Elastic pre-stack seismic inversion through Discrete Cosine Transform reparameterization and Convolutional Neural Networks

Geophysics ◽  
2020 ◽  
pp. 1-70
Author(s):  
Mattia ALEARDI ◽  
Alessandro Salusti
Keyword(s):  
Discrete Cosine Transform ◽  
Elastic Properties ◽  
Seismic Data ◽  
Orthogonal Transformation ◽  
Seismic Inversion ◽  
Joint Probability Distribution ◽  
Elastic Model ◽  
Inversion Algorithm ◽  
Elastic Parameters ◽  
Cosine Transform

We develop a pre-stack inversion algorithm that combines a Discrete Cosine Transform (DCT) reparameterization of data and model spaces with a Convolutional Neural Network (CNN). The CNN is trained to predict the mapping between the DCT-transformed seismic data and the DCT-transformed 2-D elastic model. A convolutional forward modeling based on the full Zoeppritz equations constitutes the link between the elastic properties and the seismic data. The direct sequential co-simulation algorithm with joint probability distribution is used to generate the training and validation datasets under the assumption of a stationary non-parametric prior and a Gaussian variogram model for the elastic properties. The DCT is an orthogonal transformation that is here used as an additional feature extraction technique that reduces the number of unknown parameters in the inversion and the dimensionality of the input and output of the network. The DCT reparameterization also acts as a regularization operator in the model space and allows for the preservation of the lateral and vertical continuity of the elastic properties in the recovered solution. We also implement a Monte Carlo simulation strategy that propagates onto the estimated elastic model the uncertainties related to both noise contamination and network approximation. We focus on synthetic inversions on a realistic subsurface model that mimics a real gas-saturated reservoir hosted in a turbiditic sequence. We compare the outcomes of the implemented algorithm with those provided by a popular linear inversion approach and we also assess the robustness of the CNN inversion to errors in the estimated source wavelet and to erroneous assumptions about the noise statistic. Our tests confirm the applicability of the proposed approach, opening the possibility of estimating the subsurface elastic parameters and the associated uncertainties in near real-time while satisfactorily preserving the assumed spatial variability and the statistical properties of the elastic parameters.

Geostatistical inversion of prestack seismic data for the joint estimation of facies and impedances using stochastic sampling from Gaussian mixture posterior distributions

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. M55-M65 ◽  
Author(s):  
Xiaozheng Lang ◽  
Dario Grana
Keyword(s):  
Elastic Properties ◽  
Posterior Distribution ◽  
Seismic Data ◽  
Gaussian Mixture ◽  
Seismic Inversion ◽  
Joint Estimation ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Data Set ◽  
Geostatistical Approach

We have developed a seismic inversion method for the joint estimation of facies and elastic properties from prestack seismic data based on a geostatistical approach. The objectives of our inversion methodology are to sample from the posterior distribution of seismic properties and to simultaneously classify the lithology conditioned by seismic data. The inversion algorithm is a sequential Gaussian mixture inversion based on Bayesian linearized amplitude variation with offset inverse theory and sequential geostatistical simulations. The stochastic approach to the inversion allows generating multiple elastic models that match the seismic data. To mathematically represent the multimodal behavior of elastic properties due to their variations within different lithologies, we adopt a Gaussian mixture distribution for the prior model of the elastic properties and we use the prior probability of the facies as weights of the Gaussian components of the mixture. The solution of the inverse problem is achieved by deriving the explicit analytical expression of the posterior distribution of the elastic properties and facies and by sampling from this distribution according to a spatial correlation model. The inversion methodology has been validated using well logs and synthetic seismic data with different noise levels, and it is then applied to a real 3D seismic data set in North Sea.

Mineralogy-based brittleness prediction from surface seismic data: Application to the Barnett Shale

2014 ◽  
Vol 2 (4) ◽  
pp. T255-T271 ◽  
Author(s):  
Roderick Perez Altamar ◽  
Kurt Marfurt
Keyword(s):  
Seismic Data ◽  
Seismic Inversion ◽  
Barnett Shale ◽  
Elastic Parameters ◽  
Well Location ◽  
Data Application ◽  
Empirical Calibration ◽  
Two Measures ◽  
Prestack Seismic Inversion ◽  
Microseismic Event

Differentiating brittle and ductile rocks from surface seismic data is the key to efficient well location and completion. Brittleness average estimates based only on elastic parameters are easy to use but require empirical calibration. In contrast, brittleness index (BI) estimates are based on mineralogy laboratory measurements and, indeed, cannot be directly measured from surface seismic data. These two measures correlate reasonably well in the quartz-rich Barnett Shale, but they provide conflicting estimates of brittleness in the calcite-rich Viola, Forestburg, Upper Barnett, and Marble Falls limestone formations. Specifically, the BI accurately predicts limestone formations that form fracture barriers to be ductile, whereas the brittleness average does not. We used elemental capture spectroscopy and elastic logs measured in the same cored well to design a 2D [Formula: see text] to brittleness template. We computed [Formula: see text] and [Formula: see text] volumes through prestack seismic inversion and calibrate the results with the [Formula: see text] template from well logs. We then used microseismic event locations from six wells to calibrate our prediction, showing that most of the microseismic events occur in the brittle regions of the shale, avoiding more ductile shale layers and the ductile limestone fracture barriers. Our [Formula: see text] to brittleness template is empirical and incorporates basin- and perhaps even survey-specific correlations of mineralogy and elastic parameters through sedimentation, oxygenation, and diagenesis. We do not expect this specific template to be universally applicable in other mudstone rock basins; rather, we recommend interpreters generate similar site-specific templates from logs representative of their area, following the proposed workflow.

Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: A review

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A165-75A176 ◽  
Author(s):  
Miguel Bosch ◽  
Tapan Mukerji ◽  
Ezequiel F. Gonzalez
Keyword(s):  
Elastic Properties ◽  
Quantitative Estimation ◽  
Rock Physics ◽  
Seismic Inversion ◽  
Elastic Parameters ◽  
Reservoir Properties ◽  
Sequential Approach ◽  
Geostatistical Methods ◽  
Bayesian Formulation ◽  
Statistical Rock Physics

There are various approaches for quantitative estimation of reservoir properties from seismic inversion. A general Bayesian formulation for the inverse problem can be implemented in two different work flows. In the sequential approach, first seismic data are inverted, deterministically or stochastically, into elastic properties; then rock-physics models transform those elastic properties to the reservoir property of interest. The joint or simultaneous work flow accounts for the elastic parameters and the reservoir properties, often in a Bayesian formulation, guaranteeing consistency between the elastic and reservoir properties. Rock physics plays the important role of linking elastic parameters such as impedances and velocities to reservoir properties of interest such as lithologies, porosity, and pore fluids. Geostatistical methods help add constraints of spatial correlation, conditioning to different kinds of data and incorporating subseismic scales of heterogeneities.

Accuracy Comparison of Elastic Impedance Formula

2012 ◽  
Vol 466-467 ◽  
pp. 400-404
Author(s):  
Jin Zhang ◽  
Huai Shan Liu ◽  
Si You Tong ◽  
Lin Fei Wang ◽  
Bing Xu
Keyword(s):  
Seismic Data ◽  
Poisson Ratio ◽  
Seismic Inversion ◽  
P Wave ◽  
S Wave ◽  
Elastic Parameters ◽  
Accuracy Comparison ◽  
Elastic Impedance ◽  
Prestack Seismic Inversion ◽  
Lamé Coefficients

Elastic impedance (EI) inversion is one of the prestack seismic inversion methods, which can obtain P-wave and S-wave velocity, density, Poisson ratio, Lame coefficients and other elastic parameters. But there have been many EI formulas nowadays, so which formula should be used in inversion is an urgent problem. This paper divides these formulas into two categories, and use several forward modeling to test the accuracy of these EI formulas. It shows that using the first kind of EI formulas in near offset seismic data can get high precision results.

Seismic Quantitative Interpretation for Uncertainty Reduction of Subsurface Modeling of the Deep Visean Reservoirs

2021 ◽  
Author(s):  
Pavlo Kuzmenko ◽  
Rustem Valiakhmetov ◽  
Francesco Gerecitano ◽  
Viktor Maliar ◽  
Grigori Kashuba ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Seismic Data ◽  
Seismic Anisotropy ◽  
Rock Physics ◽  
Seismic Inversion ◽  
Well Logs ◽  
Quantitative Interpretation ◽  
Structural Interpretation ◽  
Elastic Inversion ◽  
Subsurface Modeling

Abstract The seismic data have historically been utilized to perform structural interpretation of the geological subsurface. Modern approaches of Quantitative Interpretation are intended to extract geologically valuable information from the seismic data. This work demonstrates how rock physics enables optimal prediction of reservoir properties from seismic derived attributes. Using a seismic-driven approach with incorporated prior geological knowledge into a probabilistic subsurface model allowed capturing uncertainty and quantifying the risk for targeting new wells in the unexplored areas. Elastic properties estimated from the acquired seismic data are influenced by the depositional environment, fluid content, and local geological trends. By applying the rock physics model, we were able to predict the elastic properties of a potential lithology away from the well control points in the subsurface whether or not it has been penetrated. Seismic amplitude variation with incident angle (AVO) and azimuth (AVAZ) jointly with rock-derived petrophysical interpretations were used for stochastical modeling to capture the reservoir distribution over the deep Visean formation. The seismic inversion was calibrated by available well log data and by traditional structural interpretation. Seismic elastic inversion results in a deep Lower Carboniferous target in the central part of the DDB are described. The fluid has minimal effect on the density and Vp. Well logs with cross-dipole acoustics are used together with wide-azimuth seismic data, processed with amplitude control. It is determined that seismic anisotropy increases in carbonate deposits. The result covers a set of lithoclasses and related probabilities: clay minerals, tight sandstones, porous sandstones, and carbonates. We analyzed the influence of maximum angles determination for elastic inversion that varied from 32.5 to 38.5 degrees. The greatest influence of the far angles selection is on the density. AI does not change significantly. Probably the 38,5 degrees provides a superior response above the carbonates. It does not seem to damage the overall AVA behavior, which result in a good density outcome, as higher angles of incidence are included. It gives a better tie to the wells for the high density layers over the interval of interest. Sand probability cube must always considered in the interpretation of the lithological classification that in many cases may be misleading (i.e. when sand and shale probabilities are very close to each other, because of small changes in elastic parameters). The authors provide an integrated holistic approach for quantitative interpretation, subsurface modeling, uncertainty evaluation, and characterization of reservoir distribution using pre-existing well logs and recently acquired seismic data. This paper underpins the previous efforts and encourages the work yet to be fulfilled on this subject. We will describe how quantitative interpretation was used for describing the reservoir, highlight values and uncertainties, and point a way forward for further improvement of the process for effective subsurface modeling.

Joint electromagnetic and seismic inversion using structural constraints

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. R99-R109 ◽  
Author(s):  
Wenyi Hu ◽  
Aria Abubakar ◽  
Tarek M. Habashy
Keyword(s):  
Seismic Data ◽  
Joint Inversion ◽  
Monitoring And Evaluation ◽  
Structural Similarity ◽  
Compressional Wave ◽  
Seismic Inversion ◽  
P Wave ◽  
Optimization Approach ◽  
Structural Constraints ◽  
Inversion Algorithm

We have developed a frequency-domain joint electromagnetic (EM) and seismic inversion algorithm for reservoir evaluation and exploration applications. EM and seismic data are jointly inverted using a cross-gradient constraint that enforces structural similarity between the conductivity image and the compressional wave (P-wave) velocity image. The inversion algorithm is based on a Gauss-Newton optimization approach. Because of the ill-posed nature of the inverse problem, regularization is used to constrain the solution. The multiplicative regularization technique selects the regularization parameters automatically, improving the robustness of the algorithm. A multifrequency data-weighting scheme prevents the high-frequency data from dominating the inversion process. When the joint-inversion algorithm is applied in integrating marine controlled-source electromagnetic data with surface seismic data for subsea reservoir exploration applications and in integrating crosswell EM and sonic data for reservoir monitoring and evaluation applications, results improve significantly over those obtained from separate EM or seismic inversions.

scholarly journals Poisson impedance for lithology characterization

2021 ◽  
Vol 6 (1) ◽  
pp. 23-28
Author(s):  
A. V. Khitrenko ◽  
K. A. Groman ◽  
A. V. Lobusev
Keyword(s):  
Elastic Properties ◽  
Seismic Data ◽  
Western Siberia ◽  
Oil And Gas ◽  
Seismic Attributes ◽  
Seismic Inversion ◽  
Seismic Survey ◽  
Lateral Heterogeneity ◽  
Main Method

Tyumen formation is a formation with very considerably lateral heterogeneity. It influences on process of exploration oil and gas traps. No one can deny that seismic survey is a main method for prediction lateral heterogeneity. Nowadays, geoscientists can model different useful seismic attributes, apart from structural maps. Seismic inversion is most effective tool for transformation amplitude seismic data into elastic properties. However, sometimes result of seismic inversion is very hard to understand and analyze. In this work, authors will show additional methods for better understanding results of seismic inversion using Impedance Poisson. Area of research is located in the Western Siberia.

APPLICATIONS OF LEFT CIRCULANT MATRICES IN SIGNAL AND IMAGE PROCESSING

2008 ◽  
Vol 22 (04) ◽  
pp. 231-241 ◽  
Author(s):  
M. ANDRECUT
Keyword(s):  
Image Processing ◽  
Discrete Cosine Transform ◽  
Orthogonal Transformation ◽  
Circulant Matrices ◽  
Signal And Image Processing ◽  
Cosine Transform ◽  
Similar Performance ◽  
Signal Image

We show numerically that the orthogonal transformation corresponding to the eigenvectors of (random) left circulant matrices, has similar performance in signal/image processing like the discrete cosine transform.

Prestack and poststack inversion using a physics-guided convolutional neural network

2019 ◽  
Vol 7 (3) ◽  
pp. SE161-SE174 ◽  
Author(s):  
Reetam Biswas ◽  
Mrinal K. Sen ◽  
Vishal Das ◽  
Tapan Mukerji
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Elastic Properties ◽  
Wave Velocity ◽  
Seismic Data ◽  
Synthetic Data ◽  
P Wave ◽  
Distinct Advantage ◽  
Elastic Parameters ◽  
Data Set

An inversion algorithm is commonly used to estimate the elastic properties, such as P-wave velocity ([Formula: see text]), S-wave velocity ([Formula: see text]), and density ([Formula: see text]) of the earth’s subsurface. Generally, the seismic inversion problem is solved using one of the traditional optimization algorithms. These algorithms start with a given model and update the model at each iteration, following a physics-based rule. The algorithm is applied at each common depth point (CDP) independently to estimate the elastic parameters. Here, we have developed a technique using the convolutional neural network (CNN) to solve the same problem. We perform two critical steps to take advantage of the generalization capability of CNN and the physics to generate synthetic data for a meaningful representation of the subsurface. First, rather than using CNN as in a classification type of problem, which is the standard approach, we modified the CNN to solve a regression problem to estimate the elastic properties. Second, again unlike the conventional CNN, which is trained by supervised learning with predetermined label (elastic parameter) values, we use the physics of our forward problem to train the weights. There are two parts of the network: The first is the convolution network, which takes the input as seismic data to predict the elastic parameters, which is the desired intermediate result. In the second part of the network, we use wave-propagation physics and we use the output of the CNN to generate the predicted seismic data for comparison with the actual data and calculation of the error. This error between the true and predicted seismograms is then used to calculate gradients, and update the weights in the CNN. After the network is trained, only the first part of the network can be used to estimate elastic properties at remaining CDPs directly. We determine the application of physics-guided CNN on prestack and poststack inversion problems. To explain how the algorithm works, we examine it using a conventional CNN workflow without any physics guidance. We first implement the algorithm on a synthetic data set for prestack and poststack data and then apply it to a real data set from the Cana field. In all the training examples, we use a maximum of 20% of data. Our approach offers a distinct advantage over a conventional machine-learning approach in that we circumvent the need for labeled data sets for training.

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