Pre-stack AVO inversion with adaptive edge preserving smooth filter regularization based on Aki-Richard approximation

With the development of exploration of oil and gas resources,the requirements for seismic inversion results are getting more accurate.In particular,it is hoped that the distribution patterns of oil and gas reservoirs can be finely characterized,and the seismic inversion results can clearly characterize the location of stratigraphic boundaries and meet the needs of accurate geological description.Specifically,for pre-stack AVO inversion,it is required to be able to distinguish smaller geological targets in the depth or time domain,and clearly depict the vertical boundaries of the geological objects.In response to the above requirements,we introduce the preprocessing regularization of the adaptive edge-preserving smooth filter into the pre-stack AVO elastic parameter inversion to clearly invert the position of layer boundary and improve the accuracy of the inversion results.

Converted wave AVO inversion for average velocity ratio and shear wave reflection coefficient

Based on the empirical Gardner equation describing the relationship between density and compressional wave velocity, the converted wave reflection coefficient extrema attributes for AVO analysis are proposed and the relations between the extrema position and amplitude, average velocity ratio across the interface, and shear wave reflection coefficient are derived. The extrema position is a monotonically decreasing function of average velocity ratio, and the extrema amplitude is a function of average velocity ratio and shear wave reflection coefficient. For theoretical models, the average velocity ratio and shear wave reflection coefficient are inverted from the extrema position and amplitude obtained from fitting a power function to converted wave AVO curves. Shear wave reflection coefficient sections have clearer physical meaning than conventional converted wave stacked sections and establish the theoretical foundation for geological structural interpretation and event correlation. ＂The method of inverting average velocity ratio and shear wave reflection coefficient from the extrema position and amplitude obtained from fitting a power function is applied to real CCP gathers. The inverted average velocity ratios are consistent with those computed from compressional and shear wave well logs.

AVO approximation for PS-wave and its application in PP/PS joint inversion

Multi-component exploration has many advantages over ordinary P-wave exploration. PP/PS joint AVO analysis and inversion are useful and powerful methods to discriminate between reservoir and non-productive lithology. In this paper, we derive a new PS-wave reflection coefficient approximation equation which is more accurate at larger incidence angles. The equation is simplified for small incidence angles, which makes AVO analysis clearer and easier for angles less than 30 degrees. Based on this approximation, a PP/PS joint inversion is introduced. A real data example shows that oil sands, brine sands and shales can be differentiated based on the P- to S-wave velocity ratio from the PP/PS joint inversion. Fluid factors and Poisson＇s ratio also indicate an anomaly in the target zone at the oil well location.

Cauchy prior distribution-based AVO elastic parameter estimation via weakly nonlinear waveform inversion

Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized terms requires prior estimation of model parameters, which makes the iterative inversion weakly nonlinear. At the same time, the relations among the model parameters are assumed linear. Furthermore, the reflectivities, the results of the inversion, or the elastic parameters with cumulative error recovered by integrating reflectivities are not well suited for detecting hydrocarbons and fuids. In contrast, in Bayesian linear AVO inversion, the elastic parameters can be directly extracted from prestack seismic data without linear assumptions for the model parameters. Considering the advantages of the abovementioned methods, the Bayesian AVO reflectivity inversion process is modified and Cauchy distribution is explored as a prior probability distribution and the time-variant covariance is also considered. Finally, we propose a new method for the weakly nonlinear AVO waveform inversion. Furthermore, the linear assumptions are abandoned and elastic parameters, such as P-wave velocity, S-wave velocity, and density, can be directly recovered from seismic data especially for interfaces with large reflectivities. Numerical analysis demonstrates that all the elastic parameters can be estimated from prestack seismic data even when the signal-to-noise ratio of the seismic data is low.

Nonlinear joint PP-PS AVO inversion based on improved Bayesian inference and LSSVM

Multiwave seismic technology promotes the application of joint PP–PS amplitude versus offset (AVO) inversion;however conventional joint PP–PS AVO inversioan is linear based on approximations of the Zoeppritz equations for multiple iterations. Therefore the inversion results of P-wave, S-wave velocity and density exhibit low precision in the faroffset;thus, the joint PP–PS AVO inversion is nonlinear. Herein, we propose a nonlinear joint inversion method based on exact Zoeppritz equations that combines improved Bayesian inference and a least squares support vector machine (LSSVM) to solve the nonlinear inversion problem. The initial parameters of Bayesian inference are optimized via particle swarm optimization (PSO). In improved Bayesian inference, the optimal parameter of the LSSVM is obtained by maximizing the posterior probability of the hyperparameters, thus improving the learning and generalization abilities of LSSVM. Then, an optimal nonlinear LSSVM model that defi nes the relationship between seismic refl ection amplitude and elastic parameters is established to improve the precision of the joint PP–PS AVO inversion. Further, the nonlinear problem of joint inversion can be solved through a single training of the nonlinear inversion model. The results of the synthetic data suggest that the precision of the estimated parameters is higher than that obtained via Bayesian linear inversion with PP-wave data and via approximations of the Zoeppritz equations. In addition, results using synthetic data with added noise show that the proposed method has superior anti-noising properties. Real-world application shows the feasibility and superiority of the proposed method, as compared with Bayesian linear inversion.

AVO inversion based on common shot migration

Conventional AVO inversion utilizes the trace amplitudes of CMP gathers. There are three main factors affecting the accuracy of the inversion. First, CMP gathers are based on the hypothesis of horizontal layers but most real layers are not horizontal. Greater layer dip results in a greater difference between the observed CMP gathers and their real location. Second, conventional processing flows such as NMO, DMO, and deconvolution will distort amplitudes. Third, the formulation of reflection coefficient is related to incidence angles and it is difficult to get the relationship between amplitude and incidence angle. Wave equation prestack depth migration has the ability of imaging complex media and steeply dipping layers. It can reduce the errors of conventional processing and move amplitudes back to their real location. With true amplitude migration, common angle gathers abstraction, and AVO inversion, we suggest a method of AVO inversion from common shot gathers in order to reduce the effect of the above factors and improve the accuracy of AVO inversion.

Pre-stack inversion for caved carbonate reservoir prediction:A case study from Tarim Basin,China

The major storage space types in the carbonate reservoir in the Ordovician in the TZ45 area are secondary dissolution caves.For the prediction of caved carbonate reservoir,post-stack methods are commonly used in the oilfield at present since pre-stack inversion is always limited by poor seismic data quality and insufficient logging data.In this paper,based on amplitude preserved seismic data processing and rock-physics analysis,pre-stack inversion is employed to predict the caved carbonate reservoir in TZ45 area by seriously controlling the quality of inversion procedures.These procedures mainly include angle-gather conversion,partial stack,wavelet estimation,low-frequency model building and inversion residual analysis.The amplitude-preserved data processing method can achieve high quality data based on the principle that they are very consistent with the synthetics.Besides,the foundation of pre-stack inversion and reservoir prediction criterion can be established by the connection between reservoir property and seismic reflection through rock-physics analysis.Finally,the inversion result is consistent with drilling wells in most cases.It is concluded that integrated with amplitude-preserved processing and rock-physics,pre-stack inversion can be effectively applied in the caved carbonate reservoir prediction.

Joint PP and PS AVO inversion based on Zoeppritz equations

Considering Zoeppritz equations, reflections of PP and PS are only the function of ratios of density and velocity. So the inversion results will be the same if the ratios are the same but values of density, velocities of P- wave and S-wave are different without strict constraint. This paper makes efforts to explore nonlinear simultaneous PP and PS inversion with expectation to reduce the ambiguity of AVO analysis by utilizing the redundancy of multi-component AVO measurements. Accurate estimation of ratio parameters depends on independence of input data. There are only two independent AVO attributes for PP reflectivity （i.e. intercept and gradient） and two for PS reflectivity （i.e. pseudo-intercept and pseudo-gradient or extreme amplitude）, respectively. For individual PP and PS inversion, the values of least-squares objective function do not converge around a large neighborhood of chosen true model parameters. Fortunately for joint PP and PS inversion the values of the least-squares objective function show closed contours with single minima. Finally the power function fitting is used to provide a higher precision AVO attributes than traditional polynomial fitting. By using the four independent fitting attributes （two independent attributes for PP and PS respectively）, the inversion of four ratio parameters （velocities and densities） would be estimated with less errors than that in traditional method.

Seismic AVO statistical inversion incorporating poroelasticity

Seismic amplitude variation with offset(AVO) inversion is an important approach for quantitative prediction of rock elasticity,lithology and fluid properties.With Biot-Gassmann's poroelasticity,an improved statistical AVO inversion approach is proposed.To distinguish the influence of rock porosity and pore fluid modulus on AVO reflection coefficients,the AVO equation of reflection coefficients parameterized by porosity,rock-matrix moduli,density and fluid modulus is initially derived from Gassmann equation and critical porosity model.From the analysis of the influences of model parameters on the proposed AVO equation,rock porosity has the greatest influences,followed by rock-matrix moduli and density,and fluid modulus has the least influences among these model parameters.Furthermore,a statistical AVO stepwise inversion method is implemented to the simultaneous estimation of rock porosity,rock-matrix modulus,density and fluid modulus.Besides,the Laplace probability model and differential evolution,Markov chain Monte Carlo algorithm is utilized for the stochastic simulation within Bayesian framework.Models and field data examples demonstrate that the simultaneous optimizations of multiple Markov chains can achieve the efficient simulation of the posterior probability density distribution of model parameters,which is helpful for the uncertainty analysis of the inversion and sets a theoretical fundament for reservoir characterization and fluid discrimination.

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.

Multiwave Amplitude Compensation and Its SensitivityAnalysis to AVO Inversion in Viscoelastic Media

We derive formulae of correction for multi-wave geometric spreading and absorption in layered viscoelastic media, this provides the theoretical foundation for true amplitude compensation of field data and for our sensitivity analysis. The imaging matrix at a plane reflector between viscoelastic media can be determined in the frequency domain using linearized reflection coefficients through Born approximation. We quantitatively analyze the sensitivity by studying eigenvalues and eigenvectors of the imaging matrix. The results show that two linear combinations of petrophysical parameters can be determined from the multi-wave AVO inversion in the case of amplitude compensation. Multi-wave AVO contains the information of attenuation in the media. However, the sensitivity of multi-wave AVO inversion to attenuation is small.

Elastic modulus extraction based on generalized pre-stack PP–PS wave joint linear inversion

Joint PP–PS inversion offers better accuracy and resolution than conventional P-wave inversion. P-and S-wave elastic moduli determined through data inversions are key parameters for reservoir evaluation and fluid characterization. In this paper, starting with the exact Zoeppritz equation that relates P-and S-wave moduli, a coefficient that describes the reflections of P-and converted waves is established. This method effectively avoids error introduced by approximations or indirect calculations, thus improving the accuracy of the inversion results. Considering that the inversion problem is ill-posed and that the forward operator is nonlinear, prior constraints on the model parameters and modified low-frequency constraints are also introduced to the objective function to make the problem more tractable. This modified objective function is solved over many iterations to continuously optimize the background values of the velocity ratio, which increases the stability of the inversion process. Tests of various models show that the method effectively improves the accuracy and stability of extracting P and S-wave moduli from underdetermined data. This method can be applied to provide inferences for reservoir exploration and fluid extraction.

Impedance inversion of pre-stack seismic data in the depth domain

The extensive application of pre-stack depth migration has produced huge volumes of seismic data,which allows for the possibility of developing seismic inversions of reservoir properties from seismic data in the depth domain.It is difficult to estimate seismic wavelets directly from seismic data due to the nonstationarity of the data in the depth domain.We conduct a velocity transformation of seismic data to make the seismic data stationary and then apply the ridge regression method to estimate a constant seismic wavelet.The estimated constant seismic wavelet is constructed as a set of space-variant seismic wavelets dominated by velocities at different spatial locations.Incorporating the weighted superposition principle,a synthetic seismogram is generated by directly employing the space-variant seismic wavelets in the depth domain.An inversion workflow based on the model-driven method is developed in the depth domain by incorporating the nonlinear conjugate gradient algorithm,which avoids additional data conversions between the time and depth domains.The impedance inversions of the synthetic and field seismic data in the depth domain show good results,which demonstrates that seismic inversion in the depth domain is feasible.The approach provides an alternative for forward numerical analyses and elastic property inversions of depth-domain seismic data.It is advantageous for further studies concerning the stability,accuracy,and efficiency of seismic inversions in the depth domain.

The applicability and underlying factors of frequency-dependent amplitude-versus-offset(AVO)inversion

Recently,the great potential of seismic dispersion attributes in oil and gas exploration has attracted extensive attention.The frequency-dependent amplitude versus offset(FAVO)technology,with dispersion gradient as a hydrocarbon indicator,has developed rapidly.Based on the classical AVO theory,the technology works on the assumption that elastic parameters are frequency-dependent,and implements FAVO inversion using spectral decomposition methods,so that it can take dispersive effects into account and effectively overcome the limitations of the classical AVO.However,the factors that affect FAVO are complicated.To this end,we construct a unified equation for FAVO inversion by combining several Zoeppritz approximations.We study and compare two strategies respectively with(strategy 1)and without(strategy 2)velocity as inversion input data.Using theoretical models,we investigate the influence of various factors,such as the Zoeppritz approximation used,P-and S-wave velocity dispersion,inversion input data,the strong reflection caused by non-reservoir interfaces,and the noise level of the seismic data.Our results show that FAVO inversion based on different Zoeppritz approximations gives similar results.In addition,the inversion results of strategy 2 are generally equivalent to that of strategy 1,which means that strategy 2 can be used to obtain dispersion attributes even if the velocity is not available.We also found that the existence of non-reservoir strong reflection interface may cause significant false dispersion.Therefore,logging,geological,and other relevant data should be fully used to prevent this undesirable consequence.Both the P-and S-wave related dispersion obtained from FAVO can be used as good indicators of a hydrocarbon reservoir,but the P-wave dispersion is more reliable.In fact,due to the mutual coupling of P-and S-wave dispersion terms,the P-wave dispersion gradient inverted from PP reflection seismic data has a stronger hydrocarbon detection ability than the S-wave dispersion gradient.Moreover,there is little difference in using post-stack data or pre-stack angle gathers as inversion input when only the P-wave dispersion is desired.The real application examples further demonstrate that dispersion attributes can not only indicate the location of a hydrocarbon reservoir,but also,to a certain extent,reveal the physical properties of reservoirs.

Quantification of Reservoir Fluid Prediction Uncertainty Using AVO Fluid Inversion (AFI)

The AVO fluid inversion (AFI) technique was used to assess for fluids at the target levels of OPL-X in the deepwater Niger Delta, Nigeria. In this study, attempt is made to get a quantitative probability estimate of the possible reservoir fluids in both the shallow and deeper target levels. This was achieved through the development of a stochastic AVO model and an inversion to probability of different fluids using the Bayesian approach. AVO Fluid Inversion (AFI) technique provides a robust and inexpensive method for identifying potential hydrocarbon-filled reservoirs and provides a quantitative estimates of the uncertainties inherent in the prediction.

Fast pre-stack multi-channel inversion constrained by seismic reflection features

Classical multi-channel technology can significantly reduce the pre-stack seismic inversion uncertainty, especially for complex geology such as high dipping structures. However, due to the consideration of complex structure or reflection features, the existing multi-channel inversion methods have to adopt the highly time-consuming strategy of arranging seismic data trace-by-trace, limiting its wide application in pre-stack inversion. A fast pre-stack multi-channel inversion constrained by seismic reflection features has been proposed to address this issue. The key to our method is to re-characterize the reflection features to directly constrain the pre-stack inversion through a Hadamard product operator without rearranging the seismic data. The seismic reflection features can reflect the distribution of the stratum reflection interface, and we obtained them from the post-stack profile by searching the shortest local Euclidean distance between adjacent seismic traces. Instead of directly constructing a large-size reflection features constraint operator advocated by the conventional methods, through decomposing the reflection features along the vertical and horizontal direction at a particular sampling point, we have constructed a computationally well-behaved constraint operator represented by the vertical and horizontal partial derivatives. Based on the Alternating Direction Method of Multipliers (ADMM) optimization, we have derived a fast algorithm for solving the objective function, including Hadamard product operators. Compared with the conventional reflection features constrained inversion, the proposed method is more efficient and accurate, proved on the Overthrust model and a field data set.

Model-data-driven AVO inversion method based on multiple objective functions

The model-driven inversion method and data-driven prediction method are eff ective to obtain velocity and density from seismic data.The former necessitates initial models and cannot provide high-resolution inverted parameters because it primarily employs medium-frequency information from seismic data.The latter can predict parameters with high resolution,but it require a signifi cant number of accurate training samples,which are typically in limited supply.To solve the problems mentioned for these two methods,we propose a model-data-driven AVO inversion method based on multiple objective functions.The proposed method implements network training,network optimization,and network inversion by using three independent objective functions.Tests on synthetic and fi eld data show that the proposed method can invert high-accuracy and high-resolution velocity and density with a few training samples.

Nonlinear amplitude inversion using a hybrid quantum genetic algorithm and the exact zoeppritz equation

The amplitude versus offset/angle(AVO/AVA)inversion which recovers elastic properties of subsurface media is an essential tool in oil and gas exploration.In general,the exact Zoeppritz equation has a relatively high accuracy in modelling the reflection coefficients.However,amplitude inversion based on it is highly nonlinear,thus,requires nonlinear inversion techniques like the genetic algorithm(GA)which has been widely applied in seismology.The quantum genetic algorithm(QGA)is a variant of the GA that enjoys the advantages of quantum computing,such as qubits and superposition of states.It,however,suffers from limitations in the areas of convergence rate and escaping local minima.To address these shortcomings,in this study,we propose a hybrid quantum genetic algorithm(HQGA)that combines a self-adaptive rotating strategy,and operations of quantum mutation and catastrophe.While the selfadaptive rotating strategy improves the flexibility and efficiency of a quantum rotating gate,the operations of quantum mutation and catastrophe enhance the local and global search abilities,respectively.Using the exact Zoeppritz equation,the HQGA was applied to both synthetic and field seismic data inversion and the results were compared to those of the GA and QGA.A number of the synthetic tests show that the HQGA requires fewer searches to converge to the global solution and the inversion results have generally higher accuracy.The application to field data reveals a good agreement between the inverted parameters and real logs.

Petrophysical parameters inversion for heavy oil reservoir based on a laboratory-calibrated frequency-variant rock-physics model

Heavy oil has high density and viscosity, and exhibits viscoelasticity. Gassmann's theory is not suitable for materials saturated with viscoelastic fluids. Directly applying such model leads to unreliable results for seismic inversion of heavy oil reservoir. To describe the viscoelastic behavior of heavy oil, we modeled the elastic properties of heavy oil with varying viscosity and frequency using the Cole-Cole-Maxwell (CCM) model. Then, we used a CCoherent Potential Approximation (CPA) instead of the Gassmann equations to account for the fluid effect, by extending the single-phase fluid condition to two-phase fluid (heavy oil and water) condition, so that partial saturation of heavy oil can be considered. This rock physics model establishes the relationship between the elastic modulus of reservoir rock and viscosity, frequency and saturation. The viscosity of the heavy oil and the elastic moduli and porosity of typical reservoir rock samples were measured in laboratory, which were used for calibration of the rock physics model. The well-calibrated frequency-variant CPA model was applied to the prediction of the P- and S-wave velocities in the seismic frequency range (1–100 Hz) and the inversion of petrophysical parameters for a heavy oil reservoir. The pre-stack inversion results of elastic parameters are improved compared with those results using the CPA model in the sonic logging frequency (∼10 kHz), or conventional rock physics model such as the Xu-Payne model. In addition, the inversion of the porosity of the reservoir was conducted with the simulated annealing method, and the result fits reasonably well with the logging curve and depicts the location of the heavy oil reservoir on the time slice. The application of the laboratory-calibrated CPA model provides better results with the velocity dispersion correction, suggesting the important role of accurate frequency dependent rock physics models in the seismic prediction of heavy oil reservoirs.

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.