Conventional Seismic Inversion Research Articles

Pre-stack seismic inversion based on model-constrained generative adversarial network

Pre-stack seismic inversion usually uses various traditional algorithms to estimate elastic parameters such as P-wave velocity, S-wave velocity, and density. It is hard to derive accurate elastic parameters due to their non-uniqueness and high dimensionality between elastic parameters and seismic data, the calculation of elastic parameters is inaccurate. Convolutional Neural Networks (CNNs) have high-dimensional feature space mapping capabilities, which are utilized to establish mapping relationships between seismic data and elasticity parameters. However, their effectiveness is greatly affected by label data, and at the same time, due to the lack of enough label data, resulting in a low degree of fitting between prediction results and real data. In addition, conventional seismic inversion methods based on CNNs lack physical model constraints, resulting in low accuracy and poor interpretability of prediction results. We propose a Cycle-consistent Generative Adversarial Network based on a geophysical mechanism (SeisInv-CycleGAN). Deterministic inversion results and labeled data are combined into hybrid geophysical data as a training set of SeisInv-CycleGAN with geophysical constraints. At the same time, the residual (seismic loss) between the seismic data synthesized by forward modeling and the actual data is used as part of the loss function. The SeisInv-CycleGAN does not require building an initial model, and it can achieve higher accuracy in prediction results with a small amount of labeled data.

A New Robust Weak Supervision Deep Learning Approach for Reservoir Properties Prediction in Malaysian Basin Field

The conventional seismic inversion approach is practical for operational work, as it only uses simple linearized algorithms and assumptions, but may be less applicable when dealing with a complex geological setting, especially in the Malay basin fields, as it may introduce non-linear noises and non-unique solutions. In the Malay basin, we also frequently struggle with a scarcity of reliable well data when performing seismic inversions. This makes finding an accurate prior model for inversion challenging and contributes to high uncertainty in properties’ estimation. Implementation of deep learning for seismic inversion has become routine and has shown increasing capability in addressing nonlinearity in inverse problems. In this work, we develop a robust approach to deep learning-based seismic inversion to predict elastic properties from seismic data. The approach incorporates synthetic well and seismic data generation from a set of rock physics knowledge called the rock physics library, which plays a significant role in dataset input for network training, validation, and testing to improve elastic properties in this field. The deep learning network architecture comprising UNET and RESNET-18 with weak supervision networks has proven to be useful to enhance computational work efficiency and prediction accuracy while handling the non-linearity of the data and the non-uniqueness of the solutions. We successfully validated the proposed method on actual field data from a clastic fluvial-dominated field in the Malay basin. Upon comparative analysis with the conventional method, both inversion results are comparable and capable of identifying the reservoir occurrence and distribution. The conventional method exposed the presence of scattered amplitude noises and prominent seismic imprints masking the reservoir. Meanwhile, the proposed method showed more stable, clearer definition and fewer noise inversion results but with a faster turn-around time and a more efficient workflow. There are substantial improvements of up to 31% in correlation accuracy achieved upon implementing the proposed method for elastic properties prediction compared to the conventional. The result implies that the proposed method can provide a good elastic properties prediction framework while addressing data limitations and sparsity issues in typical deep learning-based inversions.

Prediction of Marine Thin Shale Gas Reservoir with Seismic Phase-Controlled Nonlinear Stochastic Inversion

Due to the complicated interference sources and low signal-to-noise ratio of seismic records, conventional seismic inversion methods are difficult to accurately identify shale gas reservoirs with a thickness of less than 10 m. This presents great challenges to shale gas exploration and development in China. Seismic phase-controlled nonlinear stochastic inversion (SPCNSI) is related to the heterogeneity of underground media. With the constraints of the stratigraphic sequence or seismic facies models, the minimum value between the seismic model and seismic record can be solved through iterative processes. Based on the solved acoustic velocity in formation, the constraints for SPCNSI can be formed with the matching relationship between target layers and different sequences in three-dimensional space. The prediction resolution of an unconventional reservoir can be effectively improved by combining logging, geological and seismic information. The method is suitable for predicting thin shale gas reservoirs in complex geological structures. In this study, SPCNSI was developed to predict the thin-layer marine shale gas reservoir in the southeast of Chongqing; the horizontal and vertical distribution characteristics were proven in the Longmaxi Formation and the Wufeng Formation; thin layers with a thickness of less than 7 m were also discovered. According to the results, three sets of potential development areas were determined by the inversion method, and the accuracy and reliability of the method were verified by logging and productivity testing.

Direct inversion for the equivalent pore aspect ratio based on the theory of ellipsoid modelling

AbstractPore aspect ratio, together with porosity, is a structural parameter that represents the geometric property of rock reservoirs. We have adopted the theory of ellipsoid modelling in material mechanics to derive the dry rock modulus. Based on this derivation, the Gassmann equation, which is a constitutional equation for a fully saturated rock model, can be linearized in terms of the pore structure parameters and the elastic parameters. We have established a relationship between the seismic reflection coefficient and the pore structure parameters, where the equivalent pore aspect ratio and porosity are two key parameters. Based on this relationship, the equivalent pore aspect ratio can be inverted directly from seismic reflection data instead of being converted from the intermediate parameters of conventional seismic inversion. Therefore, seismic inversion is a simultaneous inversion in which seven parameters are inverted: the elastic moduli (matrix bulk modulus and shear modulus, fluid bulk modulus), the densities (matrix and fluid densities) and the pore structure parameters (the equivalent pore aspect ratio and porosity). We applied this direct inversion scheme to a carbonate reservoir to predict the fracture development zone with low porosity and low aspect ratio.

Seismic inverse modeling method based on generative adversarial networks

Seismic inverse modeling is a common method in reservoir architecture characterization associated with geology. The conventional seismic inversion method is difficult to combine with complicated and abstract knowledge on geological modes, and its uncertainty is difficult to be assessed. In this paper, an inversion modeling method based on a wasserstein generative adversarial networks with gradient penalty (WGAN-GP) is introduced to integrate geology, well data and seismic data. A WGAN-GP is a generation model algorithm based on generative adversarial networks (GANs) that extracts spatial structure and abstract features of a training image. A gradient penalty function is added to an original loss function of GANs to improve the robustness. After assessment of the loss function, variograms and connectivity functions, the trained network is applied to seismic inversion simulation. In inversion, an optimal model is selected by the Metropolis with Markov chain Monte Carlo algorithm. Results show that the trained network can reproduce a thousand models containing millions of grid cells with a specific mode similar to a training image in 1 s. The inversion models conform to well data with 100% accuracy and have an efficient correspondence with prior seismic data. A whole inversion process completes 360,000 iterations in 4 h. The optimal inversion model has a subequal Root Mean Square Error (RMSE) with the true model and visually resembles a channel. With the proposed method, geological knowledge has a stable characterization in model realizations.

High-resolution seismic acoustic impedance inversion with the sparsity-based statistical model

Seismic acoustic impedance inversion plays an important role in subsurface quantitative interpretation. Due to the band-limited property of the seismic record and the discretization of the continuous elastic parameters with a limited sampling interval, the inverse problem suffers from serious ill-posedness. Various regularization methods are introduced into the seismic inversion to make the inversion results comply with the prespecified characteristics. However, conventional seismic inversion methods can only reflect fixed distribution characteristics and do not take into account discretization challenges. We have adopted a new poststack seismic impedance inversion method with upsampling and adaptive regularization. The adaptive regularization is constructed with two trained dictionaries from the true model and upsampled model-based inversion result to capture the features of high- and low-resolution details, and a sparsity-based statistical model is proposed to build the relationship between their sparse representations. The high-resolution components can be recovered based on the prediction model and low-resolution sparse representations, and the parameters of the statistical prediction model can be obtained effectively with conventional optimization algorithms. The synthetic and field data tests show that the model-based inversion is dependent on the sample interval, and our method can reveal more thin layers and enhance the extension of the strata compared with conventional inversion methods. Moreover, the inverted impedance variance of our method matches well with the borehole observations. The tests demonstrate that the interpolated model-based inversion result combined with the sparsity-based prediction model can effectively improve the resolution and accuracy of the inversion results.

High-resolution fixed-point seismic inversion

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.

Retrieving Low-Wavenumber Information in FWI: An Efficient Solution for Cycle Skipping

Full waveform inversion (FWI) plays a central role in the field of seismic processing due to the advantage in recovering the properties of the subsurface from seismograms. However, it suffers from more local minima convergence and more serious nonlinearity than the conventional seismic inversion method mainly caused by the lack of low-frequency information in the seismic data or the low-wavenumber components in the starting model. In this letter, we present a novel technique for seismic FWI based the angle difference identity for cosine, which builds an internal connection between high- and low-frequency signals. Thus, we can use the high-frequency information to get a plausible recovery of the low-wavenumber velocity. In addition, we choose the amplitude-independent objective function, which is given by maximizing the cross correlation between the modeled and observed data, to deal with the imperfect amplitude matching in the real case. Finally, a synthetic example of SEG/EAGE salt model is employed to demonstrate the validity of the proposed method, when low-frequency signals are absent.

Amplitude variation with incident angle inversion for fluid factor in the depth domain

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.

A depth variant seismic wavelet extraction method for inversion of poststack depth-domain seismic data

Prestack depth seismic imaging is increasingly being used in industry, which has also led to an increasing need for its inversion results, such as acoustic impedance (AI), for reservoir characterization. Conventional seismic inversion methods for reservoir characterization are usually implemented in the time domain. A depth-time conversion would be required before inversion of depth-domain seismic data, which would depend on an accurate velocity model and a fine time-depth conversion algorithm. Thus, it could be beneficial that we can directly invert the depth migrated seismic data. Depth-domain seismic data could indicate a strong nonstationarity, such as spectral variation, which makes it difficult to use a constant wavelet for direct inversion in depth. To address this issue, we have developed a new wavelet extraction method by using a depth-wavenumber decomposition technique, which can generate depth variant wavelets to accommodate the nonstationarity of the depth-domain seismic data. The synthetic and real data applications have been used to test the effectiveness of our method. The directly inverted depth-domain AI indicates a good correlation with well-log data and a strong potential for reservoir characterization.

Two-parameter prestack seismic inversion of porosity and pore structure parameter of fractured carbonate reservoirs: Part 1 — Methods

Fractured zones in deeply buried carbonate hills are important because they often have better permeability resulting in prolific production than similar low-porosity rocks. Nevertheless, their detection poses great challenge to conventional seismic inversion methods because they are mostly low in acoustic impedance and bulk modulus, hardly distinguishable from high-porosity zones or mudstones. A proxy parameter of pore structure defined in a rock-physics model, the so-called Sun model, has been used for delineating fractured zones in which the pore structure parameter is relatively high, whereas the porosity is low in general. Simultaneous seismic inversion of the pore structure parameter and porosity proves to be difficult and nontrivial in practice. Although the pore structure parameter is well-defined at locations where density, P-, and S-velocity are known from logs, estimation of P- and S-velocity information, especially density information from prestack seismic data is rather challenging. A three-step iterative inversion method, which uses acoustic, gradient, and elastic impedance from angle-stacked seismic data as input to the rock-physics model for calculating porosity and bulk and shear pore structure parameters simultaneously, is proposed and implemented to solve this problem. The methodology is successfully tested with well logs and seismic data from a deeply buried carbonate hill in the Bohai Bay Basin, China.

Elastic Impedance Inversion Based on Improved Particle Swarm Optimization

Particle Swarm Optimization has the advantages of fast convergence, simple programming and less parameters, therefore it has been widely used in solving the problems of continuous function optimization in many fields. In recent years, it begins to apply to seismic data inversion. Conventional seismic inversion adopts linear inversion methods, which strongly depend on the initial models and easily fall into local extremum. We propose an improved particle swarm optimization by adding simulated annealing, which enhances the efficiency and feasibility of the algorithm. Then we apply the improve algorithm to seismic elastic impedance inversion. After the model test of this algorithm, it is used to invert the seismic data of a certain area in Shengli Oilfield, and a number of elastic parameter profiles are obtained, which are in agreement with the actual drilling results. This method provides an effective and feasible way for the exploration and development of complex oil and gas reservoirs.

Reliability enhancement of mixed-domain seismic inversion with bounding constraints

ABSTRACTSeismic inversion works as one of pragmatic and effective approaches to estimate the subsurface parameters. One robust Bayesian sparse inversion method incorporating the mixed-domain convolution with model bounding constraints is proposed in this study. The time-domain response and partial frequency components are utilized in mixed-domain seismic inversion to improve the resolution and stability of seismic inversion. First, the objective updated function is yielded with Bayesian inference in joint time and frequency domain. And, the sparse constraint is incorporated into the objective function to improve robustness of inversion algorithm. Conventional seismic inversion methods always don’t focus on the lower and upper bounding constraints on subsurface model parameters, due to which unrealistic predicted results may arise. To get rid of the problem, the bounding constraints on P-wave impedance elaborated by logarithmic or inverse hyperbolic tangent formulas is introduced in mixed-domain seismic inversion as it renders to reduce the unrealistic parameters and enhance the reliability of prediction effectively. In addition, the synthetic examples demonstrate the effectiveness and robustness of the proposed inversion algorithm. Finally, one field case is studied carefully and the estimated parameters with bounding constraints at the borehole-side location can preserve a high degree of agreements with real logging data to verify the practicability of the bounding-constraining mixed-domain Bayesian inversion.

Application of attribute-based inversion and spectral decomposition with red–green–blue colour blending for visualization of geological features: a case study from the Kalol Field, Cambay Basin, India

The Kalol Field in the Cambay Basin of India was discovered in 1961 and has been producing through more than 608 wells from Kalol reservoirs but the cumulative production up until 2008 was only 95.19 MMbbl. Reasons for low recovery have been ascribed to poor reservoir facies and limited reservoir thicknesses. In the Kalol Field, several thin clastic reservoirs are sandwiched within the main reservoir and exhibit lateral variations in lithology. Attribute-based inversion (ABI) is effective at delineating potentially prospective areas and reveals the existence of a good reservoir facies cluster in the south, SE and NW corners of our study area, near the Kalol Field. However, this method cannot decipher the depositional setting or the finer details of facies elements. To obtain a smooth and fine-tuned facies model, geostatistical modelling is adopted taking the ABI output (seismic-facies model) as the initial model. The advantage of geostatistical modelling is that it always honours the input data and respects the positional variograms of the geology. Adding spectral decomposition with red–green–blue (SD-RGB) colour blending reveals the existence of a meandering river in the study area. This river is interpreted to have deposited crevasse splays and channel facies along the river banks. These two facies are the main producing contributors to a well that has maintained a higher production than any other well in this field. This facies-based approach is also effective in determining the reservoir geometry and quality consistent with the interpretation of the depositional environment. In ABI, 3D attribute volumes of petrophysical properties are calculated using a genetic algorithm inversion and artificial neural network using a non-linear correlation between seismic and log properties. The calculated 3D attribute volumes of petrophysical properties are subsequently utilized for seismic facies classification. In contrast to ABI, SD-RGB colour blending has been solely utilized for co-visualization of different band-limited amplitude volumes from spectral decomposition. Conventional seismic inversion has now been replaced by an integrated approach combining ABI, geostatistical modelling and SD-RGB colour blending in an effort to delineate the remaining potential of the field, and to improve the geological success and ultimate recovery.

Understanding stochastic inversion: part 1

Ashley Francis, managing director of UK consultancy Earthworks Environment & Resources, provides the first of a two-part tutorial on the theory of deterministic and stochastic inversion with some comparison of the pros and cons of the two methods. The second part will appear in the December issue of First Break. Seismic inversion tools designed to estimate impedance have been available to geophysicists for over 20 years. Most of the available methods are based on forward convolution of a reflectivity model with the estimated wavelet, comparison of the modelled output with the observed seismic trace and then updating the reflectivity model (inverting) to minimize the difference between the modelled and observed traces. Whether generalized linear inversion, sparse spike, or simulated annealing, all the algorithms work on this basic principle of minimization. Methods based on minimization are commonly referred to as ‘deterministic’. The output of a deterministic inversion is a relatively smooth (or blocky) estimate of the impedance. Because of its smoothness deterministic inversion is generally unsuited for constraining reservoir models used for volumetric calculations, estimation of connectivity, or fluid flow simulation. Stochastic seismic inversion generates a suite of alternative heterogeneous impedance representations that agree with the 3D seismic volume. Taken together, the suite of possible impedance models or realizations capture the uncertainty or non-uniqueness associated with the seismic inversion process. Stochastic seismic inversion is complementary to deterministic inversion. The deterministic seismic inversion is the average of all the possible non-unique stochastic realizations. Although the principles of stochastic seismic inversion were published over 12 years ago, commercial implementation and application have only started to grow in the last five years or so. For many geophysicists, understanding and being able to make a discerning judgement on the possible benefits of this new technique is difficult. A number of misconceptions concerning stochastic seismic inversion have arisen, particularly related to resolution. A commonplace but incorrect statement is that stochastic techniques can ‘…allow substantially increased resolution, capturing details well beyond seismic bandwidth’. It is the purpose of this tutorial to provide a clear theoretical basis for deterministic and stochastic inversion and assist the geophysicist in making an informed decision concerning the application of stochastic seismic inversion to his or her particular reservoir description problem. In order to understand stochastic seismic inversion we will have to understand some of the limitations of conventional seismic inversion (often referred to as ‘deterministic’ inversion), provide a grounding in some geostatistical concepts, and also consider the general problem of estimation at unmeasured locations. This tutorial will only consider seismic inversion in the sense of estimating an impedance model of the subsurface. ‘Impedance’ will be taken in a very general sense to refer to any rock property estimated from surface seismic data. This could include acoustic or elastic impedance, extended elastic impedance, or any other more elaborate pre-stack inversion scheme to estimate Vp, Vs, and density. Stochastic inversion may be applied to any of these objectives and the aim of this tutorial is to describe only the general limitations of deterministic inversion and the possible advantages of a stochastic inversion framework and not to consider the specifics of pre-or post-stack inversion objectives.