters of shale oil are projected to data sets with low dimensions in each shale oil facies. Furthermore, the posterior distribution of different shale oil facies is built based on the classification of each shale oil facies. Various key physical parameters of shale oil facies are inversed by the Bayesian method, and important elastic properties are extracted from the elastic impedance inversion (EVA-DSVD method). The method proposed in this paper has been successfully used to delineate the sweet spots of shale oil reservoirs with multiple attributes from the real pre-stack seismic data sets and is validated by the well log data.

The estimation of petrophysical and fluid-filling properties of subsurface reservoirs from seismic data is a crucial component of reservoir characterization. Seismic amplitude-variation-with-offset (AVO) inversion driven by rock physics is an effective approach to characterize reservoir properties. In general, PP-wave reflection coefficients, elastic moduli, and petrophysical parameters are nonlinearly coupled, especially in multiple-type pore-space reservoirs, which makes seismic AVO petrophysics inversion ill-posed. We have developed a new approach that combines Biot-Gassmann’s poroelasticity theory with Russell’s linear AVO approximation, to estimate the reservoir properties including elastic moduli and petrophysical parameters based on multitrace probabilistic AVO inversion algorithm. We first derive a novel PP-wave reflection coefficient formulation in terms of porosity, stiff-pore volume fraction, rock-matrix shear modulus, and fluid bulk modulus to incorporate the effect of pore structures on elastic moduli by considering the soft and stiff pores with different aspect ratios in sandstone reservoirs. Through the analysis of the four types of PP-wave reflection coefficients, the approximation accuracy and inversion feasibility of the derived formulation are verified. Our stochastic inversion method aims to predict the posterior probability density function in a Bayesian setting according to a prior Laplace distribution with vertical correlation and prior Gaussian distribution with lateral correlation of model parameters. A Metropolis-Hastings stochastic sampling algorithm with multiple Markov chains is developed to simulate the posterior models of porosity, stiff-pore volume fraction, rock-matrix shear modulus, and fluid bulk modulus from seismic AVO gathers. The applicability and validity of our inversion method is illustrated with synthetic examples and a real data application.

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.

Time–frequency analysis of the nonstationary signals is one of the hot researches in geophysics, environmental science, geology, and other fields. Matching pursuit (MP) has been widely used to reveal the characteristics in time–frequency domain, which helps to study the changes and differences of subtle geological structures. Compared with traditional time–frequency analysis methods, MP has higher time–frequency resolution. The synchrosqueezing transforms (SSTs) have been proven to be an effective methodology to improve the time–frequency resolution by squeezing and redistributing the time–frequency coefficients in the frequency direction. Considering the superiority of the SSTs, this letter proposes a novel time–frequency analysis method called synchrosqueezing MP to enhance the energy aggregation of the time–frequency plane. The proposed method can squeeze the time–frequency distribution into near the center time and frequency of the selected wavelet by a 2-D Gaussian function. We used synthetic and field seismic data to demonstrate the feasibility of our method. The results prove the superiority of our method in describing reservoir boundaries.

Horizontal layered formations with a suite of vertical or near-vertical fractures are usually assumed to be an approximate orthotropic medium and are more suitable for estimating fracture properties with wide-azimuth prestack seismic data in shale reservoirs. However, the small contribution of anisotropic parameters to the reflection coefficients highly reduces the stability of anisotropic parameter estimation by using seismic inversion approaches. Therefore, a novel model parameterization approach for the reflectivity and a pragmatic inversion method are proposed to enhance the stability of the inversion for orthotropic media. Previous attempts to characterize orthotropic media properties required using four or five independent parameters. However, we have derived a novel formulation that reduces the number of parameters to three. The inversion process is better conditioned with fewer degrees of freedom. An accuracy comparison of our formula with the previous ones indicates that our approach is sufficiently precise for reasonable parameter estimation. Furthermore, a Bayesian inversion method is developed that uses the amplitude variation with angle and azimuth (AVAZ) of the seismic data. Smooth background constraints reduce the similarity between the inversion result and the initial model, thereby reducing the sensitivity of the initial model to the inversion result. Cauchy and Gaussian probability distributions are used as prior constraints on the model parameters and the likelihood function, respectively. These ensure that the results are within the range of plausibility. Synthetic examples demonstrate that the adopted orthotropic AVAZ inversion method is feasible for estimating the anisotropic parameters even with moderate noise. The field data example illustrates the inversion robustness and stability of the adopted method in a fractured reservoir with a single well control.

SUMMARY The plane-wave reflection coefficient (PRC) plays a remarkable role in conventional amplitude variation with offset (AVO) analysis and inversion. Compared with the widely exploited PRC that breaks down at the near- and supercritical incidence angles, the spherical-wave reflection coefficient (SRC) can overcome the influence of wide-angle reflection and give an accurate description of the actual seismic wave reflection phenomenon based on spherical-wave fronts. However, SRC is not widely used in AVO inversion due to its nonlinearity and computational complexity. In our study, the characteristics of frequency–depth-dependent monochromatic SRC are discussed and a novel three-parameter SRC is derived. Compared with the conventional six-parameter SRC, the novel three-parameter SRC improves the stability of spherical-wave AVO inversion. In addition, the concept of SRC within the Fresnel zone is proposed, and the accuracy of SRC within the Fresnel zone in the deep subsurface is tested. Finally, a nonlinear spherical-wave AVO inversion method for elastic media is proposed, which can make full use of all frequency components of wavelet. The robustness of the proposed method is verified by the application on synthetic seismogram with white Gaussian noise. The feasibility and practicability of this method are verified by comparing the spherical-wave AVO inversion results with the filtered well logs at the known well location.

With the continuous petroleum exploration around the world, the target of exploration is converting from conventional to deep, unconventional reservoirs. The pressure condition on those new target layers is different from the conventional reservoir, and pressure is one of the important factors affecting the elastic moduli and velocities of shale reservoirs. Therefore, it is necessary to take pressure effects into consideration in rock-physics modeling. We initially adopted a novel iterative rock-physical modeling approach on the basis of pore space stiffness theory to analyze pressure’s influence on shale. Pore space stiffness theory assumes that pores own their own stiffness like the solid matrix of rocks, which is related to the effective pressure. We have implemented plenty of numerical analysis on the effect of pressure on shale and found out the most contributive factor to the moduli and velocities of shale. Our result indicates that when the effective pressure is smaller than the critical value, the elastic moduli and elastic wave velocities of shale increase significantly with the increase of effective pressure. The elastic moduli and velocities tend to be constant when the effective pressure goes beyond that critical value. By comparison, we found that the most contributive mineral in shale is clay, and the porosity has the greatest effect on elastic moduli and velocities when the mineral composition of shale stays unchanged. The influence of pressure is not as obvious as other factors in shale reservoirs with low porosity (lower than 10%) because pores occupy a relatively small percentage of the total volume.

Hydrocarbon reservoirs often contain partially gas-saturated rocks that have attracted the attention of exploration geophysicists and geologists for many years. Wave-induced fluid flow (WIFF) is an effective mechanism to quantify seismic wave dispersion and attenuation in partially gas-saturated rocks. In this study, we focus on the local fluid flow induced by variations in fluids in different regions and present a new model that describes seismic wave propagation in partially gas-saturated rocks, namely, the cylindrical patchy-saturation model. Because the seismic wave velocity and attenuation oscillate at high frequencies, it is not ideal for studying dispersion and attenuation caused by WIFF. To avoid the high-frequency oscillation in the cylindrical patchy-saturated model, we use an approximation to the Newman function instead of the full Newman function to calculate the effective bulk modulus. We then calculate the P-wave velocity and attenuation of the proposed model and interpret the lab-measured data. The proposed model is an alternative patchy-saturation model that can explain the problem of high-frequency oscillation and low-frequency attenuation.

Seismic inversion is an important tool that transfers interface information of seismic data to formation information, which renders the seismic data easily understood by geologists or petroleum engineers. In this study, a novel multi‐trace basis‐pursuit inversion method based on the Bayesian theory is proposed to enhance the vertical resolution and overcome the lateral instability of inversion results between different traces occasionally seen in the traditional trace‐by‐trace basis‐pursuit inversion method. The Markov process is initially introduced to describe the relationship between adjacent seismic traces and their correlation, which we then close couple in the equation of our new inversion method. A recursive function is further derived to simplify the inversion process by considering the particularity of the coefficient matrix in the multi‐trace inversion equation. A series of numerical‐analysis and field data examples demonstrates that both the traditional and the new methods for P‐wave impedance inversion are helpful in enhancing the resolution of thin beds that are usually difficult to discern from original seismic profiles, thus highlighting the importance of acoustic‐impedance inversion for thin bed interpretation. Furthermore, in addition to yielding thin bed inversion results with enhanced lateral continuity and high vertical resolution, our proposed method is robust to noise and cannot be easily contaminated by it, which we verify using both synthetic and field data.

Rock physical model and amplitude variation with offset (AVO) patterns considering the content of organic matter and the composition of minerals have a wider significance for guiding the identification and prediction of the mud-rich source rock. A rock physical model is proposed for describing the elastic properties of kerogen in different maturity stages. The proposed rock physical model builds an intrinsic connection between the elastic properties and physical parameters of the mud-rich source rock, thereby providing a theoretical basis for a seismic inversion and a seismic forward modeling. To overcome the limitations of laboratory measurement, a combination-four-parameter regression (CFPR) method is further proposed to estimate the continuous total organic carbon (TOC) values for the verification and analysis of the rock physical model. The modeling results reveal that the P-wave velocity and P-wave impedance will decrease with an increase in TOC, and the Poisson ratio and Poisson impedance will increase as the mud content increases, which are consistent with the conclusions of the cross plot using the actual well data. Based on the proposed rock physical model, the seismic responses of the mud-rich source rock are further modeled. The synthetic seismic records are consistent with the well-side seismic records, the top reflection of the mud-rich source rock behaves as a stronger negative event dimming with an incident angle corresponding to a class IV AVO pattern, and the bottom reflection exhibits a class I AVO anomaly. In addition, a two-layer model is constructed to analyze an effect of the TOC content and mud content on the AVO characteristics. The results indicate that increasing the TOC content and mud content will significantly increase the interceptions and slightly change the gradients of the P-P reflection coefficients. These results help to guide the identification and evaluation of the mud-rich source rock.

This study focuses on developing a pragmatic and robust method in the estimation of fracture orientation assuming a single set of aligned fractures. The Young’s modulus in the direction of fracture orientation is larger than that in the perpendicular direction that helps to solve the problem of the ambiguity in fracture-orientation estimation existing in the method of using the variation of amplitude-variation-with-offset (AVO) gradients with azimuth. First, the relationship between the Young’s modulus and fracture density and orientation is analyzed. The Young’s modulus changes regularly with the variation of incident angles and azimuth, and the changing track is a cosine curve when the incident angle is fixed. The variation of the Young’s modulus increases with the increase of fracture density. Second, we use the Young’s modulus variation with azimuth to predict the fracture orientation. The Young’s modulus inversion algorithm for different azimuths of prestack seismic data and the ellipse fitting of the Young’s moduli in different azimuth with the least-squares algorithm are included in this proposed approach. Finally, we determine the advantage and robustness of our method in fracture-orientation estimation with synthetic and real-data examples. Compared with the conventional methods using AVO gradients, the direction of longer axis of the fitting ellipse of the Young’s modulus in different azimuth indicates the fracture orientation without ambiguity.

Seismic inversion performed in the time or frequency domain cannot always recover the long-wavelength background of subsurface parameters due to the lack of low-frequency seismic records. Since the low-frequency response becomes much richer in the Laplace mixed domains, one novel Bayesian impedance inversion approach in the complex Laplace mixed domains is established in this study to solve the model dependency problem. The derivation of a Laplace mixed-domain formula of the Robinson convolution is the first step in our work. With this formula, the Laplace seismic spectrum, the wavelet spectrum and time-domain reflectivity are joined together. Next, to improve inversion stability, the object inversion function accompanied by the initial constraint of the linear increment model is launched under a Bayesian framework. The likelihood function and prior probability distribution can be combined together by Bayesian formula to calculate the posterior probability distribution of subsurface parameters. By achieving the optimal solution corresponding to maximum posterior probability distribution, the low-frequency background of subsurface parameters can be obtained successfully. Then, with the regularization constraint of estimated low frequency in the Laplace mixed domains, multi-scale Bayesian inversion in the pure frequency domain is exploited to obtain the absolute model parameters. The effectiveness, anti-noise capability and lateral continuity of Laplace mixed-domain inversion are illustrated by synthetic tests. Furthermore, one field case in the east of China is discussed carefully with different input frequency components and different inversion algorithms. This provides adequate proof to illustrate the reliability improvement in low-frequency estimation and resolution enhancement of subsurface parameters, in comparison with conventional Bayesian inversion in the frequency domain.

Prestack seismic inversion is widely used in fluid indication and reservoir prediction. Compared with linear inversion, nonlinear inversion is more precise and can be applied to high-contrast situations. The inversion results can be affected by the parameters’ sensitivity, so the parameterization of nonlinear equations is very significant. Considering the poor nonlinear amplitude-variation-with-offset (AVO) inversion results of impedance and velocity parameters, we adjust the parameters of the nonlinear equation, avoid the inaccuracy caused by parameters sensitivity and get the ideal nonlinear AVO inversion results of the Lamé parameters. The feasibility and stability of the nonlinear equation based on the Lamé parameters and method are verified by the model and the real data examples. The resolution and the lateral continuity of nonlinear inversion results are better compared with the linear inversion results.

Seismic amplitude variation with offset (AVO) inversion is well-known as a popular and pragmatic tool used for the prediction of elastic parameters in the geosciences. Low frequencies missing from conventional seismic data are conventionally recovered from other geophysical information, such as well-log data, for estimating the absolute rock properties, which results in biased inversion results in cases of complex heterogeneous geologic targets or plays with sparse well-log data, such as marine or deep stratum. Broadband seismic data bring new opportunities to estimate the low-frequency components of the elastic parameters without well-log data. We have developed a novel AVO inversion approach with the Bayesian inference for broadband seismic data. The low-frequency components of the elastic parameters are initially estimated with the proposed broadband AVO inversion approach with the Bayesian inference in the complex frequency domain because seismic inversion in the complex frequency domain is helpful to recover the long-wavelength structures of the elastic models. Gaussian and Cauchy probability distribution density functions are used for the likelihood function and the prior information of model parameters, respectively. The maximum a posteriori probability solution is resolved to estimate the low-frequency components of the elastic parameters in the complex frequency domain. Furthermore, with those low-frequency components as initial models and constraints, the conventional AVO inversion method with the Bayesian inference in the time domain is further implemented to estimate the final absolute elastic parameters. Synthetic and field data examples demonstrate that the proposed AVO inversion in the complex frequency domain is able to predict the low-frequency components of elastic parameters well, and that those low-frequency components set a good foundation for the final estimation of the absolute elastic parameters.

In this paper, we calculate the elastic modulus of 3D digital cores using the finite element method, systematically study the equivalence between the digital core model and various rock physics models, and carefully analyze the conditions of the equivalence relationships. The influences of the pore aspect ratio and consolidation coefficient on the equivalence relationships are also further refined. Theoretical analysis indicates that the finite element simulation based on the digital core is equivalent to the boundary theory and Gassmann model. For pure sandstones, effective medium theory models (SCA and DEM) and the digital core models are equivalent in cases when the pore aspect ratio is within a certain range, and dry frame models (Nur and Pride model) and the digital core model are equivalent in cases when the consolidation coefficient is a specific value. According to the equivalence relationships, the comparison of the elastic modulus results of the effective medium theory and digital rock physics is an effective approach for predicting the pore aspect ratio. Furthermore, the traditional digital core models with two components (pores and matrix) are extended to multiple minerals to more precisely characterize the features and mineral compositions of rocks in underground reservoirs. This paper studies the effects of shale content on the elastic modulus in shaly sandstones. When structural shale is present in the sandstone, the elastic modulus of the digital cores are in a reasonable agreement with the DEM model. However, when dispersed shale is present in the sandstone, the Hill model cannot describe the changes in the stiffness of the pore space precisely. Digital rock physics describes the rock features such as pore aspect ratio, consolidation coefficient and rock stiffness. Therefore, digital core technology can, to some extent, replace the theoretical rock physics models because the results are more accurate than those of the theoretical models.

The development of Pre−stack depth migration makes the imaging of the subsurface structure in the depth possible, which set a foun− dation for the study of amplitude variation with incident angle (AVA) inversion. This leads to the increasing demanding of the seismic inversion methods in the depth domain for guiding reservoir characterization. However, the conventional seismic inversion methods in the time domain are not suitable in the depth domain due to the seismic wavelet in the depth domain is depth−variant and depending on medium velocity. To address this issue, we proposed a pragmatic seismic inversion method for fluid factor in the depth domain with amplitude variation with incident angle gathers by using a true−depth wavelet on the process of seismic inversion. This wavelet is es− timated by converting the time wavelet to the depth wavelet with seismic velocity. To guide the fluid discrimination, the proposed method directly estimates the fluid factor from the pre−stack seismic data and all the process of the method is implemented in the depth domain. To deal with the weak nonlinearity induced by the velocity, the Bayesian inference, the prior information and model constraint are in− troduced in this seismic inversion method. Tests on synthetic data show that the fluid factor can be well estimated reasonably even with moderate noise. The field data example illustrates the feasibility and efficiency of the proposed method in application and the estimated fluid factor and shear modulus are in good agreement with the drilling results.

Estimation of rock pore-fluid properties in subsurface reservoirs using seismic reflection data is an important topic in exploration geophysics. Prestack seismic inversion is a key approach for reservoir characterization and fluid discrimination. In this study, we propose a simultaneous estimation approach for discrete fluid facies (i.e., gas, oil, water) and continuous fluid indicators via a Bayesian seismic nonlinear inversion and the differential evolution Markov Chain Monte Carlo model. We derived one novel nonlinear exact PP-wave reflection coefficients equation characterized by Gassmann fluid term, shear modulus and density and the equation is more accurate and suitable for large incident angles. Besides, a mixture probability model is utilized as the prior probability density function (PDF) of the model parameters in the Bayesian seismic probabilistic inversion. Furthermore, the differential evolution Markov Chain Monte Carlo (DE-MCMC) model is developed to optimize the mixture posterior PDF in Bayesian seismic inference. The discrete fluid facies is estimated via the posterior weights of each probability component directly, which can reduce the uncertainty and the accumulation errors of seismic fluid discrimination. The main advantage of the DE-MCMC seismic probabilistic inversion is that it can simulate the posterior probability density distributions of the model parameters efficiently based on the simultaneous optimization of multiple Markov chains, which is helpful for the uncertainty assessment of the inversion results and fluid discrimination. Synthetic examples are provided to demonstrate the feasibility and stability of the proposed method. Furthermore, one field case of oil-gas exploration is presented to show the practicability of this method in reservoir fluid discrimination.

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.

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.

Pore pressure prediction plays an important role in shale gas exploration and fracking technology. The pore pressure in shale cannot be directly measured but to be inferred by the normal velocity trend, so methods based on the effective stress theory are dedicated to establishing a function between seismic interval velocity and pressure. Among them the mostly used method is Eaton’s equation. However, how to precisely quantify the state of compaction remains unsolved. In this study, the AVO/AVA simultaneous inversion was introduced to estimate P-velocity. According to the exponential relationship between the pore pressure and the ratio of velocities, three different methods including the fitting method, the direct calculation method and the model-based direct calculation method based on the Eaton’s equation were used to estimate shale gas pore pressure, respectively. And then a comparative analysis was performed to see the impact of normal compaction trend on the result. It was found that the horizontal continuity of the model-based direct calculation method was the best. The result shows that the approach of estimating the normal compaction trend impacts the pore pressure significantly.

Pore pressure prediction plays an important role in shale gas exploration and fracking technology. The pore pressure in shale cannot be directly measured but to be inferred by the normal velocity trend, so methods based on the effective stress theory are dedicated to establishing a function between seismic interval velocity and pressure. Among them the mostly used method is Eaton’s equation. However, how to precisely quantify the state of compaction remains unsolved. In this study, the AVO/AVA simultaneous inversion was introduced to estimate P-velocity. According to the exponential relationship between the pore pressure and the ratio of velocities, three different methods including the fitting method, the direct calculation method and the model-based direct calculation method based on the Eaton’s equation were used to estimate shale gas pore pressure, respectively. And then a comparative analysis was performed to see the impact of normal compaction trend on the result. It was found that the horizontal continuity of the model-based direct calculation method was the best. The result shows that the approach of estimating the normal compaction trend impacts the pore pressure significantly.

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.

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.

Stratum quality factors (P-wave and S-wave quality factors, Q p and Q s ) have gradually been utilized in the study of physical state of crust and uppermost mantle, tectonic evolution, hydrogeololgy, gas hydrates, petroleum exploration, etc. Different opinions of the seismic attenuation mechanism result in various approaches to estimate the P-wave and S-wave quality factors. Considering the viscoelasticity of the underground medium, the constitutive matrix of the Earth medium is written as the superposition of homogeneous background medium, elastic perturbation medium and viscoelastic perturbation medium. Under the hypothesis of Born integral and stationary phase approximation, the seismic reflectivity is initially raised in terms of P-wave and S-wave moduli, density, P-wave and S-wave quality factors. Furthermore, incorporating the complex seismic traces with the seismic wavelets at different offsets, a two-step inversion approach is proposed to estimate the P-wave and S-wave quality factors. The AVO/AVA Bayesian inversion approach is suggested to estimate the P-wave modulus and S-wave modulus with the real component of the pre-stack seismic data initially. Taking the estimated P-wave and S-wave moduli as prior information, the P-wave and S-wave quality factors are further estimated with the imaginary component of the complex pre-stack seismic data, which is the quadrature of the original data. Finally, synthetic examples demonstrate that the proposed approach is able to estimate P-wave and S-wave quality factors stably and properly, and two field data examples demonstrate that the proposed approach may work as an efficient approach to fluid identification.

Azimuthal elastic inversion or AVO/AVA analysis has proven to be effective for fracture description and stress evaluation in unconventional resource plays. Fracture weakness including normal and tangential weakness from linear slip theory bridge the seismic data and fracturing parameters as intermediate parameters. However, the stability of the azimuthal elastic inversion methods available for anisotropic parameters or fracture parameters in field data remains challenging. This study explores a practical azimuthal simultaneous elastic inversion method in heterogeneous medium for fracture weakness estimation. Taking the heterogeneity and anisotropy of fracture media into consideration, and based on perturbation theory and stable phase approximation, the fracture medium can be considered as the superimposition of background medium and perturbation medium, and then the seismic scattering coefficient of fracture media can be derived. This equation establishes the relationship between seismic data and fracture weakness together with elastic parameters like P-wave and S-wave moduli and weaknesses. With this equation, a heterogeneous inversion method is proposed. This method implements the estimation of P-wave and S-wave moduli and fracture weaknesses simultaneously, and the constraint from initial model and multi-iterations enhances the stability of this method. In this approach, the parameters of the perturbation medium are initially estimated, and then they can be superposed to the parameters of the known background medium as the renewal parameters of the background medium in next iteration. We can yield the final estimation of the parameters in heterogeneous medium after several iterations when the last two estimated results are similar. Model test and field data examples verify the feasibility and potential of the proposed approach.