Multiscale frequency-domain seismic inversion for fracture weakness

Tilted transverse isotropy (TTI) provides a useful model for the elastic response of a medium containing aligned fractures with a symmetry axis oriented obliquely in the vertical and horizontal coordinate directions. Robust methods for determining the TTI properties of a medium from seismic observations to characterize fractures are sought. Azimuthal differencing of seismic amplitude data produces quantities that are particularly sensitive to TTI properties. Based on the linear slip fracture model, we express the TTI stiffness matrix in terms of the normal and tangential fracture weaknesses. Perturbing stiffness parameters to simulate an interface separating an isotropic medium and a TTI medium, we derive a linearized P-to-P reflection coefficient expression in which the influence of tilt angle and fracture weaknesses separately emerge. We formulate a Bayesian inversion approach in which amplitude differences between seismic data along two azimuths, interpreted in terms of the reflection coefficient approximation, are used to determine fracture weaknesses and tilt angle. Tests with simulated data confirm that the unknown parameter vector involving fracture weakness and tilted fracture weaknesses is stably estimated from seismic data containing a moderate degree of additive Gaussian noise. The inversion approach is applied to a field surface seismic data acquired over a fractured reservoir; from it, interpretable tilted fracture weaknesses, consistent with expected reservoir geology, are obtained. We determine that our inversion approach and the established inversion workflow can produce the properties of systems of tilted fractures stably using azimuthal seismic amplitude differences, which may add important information for characterization of fractured reservoirs.

The identification and characterization of fractures is an important objective in many areas of earth and environmental sciences. Amplitude variation with offset and azimuth (AVOAz) analysis of seismic reflection data is a key method for achieving these tasks. Theoretical and experimental studies have shown that the presence of pore fluids together with the strong mechanical contrast between the fractures and their embedding background give rise to wave-induced fluid flow (WIFF) effects. This implies that the effective stiffness tensor of a fluid-saturated fractured rock defining its seismic response becomes viscoelastic and frequency-dependent. In spite of this, AVOAz analysis typically relies on end-member-type elastic stiffness models that either assume a relaxed (i.e., equilibrated) or unrelaxed (i.e., unequilibrated) state of the wave-induced fluid pressure in the rock. In general, however, neither the appropriateness of the chosen model nor the associated errors in the inversion process are known. To investigate this topic, we have considered a poroelastic medium containing parallel vertical fractures and generate synthetic seismic AVOAz data using the classic Rüger approximations for PP-wave reflection coefficients in horizontally transversely isotropic media. A Markov chain Monte Carlo method is used to perform a Bayesian inversion of the synthetic seismic AVOAz data. We quantify the influence of WIFF effects on the AVOAz inversion results when elastic relaxed and unrelaxed models are used as forward solvers of inversion schemes to estimate the fracture volume fraction, the elastic moduli, and the porosity of the background rock, as well as the overall weakness of the medium due to the presence of fractures. Our results indicate that, when dealing with single-frequency data, relaxed elastic models provide biased but overall better inversion results than unrelaxed ones, for which some fracture parameters cannot be resolved. Improved inversion performance is achieved when using frequency-dependent data, which illustrates the importance of accounting for poroelastic effects.

<p>The seismic full waveform inversion (FWI), as one of important ways to obtain the seismic wave velocity, has made rapid development in the last decade. In response to problems of cycle-skipping artifacts, dependence on the initial model, and low-frequency information in FWI, researchers have made many improvements, such as multi-scale envelope inversion and low-frequency extension. Recently, deep learning has been also adopted seismic data processing and interpretation, because of its strong nonlinear mapping ability. However, these works depend on labels used for training heavily, especially for the velocity model in the inversion, which prevents them from real application. Referring to these studies, this work combines low-frequency extension commonly as well as multiscale inversion with deep learning, and proposes a multi-scale FWI gradient optimization method based on CNN. CNN we designed is trained to predict the inversion gradient corresponding to the low-frequency band data in FWI, so that multi-scale gradient optimization can be directly used in multi-scale inversion, expanding the low-frequency information in the actual data and reducing the calculation in FWI. With a specially designed dataset, CNN is trained to optimize the gradients computed from the high-frequency band data by predicting the gradients corresponding to the low-frequency band data and the gradients corresponding to the mid-frequency band data, respectively. The predicted gradients are used in different stages of the multi-scale inversion. The low-frequency gradients are used to invert the initial structural construction so as not to rely on a good initial model, and the high-frequency gradients are used to improve the accuracy of the inversion results. In this way, low-frequency expansion and multiscale inversion can be achieved simultaneously. Our method achieves good results on the initial model for a given uniform wave velocity, effectively alleviating the reliance on the initial model in FWI. This study provides a new idea of combining deep learning and full waveform inversion, which will be effectively used in seismic data processing.</p>

Model-constrained and data-driven double-supervision acoustic impedance inversion

Seismic data interpolation and denoising play vital roles in obtaining complete and clean data in seismic data processing. Seismic data usually misses along various spatial axes and always mix with random noise. In order to obtain complete and clean seismic data, reconstruction technology can interpolate missing data and attenuate random noise. Nonsubsampled contourlet transform is an effective transform to obtain multi-scale and multi-direction sparse domain data for compression sensing interpolation and denoising. However, conventional iterative shrinkage/thresholding cannot handle ill-posed and ill-conditioned equations for solving linear inverse problem. We present a two-step iterative log thresholding method to overcome ill-posed and ill-conditioned problems and improve the convergence rate and solution accuracy, which can interpolate and denoise seismic data simultaneously in the nonsubsampled contourlet transform framework. First, we use nonsubsampled contourlet transform to convert the seismic missing data with random noise to sparse domain. Then, we apply two-step iterative log thresholding algorithm to interpolate and denoise data in sparse domain. The result of each iteration is based on the results of the previous two iterations, which can accelerate convergence rate. In addition, log thresholding can further improve convergence rate and solution accuracy. Finally, we use inverse nonsubsampled contourlet transform to obtain the interpolated and denoised seismic data. The new method can reconstruct the irregularly missing data and attenuate random noise to obtain complete and clean seismic data with high accuracy, which is crucial for seismic imaging and inversion. We demonstrate the applicability and effectiveness of this simultaneous interpolation and denoising technique with successful applications to both synthetic and field data examples.

Traditional iteration-based full-waveform inversion (FWI) methods encounter serious challenges if the initial velocity model is far from the true model or if the observed data are lacking low-frequency content. As such, the optimization algorithm may be trapped in local minima and fail to go to a global optimal model. In addition, the traditional FWI method requires long-offset data to update the deep structure of a velocity model with diving waves. To overcome the disadvantages of traditional FWI under these circumstances, we have developed a reflection intensity waveform inversion method. This method aims to minimize the seismic intensity differences between the modeled reflection data and field data. Our method is less dependent on the starting model, and long-offset data are no longer required. The wave intensity, proportional to the square of the original data amplitude, can have a low-frequency band and a higher frequency band, even for waveforms without initial low-frequency content. Our multiscale intensity inversion starts from the low-frequency information in the intensity data, and it can largely avoid the cycle-skipping problem. Synthetic and field data examples demonstrate that our method is able to overcome cycle skipping in handling data with no low-frequency information.

Time-lapse full waveform inversion based on curvelet transform: Case study of CO2 storage monitoring

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.

ABSTRACTBy analogy with P‐ and S‐wave impedances, the product of Young's modulus and density can be termed as Young's impedance, which indicates the rock lithology and brittleness of unconventional hydrocarbon reservoirs. Poisson's ratio is also an effective indicator of rock brittleness and fluid property of unconventional reservoirs, and fracture weaknesses indicate the fracture properties (fracturing intensity and fracture fillings) in fracture‐induced unconventional reservoirs. We aim to simultaneously estimate the Young's impedance, Poisson's ratio and fracture weaknesses from wide‐azimuth surface seismic data in a fracture‐induced shale gas reservoir, and use the horizontal transversely isotropic model to characterize the fractures. First, the linearized PP‐wave reflection coefficient in terms of Young's impedance, Poisson's ratio, density and fracture weaknesses is derived for the case of a weak‐contrast interface separating two weakly horizontal transversely isotropic media. In addition, an orthorhombic anisotropic case is also discussed in this paper. Then a Bayesian amplitude variation with incident angle and azimuth scheme with a model constraint is used to stably estimate Young's impedance, Poisson's ratio and fracture weaknesses with only PP‐wave azimuthal seismic data. The proposed approach is finally demonstrated on both synthetic and real data sets with reasonable results.

Over the last project six months, our project activities have concentrated on three areas: (1) performing a stochastic inversion of pattern 16 seismic data to deduce reservoir permeability, (2) development of the geochemical inversion strategy and implementation of associated software, and (3) completing the software implementation of TProGS and the geostatistical analysis that provides the information needed when using the software to produce realizations of the Midale reservoir. The report partially the following deliverables: D2: Model development: MCMC tool (synthetic fluid chemistry data); deliverable completed. D4: Model development/verification: MCMC tool (TProGS, field seismic/chemistry data) work product; deliverable requirements partially fulfilled. D5: Field-based single-pattern simulations work product; deliverable requirements partially fulfilled. When completed, our completed stochastic inversion tool will explicitly integrate reactive transport modeling, facies-based geostatistical methods, and a novel stochastic inversion technique to optimize agreement between observed and predicted storage performance. Such optimization will be accomplished through stepwise refinement of: (1) the reservoir model - principally its permeability magnitude and heterogeneity - and (2) geochemical parameters - primarily key mineral volume fractions and kinetic data. We anticipate that these refinements will facilitate significantly improved history matching and forward modeling of CO{sub 2} storage. Our tool uses the Markov Chain Monte Carlo (MCMC) methodology. Deliverable D1, previously submitted as a report titled ''Development of a Stochastic Inversion Tool To Optimize Agreement Between The Observed And Predicted Seismic Response To CO{sub 2} Injection/Migration in the Weyburn-Midale Project'' (Ramirez et al., 2009), described the stochastic inversion approach that will identify reservoir models that optimize agreement between the observed and predicted seismic response. The software that implements this approach has been completed, tested, and used to process seismic data from pattern 16. A previously submitted report titled ''Model verification: synthetic single pattern simulations using seismic reflection data'', Ramirez et al. 2010, partially fulfilled deliverable D3 by summarizing verification activities that evaluate the performance of the seismic software and its ability to recover reservoir model permeabilities using synthetic seismic reflection data. A future progress report will similarly describe summarizing verification activities of the geochemical inversion software, thereby completing deliverable D3. This document includes a chapter that shows and discusses permeability models produced by seismic inversion that used seismic data from pattern 16 in Phase 1A. It partially fulfills deliverable D5: Field-based single-pattern simulations work product. The D5 work product is supposed to summarize the results of applying NUFT/MCMC to refine the reservoir model and geochemical parameters by optimizing observation/prediction agreement for the seismic/geochemical response to CO{sub 2} injection/migration within a single pattern of Phase 1A/1B. A future progress report will show inversion results for the same pattern using geochemical data, thereby completing deliverable D5. This document also contains a chapter that fulfills deliverable D2: Model development: MCMC tool (synthetic fluid chemistry data). The chapter will summarize model development activities required to facilitate application of NUFT/MCMC to optimize agreement between the observed and predicted geochemical response to CO{sub 2} injection/migration. Lastly, this document also contains a chapter that partially fulfills deliverable D4: Model development/verification: MCMC tool (TProGS, field seismic/chemistry data) work product. This work product is supposed to summarize model development activities required for (1) application of TProGS to Weyburn, (2) use of TProGS within the MCMC tool, and (3) application of the MCMC tool to address field seismic and geochemical data. The chapter included here fulfills requirements 1 and 2. Requirement 3 will be addressed in a future progress report.

Summary We have developed a novel random noise attenuation method for seismic data based on inversion in the frequency-space (f-x) domain. The method regards ‘clean’ seismic data in f-x domain as model parameters, and the noise attenuation is equivalent to inverting these parameters from the noisy data. The prediction error filter (PEF) in the f-x prediction method is used as lateral continuity constraints of the inversion. Since the PEF is calculated from the noisy data, it should be recalculated from the denoised seismic data. The process of calculating signal, then getting a new PEF should be iterated a few times. The choice of trade-off parameters also influences the performance of this method. The proposed method overcame the problem of the generation of spurious events and reduction of the signal amplitudes in the conventional f-x prediction method. Tests on synthetic and field data examples demonstrated that, compared with f-x domain prediction, the proposed method has a better performance in noise attenuation and signal-preserving.

A description of reservoir heterogeneities in all scales is crucial for improvements in reservoir characterization. In this work a multi-scale approach was developed to integrate seismic intermediate-scale data and the conventional short and large scale data, represented by logs and surface seismic data respectively. Intermediate-scale data obtained by short and far-offset crosswell surveys, vertical seismic profiles and high resolution seismic lines can be geostatiscally incorporated in this approach in order to provide more complete reservoir descriptions. The approach employs the available seismic data as reference data in two post-matching steps. An interwell model is the final product of the first step using crosswell data. Such upscale and postmatching is then repeated to the larger-scale seismic traces, using logs and the interwell image as hard data to feed simulations. The final product is an optimal acoustic property model constrained by all logs and seismic surveys. This multi-scale incorporation was applied using field and synthetic data, showing that the main impact in modeling is caused by the incorporation of crosswell images obtained by shooting short distance surveys. Since such data provide a tool to map and recover a very fine layered lateral framework, which can be extrapolated under the constraint of conventional seismic data, the integration must prioritize data with higher frequency content, i.e., should follow two steps: only short-crosswell data are used in the first post-matching, and additional seismic data during the second.

Seismic data suffer from under-sampling along spatial dimensions due to physical and economic limitations during acquisition, which can adversely impact subsequent imaging processes. Various approaches have been proposed to address this issue, including rank-reduction, transform, and deep learning (DL) methods for reconstructing missing traces in observed seismic data. While many DL-based reconstruction methods employ convolutional neural networks (CNNs) as their core components in supervised or unsupervised settings, the accuracy of CNN-based DL reconstruction methods can still be enhanced due to the inherent localization of convolutional operators. In this study, we present an innovative method, termed Attentive CNN (ACNet), that incorporates a transformer model with a multi-head self-attention mechanism into the CNN framework for unsupervised seismic data reconstruction. ACNet consists of an encoder built with the transformer model and a CNN decoder, enabling an iterative reconstruction process within the proposed unsupervised DL-based approach. We compare the performance of our method with that of the damped rank-reduction (DRR) method using synthetic and field data examples. The results demonstrate that our proposed method exhibits superior signal reconstruction and random noise suppression capabilities compared to the DRR method.

Azimuthally variation of elastic impedances for fracture estimation

Seismic data reconstruction plays an important role in the whole seismic data processing and imaging workflow, especially for those data that are acquired from severe field environment and are missing a large portion of the reflection signals. The rank-reduction method is considered to be a very effective method for interpolating data that are of small curvature, e.g. the post-stack data. However, when the data are more complicated, the rank-reduction method may fail to achieve acceptable performance. A useful strategy is to use local windows to process the data so that the data in each local window satisfy the plane-wave assumption of the rank-reduction method. However, the rank in each window requires a careful selection. Traditional methods select a global rank for all windows. We have proposed an automatic algorithm to select the rank in each processing window. The energy ratio between two consecutive singular values is chosen as the criterion to define the optimal rank. We apply this strategy to seismic data interpolation and use both synthetic and field data examples to demonstrate its potential in practical applications.