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

Summary Seismic impedance inversion is a technique that converts seismic data interface information into stratigraphic information, serving as a bridge between seismic data, well logging, and geological information. Although the existing deep learning impedance inversion methods have improved inversion accuracy, they do not involve the quantitative evaluation of uncertainty in the inversion results. Based on these effects, we improved the existing CNN impedance inversion model by incorporating Bayesian theory and approximate Bayesian inference. We implemented two methods for impedance inversion: one based on a Bayesian convolution neural network (BCNN), and the other is a CNN based on Monte Carlo (MC) sampling and Dropout using approximate Bayesian inference. These methods allow for uncertainty modeling and incorporation of uncertainty into the inversion model. The uncertainty of the inversion results is quantified through the output probability distribution. The results of field data applications clarify the effectiveness and characteristics of the two methods. MC Dropout CNN method is superior in efficiency due to approximate theory, while BCNN shows advantages in accuracy, resolution, and uncertainty quantification.

Seismic inversion methods are routinely used to estimate attributes such as P-impedance, S-impedance, density, P-wave and S-wave velocity, and elastic impedances from seismic and well log data. These attributes help to understand subsurface lithology and fluid content. There are several types of seismic inversion methods available in which model-based inversion has got more attention. In the present study, the model-based inversion and geostatistical methods namely probabilistic neural network (PNN), multi-layer feed-forward neural network (MLFN) and radial basis function neural network (RBFNN) are implemented to estimate acoustic impedance, porosity, density, gamma-ray volume and P-wave velocity in the inter-well region of the F-3 block, Netherlands. The aim of the study is to predict a number of petrophysical parameters and demonstrate how they can be used to interpret seismic reflection data. A comparative study is also performed to estimate the best suitable method to predict various petrophysical parameters. The assessment of inverted results demonstrates that the impedance in the region varies from 2550 m/s*g/cc to 6150 m/s/*g/cc, which is relatively low and indicates the presence of loose formation in the area. The correlation between synthetic seismic trace and initial seismic trace is estimated to be 0.98, and the synthetic relative error as 0.19, indicating excellent algorithm output. Further, the assessment of the geostatistical methods is carried out to predict petrophysical parameters in conjunction with Multi-Attribute Transform Analysis. The analysis shows that among the geostatistical methods, the PNN provides slightly better results. The petrophysical parameters that are estimated in this study are porosity, density, gamma-ray, and P-wave velocity volumes. These parameters reinforce the interpretation of seismic data, which is a significant step in any project of exploration and production. The technique is first implemented to the composite traces near to the well location, and the findings are analysed with well log data. Second, the entire seismic section is inverted for porosity, density, gamma-ray, and P-wave velocity after achieving satisfactory outcomes in the first step. The assessment demonstrates very high-resolution subsurface petrophysical parameters which strengthen the seismic data interpretation.

Recurrent neural networks (RNN) are at the core of modern automatic speech recognition (ASR) systems. In particular, long short-term memory (LSTM) recurrent neural networks have achieved state-of-the-art results in many speech recognition tasks, due to their efficient representation of long and short term dependencies in sequences of inter-dependent features. Nonetheless, internal dependencies within the element composing multidimensional features are weakly considered by traditional real-valued representations. We propose a novel quaternion long short-term memory (QL-STM) recurrent neural network that takes into account both the external relations between the features composing a sequence, and these internal latent structural dependencies with the quaternion algebra. QLSTMs are compared to LSTMs during a memory copy-task and a realistic application of speech recognition on the Wall Street Journal (WSJ) dataset. QLSTM reaches better performances during the two experiments with up to 2.8 times less learning parameters, leading to a more expressive representation of the information.

Seimic impedance inversion based on semi-supervised learning

Deep learning neural networks offer some advantages over conventional methods in acoustic impedance inversion. Because labeled data may be difficult to obtain in realistic field data settings, it can be difficult to obtain high-accuracy inversion results. Some generative adversarial network (GAN)-based acoustic impedance inversion methods have been proposed to solve this problem. However, due to the existence of lateral discontinuity in inversion results of these GAN-based methods, inversion accuracy of these proposals is still not fully satisfactory. Therefore, to tackle the shortcomings of GAN, we develop an acoustic impedance inversion method based on dual Wasserstein GAN condition (dual-WGAN-c). Dual-WGAN-c can perform seismic inversion and forward calculation simultaneously and take the low-frequency information of acoustic impedance as conditional input to obtain accurate acoustic impedance inversion results in the case of insufficient labeled data. Through a data simulation experiment, compared with GAN-based seismic acoustic impedance inversion methods, dual-WGAN-c can obtain more accurate inversion results, with high robustness when the seismic data are noisy. Dual-WGAN-c also can obtain accurate results in acoustic impedance inversion of the recorded seismic data when one has insufficient labeled well-log data.

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.

Most acoustic impedance sparse inversion methods include two parts: reflectivity inversion and extraction of acoustic impedance from reflectivity. This being the case, the acoustic impedance is easily affected by reflectivity and the value of acoustic impedance at time t=0, thus may become inaccurate. In this paper, we propose a seismic acoustic impedance inversion method with multi-parameter regularization. In our method, the acoustic impedance is calculated directly from objective functions to ensure the stability and accuracy of results. In addition, the total variation regularization, L1 norm constraint, and initial model constraint are used to make the inversion results better accordant with a priori geological information. Moreover, we use multitrace inversion to reflect the spatial and temporal correlation of the data. Since the objective function contains several different types of regularization term, we have developed an algorithm based on split Bregman iteration to calculate it. The inversion results of theoretical model and field data show that the proposed method has high inversion precision, strong anti-noise ability and good performance on stratigraphy delineation.

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.

Deep learning has been applied to tackle the seismic inversion problem, bringing more efficiency and accuracy. However, bad spatial continuity and poor generalizability limit the practical application. To solve these problems, we propose a 2D end-to-end seismic inversion method based on domain adaption. Firstly, the proposed 2D network learns the inversion mapping of seismic data under the constraint of domain adaption layer, which can reduce the difference between the features of real seismic data and synthetic seismic data, improving the generalization ability on real seismic data. Then, the trained model is finetuned with well logging data. In the first process, the spatial continuity of the inversion result is guaranteed by the 2D training scheme. Meanwhile, due to the constraint of the domain adaption layer, our model not only performs well on the synthetic data but also has good generalization ability on the real seismic data. And we carefully discuss the mechanism of domain adaption layer. In the second process, finetuning introduces well logging information, which can further improve the ability to invert details. Moreover, in order to improve the inversion accuracy on real seismic data, we develop a new training data generation method that can generate the synthetic samples close to the real samples, and a 2.5D training strategy is adopted to improve the continuity of the 3D data. The experiments on both synthetic and real seismic data show that our method performs better than both the recursive inversion method and the 1D closed-loop CNN methods.

The Zoeppritz equations describe the relationship between seismic properties that are useful for the interpretation of lithology and fluid properties. Various approximations to the Zoeppritz equations are often used in linear amplitude variation with offset and amplitude variation with angle inversions, assuming low-contrast boundaries. These approximations restrict the inversion method to not-too-large-angle cases and reduce the inversion accuracy. Therefore, it is necessary to develop joint PP and PS prestack inversion methods using the exact Zoeppritz equations. We have developed a method for nonlinear joint prestack inversion using the exact Zoeppritz equations. We established an objective function to combine PP and PS information based on a least-squares approach, and we used the Taylor expansion method to derive a model updating formula for the inversion. We also used a mean shift method to improve the accuracy of inversion results. We validated our inversion using synthetic and field seismic data. The model for calculating synthetic data contained high-contrast interfaces to match the reservoir layers, which included, for example, coal seams and unconsolidated sandstone. The outputs of the inversion were the elastic parameters (P- and S-wave velocities, as well as density), rather than the changes in elastic parameters. We found that the nonlinear joint prestack inversion achieved more accurate results than the linear joint prestack inversion, regardless of incidence angle size. Furthermore, if the prestack data were of high enough quality, it was possible to identify thin layers from the inversion result.

In the previous chapters, we have seen that time domain methods are good for denoising the seismic data with moderate noisy record. In order to separate true reflection amplitudes from the noisy seismic data, in this chapter, we discuss time slice singular spectrum analysis (TSSSA), a data adaptive signal decomposition based on SSA to alleviate such coloured and complex noise. This method is the time domain version of Cadzow filter but did not gain full attention until 2012. This method is applicable to pre-stack and post-stack data for denoising. By virtue of using seismic amplitudes corresponds to particular time (time slice) to benefit their strong correlation, the method was named as Time Slice SSA. It is a time domain method. In view of the above, in this chapter, Time Slice SSA (TSSSA) denoising algorithm was presented for denoising of 2D seismic reflection data. The first part of this chapter is devoted to provide the testing of the method on synthetic seismic data in comparison with f-x deconvolution (Canales 1984) and f-x SSA (Sacchi 2009) methods. In the second part, the method was applied to high-resolution seismic pre-stack and post data field data.

SUMMARY Full waveform inversion (FWI) is a powerful method to estimate high-resolution physical parameters of the subsurface by iteratively minimizing the misfit between the observed and synthetic seismic data. Standard FWI algorithms measure seismic misfit between amplitude-preserved seismic data (true-amplitude FWI). However, in order to mitigate the variations in sources and recording systems acquired on complex geological structures and the physics that cannot be modelled using an approximation of the seismic wave equation, the observed and synthetic seismic data are normalized trace-by-trace and then used to perform FWI. Trace-by-trace normalization removes the amplitude effects related to offset variations and only keeps the phase information. Furthermore, trace-by-trace normalization changes the true amplitude difference because of different normalization factors used for the corresponding synthetic and observed traces. In this paper, we study the performance of true-amplitude FWI and trace-normalized-residual-based FWI in the time domain. The misfit function of trace-normalized-residual-based FWI is defined such that the adjoint source used in gradient calculation is the trace-normalized seismic residual. We compare the two inversion schemes with synthetic seismic data simulated on laterally invariant models and the more complex 2-D Marmousi model. In order to simulate realistic scenarios, we perform the elastic FWI ignoring attenuation to noisy seismic data and to the synthetic data modelled using a viscoelastic modelling scheme. Comparisons of seismic data and adjoint sources show that trace-by-trace normalization increases the magnitude of seismic data at far offsets, which are usually more cycle-skipped than those at near offsets. The inverted results on linear-gradient models demonstrate that trace-by-trace normalization increases the non-linearity of FWI, so an initial model with sufficient accuracy is required to guarantee the convergence to the global minimum. The inverted results and the final seismic residuals computed using seismic data without trace-by-trace normalization demonstrate that true-amplitude FWI provides inverted models with higher accuracy than trace-normalized-residual-based FWI, even when the unknown density is updated using density–velocity relationship in inversion or in the presence of noise and complex physics, such as attenuation.

Estimation of gas hydrate saturation in the Ulleung basin using seismic attributes and a neural network

Reservoir characterization has a leading role in the reservoir geophysics and reservoir management. Since the interests of the reservoir geophysics and reservoir managements are the elastic properties and reservoir properties of the subsurface rock for their purposes, a robust method is required for converting seismic data into elastic properties. Accordingly, by employing a rock physics model and using the inverted seismic data, one can describe the reservoir for purposes such as improvement in the production of the reservoir. In the present study, we employ one of the methods for converting the seismic data into the elastic properties. This method of inversion is known as simultaneous inversion, which is grouped in amplitude-variation-with-offset (AVO) inversion category. In this method, unlike the other methods of AVO inversion, the pre-stack seismic data are directly inverted into the elastic properties of the rock and an excellent lithology and fluid indicator (VP/VS) are provided. Then, this indicator is tested on one of the oilfields of the Persian Gulf. Moreover, by means of this method, one can locate the fluids contact and the lithological interlayers; also, by the inversion results, which are the cubes of the seismic properties of the rock, one can generate sections of the elastic properties of the rock such as Poisson’s ratio and Young modulus which are useful for geomechanical analysis. Therefore, this kind of method is a quick way for the prior analysis of the studied area.

Capturing long-range interactions between structural but not sequence neighbors of proteins is a long-standing challenging problem in bioinformatics. Recently, long short-term memory (LSTM) networks have significantly improved the accuracy of speech and image classification problems by remembering useful past information in long sequential events. Here, we have implemented deep bidirectional LSTM recurrent neural networks in the problem of protein intrinsic disorder prediction. The new method, named SPOT-Disorder, has steadily improved over a similar method using a traditional, window-based neural network (SPINE-D) in all datasets tested without separate training on short and long disordered regions. Independent tests on four other datasets including the datasets from critical assessment of structure prediction (CASP) techniques and >10 000 annotated proteins from MobiDB, confirmed SPOT-Disorder as one of the best methods in disorder prediction. Moreover, initial studies indicate that the method is more accurate in predicting functional sites in disordered regions. These results highlight the usefulness combining LSTM with deep bidirectional recurrent neural networks in capturing non-local, long-range interactions for bioinformatics applications. SPOT-disorder is available as a web server and as a standalone program at: http://sparks-lab.org/server/SPOT-disorder/index.php . j.hanson@griffith.edu.au or yuedong.yang@griffith.edu.au or yaoqi.zhou@griffith.edu.au. Supplementary data is available at Bioinformatics online.