Bayesian acoustic impedance inversion with gamma distribution

Stochastic seismic acoustic impedance inversion via a Markov-chain Monte Carlo method using a single GPU card

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.

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.

Seismic impedance inversion is a vital way of geological interpretation and reservoir investigation from a geophysical perspective. However, it is inevitably an ill-posed problem due to the noise or the band-limited characteristic of seismic data. Artificial neural network have been used to solve nonlinear inverse problems in recent years. This research obtained an acoustic impedance profile by feeding seismic profile and background impedance into a well-trained self-attention U-Net. The U-Net got convergence by appropriate iteration, and the output predicted the impedance profiles in the test. To value the quality of predicted profiles from different perspectives, e.g., correlation, regression, and similarity, we used four kinds of indexes. At the same time, our results were predicted by conventional methods (e.g., deconvolution with recursive inversion, and TV regularization) and a 1D neural network was calculated in contrast. Self-attention U-Net showed to be robust to noise and does not require prior knowledge. Furthermore, spatial continuity is also better than deconvolution, regularization, and 1D deep learning methods in contrast. The U-Net in this paper is a type of full convolutional neural network, so there are no limits to the shape of the input. Based on this, a large impedance profile can be predicted by U-Net, which is trained by a patchy training dataset. In addition, this paper applied the proposed method to the field data obtained by the Ceduna survey without any label. The predictions prove that this well-trained network could be generalized from synthetic data to field data.

Objective The Bayesian model plays an important role in diagnostic test evaluation in the absence of the gold standard, which used the external prior distribution of a parameter combined with sample data to yield the posterior distribution of the test characteristics. However, the correlation between diagnostic tests has always been a problem that cannot be ignored in the Bayesian model evaluation. This study will discuss how different Bayesian model, correlation scenarios, and prior distribution affect the outcome. MethodsThe data analyzed in this study was gathered during studies of patients presenting to the Nanjing Chest Hospital with suspected tuberculosis. The diagnostic character of T-SPOT.Tb and KD38 tuberculosis antibody test were evaluated in different Bayesian model, and discharge diagnosis as a gold standard was used to verify the model results in the end. Result The comparison of four models under the conditional independence situation found that Bayesian probabilistic constraint model was consistent with the Conditional Covariance Bayesian model. The results were mainly affected by prior information. The sensitivity and specificity of the two tests in Conditional Covariance Bayesian model in prior constraint situation were considerably higher than the Bayesian probabilistic constraint model in prior constraint situation. The results of the four models under the conditional dependence situation were similar to the conditional independence situation; pD was also negative with no prior constraint situation in both model Bayesian probabilistic constraint model and Conditional Covariance Bayesian model. The Deviance Information Criterion of Bayesian probabilistic constraint model was close to model Conditional Covariance Bayesian model, but pD of Conditional Covariance Bayesian model in Prior constraint situation (pD=2.40) was higher than the Bayesian probabilistic constraint model in Prior constraint situation (pD=1.66). Conclusion The result of Conditional Covariance Bayesian model in prior constraint with conditional independence situation was closest to the result of gold standard evaluation in our data. Both of the two Bayesian methods are the feasible way for the evaluation of diagnostic test in the absence of the gold standard diagnostic. Prior source, priority number, and conditional dependencies should be considered in the method selection, the accuracy of posterior estimation mainly depending on the prior distribution.

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.

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

Impact of the Scientific Registry of Transplant Recipients’ New Bayesian Method on Estimating Center Effects and Flagging of Centers as Worse Than Expected

Combining impedance inversion and seismic similarity for robust gas hydrate concentration assessments – A case study from the Krishna–Godavari basin, East Coast of India

In the current age of declining oil prices, mature fields matter today more than ever. About 70% of the current world oil production is from mature fields. To unlock the remaining potential from these fields, new wells need to be implemented by utilising technological advancements in reservoir characterisation, well engineering and reservoir engineering. This paper focuses on improving reservoir understanding by using rock physics and seismic inversion technology on a mature field, which is located in offshore Sarawak Malaysia. Seismic data can be incorporated into an integrated workflow of predicting rock properties by utilising inversion processes that transform seismic data into a quantitative rock property, a descriptive measure of the reservoir. In this paper, an integrated workflow is adopted and it involves the application of rock physics driven seismic inversion for acoustic impedance (AI) prediction and geobody extraction. The extracted geobodies describe the areal extent of oil reservoir and changes in the rock property. The field being studied consists of multi-stacked channelised reservoirs containing substantial amount of crevasse splay sands. The main producing units are thin oil sands with initial gas caps. These reservoirs typically display a high degree of vertical and lateral heterogeneity. Seismic inversion and geobody prediction were used as a method for the prediction of petrophysical properties including porosity, Net-to-Gross (NTG), water saturation and permeability at geo-cellular scale. To this end, the information from different fault blocks was integrated for the simulation study and incorporated into the evaluation of the oil potential in this mature field. A holistic approach that comprises both a material balance study and a simulation study was adopted. The material balance study was used to verify the drive mechanism and to evaluate the transmissivity between different fault blocks. Prolific reservoirs were identified on inverted AI data and integrated into the static model for volumetric estimations and further high grading of the development drilling locations. As seismic inversion offers non-unique solutions, the integration of well log data allowed a technically acceptable answer as well as an estimation of the associated uncertainty. It can be concluded that rock physics driven seismic inversion results reduces uncertainty in property estimation during reservoir modelling while simultaneously improving field development plans. This paper focuses on how the integration of seismic and well data was used to optimally characterise an oil reservoir in a mature field development and create a fit-for- purpose reservoir model. The goal was to optimise reservoir characterisation and production management which leads to success and low risk re-development. Ultimately, the economics were improved through reducing the uncertainties in monetising the remaining by-passed oil reserves to a manageable range.

Multi-trace acoustic impedance inversion with multiplicative regularization

Summary Seismic inversion for acoustic impedance can be robustly and efficiently performed through the application of a spectral shaping filter combined with a -90 o phase rotation. We show that this process, first published by Lancaster and Whitcombe (2000), is rigorously accurate and mathematically equivalent to all other methods of acoustic inversion based on a onedimensional convolutional model. Yet, the one-dimensional convolutional model is inadequate for describing migrated traces, because it ignores the dip dependence of the wavelet after migration. Any seismic inversion method assuming such a model, will cause severe amplitude distortions when applied to migrated data, excessively amplifying dipping events, signal or noise. We describe here three methods to perform seismic inversion, that overcome the problem described above, n amely: (i) applying spectral shaping before migration; (ii) applying spectral shaping to demigrated data, that are then remigrated; (iii) applying a multi-dimensional spectral shaping operator after migration.

A fluid discrimination approach incorporating linearized poroelasticity theory and pre-stack seismic reflection inversion with Bayesian inference is proposed to identify the fluid underground. The fluid modulus is defined as the fluid indicator which is mainly affected by the fluid contained in reservoirs. A novel linearized P-wave reflectivity equation coupling the fluid modulus is derived to avoid the complicated nonlinear relationship between the fluid modulus with seismic data. Convoluting this linearized P-wave reflectivity with seismic wavelets as the forward solver, a practical pre-stack Bayesian seismic inversion method is presented to estimate the fluid modulus directly. Cauchy and Gaussian distribution are utilized for prior probability distribution of the model parameters and the likelihood function to enhance the inversion resolution. The preconditioned conjugate gradient method is coupled in the optimization of the inversion objective function to weaken the strong degree of correlation among the four model parameters and enhance the stability of multiple parameters estimation simultaneously. The synthetic test demonstrates the feasibility and stability of the proposed novel seismic coefficient equation and inversion approach. Test on a real data set illustrates the efficiency and success of the proposed approach in differentiating the fluid filled reservoirs.

We combine acoustic impedance inversion of 3D seismic data, log-to-seismic correlation, and seismic attribute analyses to delineate gas-hydrate zones at the Mallik site, Mackenzie Delta, Northwest Territories, Canada. Well-log data define three distinct hydrate zones over a depth range of 890–1100 m. Synthetic seismic modeling indicates the base of the two deeper hydrate zones are prominent reflectors. The uppermost gas-hydrate zone correlates to seismic data with a lower degree of confidence. The extent and geometry of the two lower hydrate zones suggest that local geology plays a significant role in the lateral and vertical distribution of gas hydrate at Mallik. The reliability of the hydrate concentrations calculated from the inverted impedances isqualified by the match between original and synthetic seismic data to produce confidence maps for the two lower gas-hydrate-bearing intervals. A total in-place volume estimate of solid gas hydrate for an area of [Formula: see text] around well 5L-38 yields a value of approximately [Formula: see text] (equivalently, [Formula: see text] of gas). We further qualify our mapping of gas hydrates by some amount of continuous resource, defined as lateral continuity measured by seismic attribute similarity and sand-dominated rock. Using these attributes, the continuous amount of hydrate at Mallik is about half the in-place volume (i.e., [Formula: see text]). Elsewhere within the 3D seismic cube, the seismic impedance inversion yields evidence of potential gas-hydrate deposits near wells A-06 and P-59 at levels near the predicted base of the hydrate stability zone.