High resolution fixed-point seismic inversion

2021 ◽  
pp. 1-54
Author(s):  
Song Pei ◽  
Xingyao Yin ◽  
Zhaoyun Zong ◽  
Kun Li
Keyword(s):  
Fixed Point ◽  
Objective Function ◽  
Seismic Data ◽  
Target Function ◽  
Recursive Formula ◽  
Frequency Component ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Good Convergence ◽  
Band Limited

Resolution improvement always presents the crucial task in geological inversion. Band-limited characteristics of seismic data and noise make seismic inversion complicated. Specifically, geological inversion suffers from the deficiency of both low- and high-frequency components. We propose the fixed-point seismic inversion method to alleviate these issues. The problem of solving objective function is transformed into the problem of finding the fixed-point of 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 around zero after 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 the moderate noise, the optimal inverted results can still be obtained with the proposed 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 (SVD) method is applied to the inversion framework, thus making a high improvement of anti-noise ability. At last, the synthetic models and seismic data are investigated following the proposed 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.

Depth-domain seismic reflectivity inversion with compressed sensing technique

2017 ◽  
Vol 5 (1) ◽  
pp. T1-T9 ◽  
Author(s):  
Rui Zhang ◽  
Kui Zhang ◽  
Jude E. Alekhue
Keyword(s):  
Compressed Sensing ◽  
Time Domain ◽  
Seismic Data ◽  
Reservoir Characterization ◽  
Synthetic Data ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Depth Migration ◽  
Band Limited ◽  
The Time Domain

More and more seismic surveys produce 3D seismic images in the depth domain by using prestack depth migration methods, which can present a direct subsurface structure in the depth domain rather than in the time domain. This leads to the increasing need for applications of seismic inversion on the depth-imaged seismic data for reservoir characterization. To address this issue, we have developed a depth-domain seismic inversion method by using the compressed sensing technique with output of reflectivity and band-limited impedance without conversion to the time domain. The formulations of the seismic inversion in the depth domain are similar to time-domain methods, but they implement all the elements in depth domain, for example, a depth-domain seismic well tie. The developed method was first tested on synthetic data, showing great improvement of the resolution on inverted reflectivity. We later applied the method on a depth-migrated field data with well-log data validated, showing a great fit between them and also improved resolution on the inversion results, which demonstrates the feasibility and reliability of the proposed method on depth-domain seismic data.

Sensitivity analysis of optimization parameters on cooperative inversion of seismic reflection and gravity data

2020 ◽  
Author(s):  
Maiara Gonçalves ◽  
Emilson Leite
Keyword(s):  
Sensitivity Analysis ◽  
Objective Function ◽  
Seismic Data ◽  
Optimization Methods ◽  
Inversion Method ◽  
Standard Case ◽  
Reflection Seismic ◽  
Gravimetric Data ◽  
Standard Values ◽  
Cooperative Inversion

<p>Reflections of seismic waves are strongly distorted by the presence of complex geological structures (e.g. salt bodies) and their vertical resolution is usually of the order of a few tens of meters, imposing limitations in the construction of subsurface models. One way to improve the reliability of such models is to integrate reflection seismic data with other types of geophysical data, such as gravimetric data, since the latter provide an additional link to map geological structures that exhibit density contrasts with respect to their surroundings. In a previous study, we developed a cooperative inversion method of 2D post-stack and migrated reflection seismic data, and gravimetric data. Using that inversion method, we minimize two problems: (1) the problem of the distortion of reflection seismic data due to the presence of complex geological bodies and (2) the problem of the greater ambiguity and the commonly lower resolution of the models obtained only from gravimetric anomalies. The method incorporates a technique to decrease the number of variables and is solved by optimization of the gravity inverse problem, thus reducing computing time. The objective function of cooperative inversion was minimized using three different methods of optimization: (1) simplex, (2) simulated annealing, and (3) genetic algorithm. However, these optimization methods have internal parameters which affect the convergence rate and objective function values. These parameters are usually chosen accordingly to previous references. Although the usage of these standard values is widely accepted, the best values to assure effectiveness and stability of convergence are case-dependent. In the present study, we propose a sensitivity analysis on the internal parameters of the optimization methods for the previously presented cooperative inversion. First, we developed the standard case, which is an inversion performed using all parameters at their standard values. Then, the sensitivity analysis is performed by running multiple inversions, each one with a set of parameters. Each set is obtained by modifying the value of a single parameter either for a lower or for a higher value, keeping all other values at their standard values. The results obtained by each setting are compared to the results of the standard case. The compared results are both the number of evaluations and the final value of the objective function. We then classify parameters accordingly to their relative influence on the optimization processes. The sensitivity analysis provides insight into the best practices to deal with object-based cooperative inversion schemes. The technique was tested using a synthetic model calculated from the Benchmark BP 2004, representing an offshore sedimentary basin containing salt bodies and small hydrocarbons reservoirs.</p>

Low frequency component of seismic data estimation and its application in seismic inversion

2020 ◽  
Author(s):  
Ding Jicai ◽  
Zhao Xiaolong ◽  
Jiang Xiudi ◽  
Wang Yandong ◽  
Huang Xiaogang ◽  
...  
Keyword(s):  
Seismic Data ◽  
Low Frequency ◽  
Frequency Component ◽  
Seismic Inversion ◽  
Data Estimation

Accuracy of wavelets, seismic inversion, and thin-bed resolution

2017 ◽  
Vol 5 (4) ◽  
pp. T523-T530
Author(s):  
Ehsan Zabihi Naeini ◽  
Mark Sams
Keyword(s):  
Seismic Data ◽  
Reservoir Characterization ◽  
Low Frequency ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Frequency Content ◽  
Frequency Model ◽  
North West ◽  
The North ◽  
Well Data

Broadband reprocessed seismic data from the North West Shelf of Australia were inverted using wavelets estimated with a conventional approach. The inversion method applied was a facies-based inversion, in which the low-frequency model is a product of the inversion process itself, constrained by facies-dependent input trends, the resultant facies distribution, and the match to the seismic. The results identified the presence of a gas reservoir that had recently been confirmed through drilling. The reservoir is thin, with up to 15 ms of maximum thickness. The bandwidth of the seismic data is approximately 5–70 Hz, and the well data used to extract the wavelet used in the inversion are only 400 ms long. As such, there was little control on the lowest frequencies of the wavelet. Different wavelets were subsequently estimated using a variety of new techniques that attempt to address the limitations of short well-log segments and low-frequency seismic. The revised inversion showed greater gas-sand continuity and an extension of the reservoir at one flank. Noise-free synthetic examples indicate that thin-bed delineation can depend on the accuracy of the low-frequency content of the wavelets used for inversion. Underestimation of the low-frequency contents can result in missing thin beds, whereas underestimation of high frequencies can introduce false thin beds. Therefore, it is very important to correctly capture the full frequency content of the seismic data in terms of the amplitude and phase spectra of the estimated wavelets, which subsequently leads to a more accurate thin-bed reservoir characterization through inversion.

Probabilistic petrophysical-properties estimation integrating statistical rock physics with seismic inversion

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. O21-O37 ◽  
Author(s):  
Dario Grana ◽  
Ernesto Della Rossa
Keyword(s):  
Seismic Data ◽  
Measurement Errors ◽  
Rock Physics ◽  
Seismic Inversion ◽  
Joint Estimation ◽  
Physical Models ◽  
Inversion Method ◽  
Petrophysical Properties ◽  
Reservoir Properties ◽  
Statistical Rock Physics

A joint estimation of petrophysical properties is proposed that combines statistical rock physics and Bayesian seismic inversion. Because elastic attributes are correlated with petrophysical variables (effective porosity, clay content, and water saturation) and this physical link is associated with uncertainties, the petrophysical-properties estimation from seismic data can be seen as a Bayesian inversion problem. The purpose of this work was to develop a strategy for estimating the probability distributions of petrophysical parameters and litho-fluid classes from seismics. Estimation of reservoir properties and the associated uncertainty was performed in three steps: linearized seismic inversion to estimate the probabilities of elastic parameters, probabilistic upscaling to include the scale-changes effect, and petrophysical inversion to estimate the probabilities of petrophysical variables andlitho-fluid classes. Rock-physics equations provide the linkbetween reservoir properties and velocities, and linearized seismic modeling connects velocities and density to seismic amplitude. A full Bayesian approach was adopted to propagate uncertainty from seismics to petrophysics in an integrated framework that takes into account different sources of uncertainty: heterogeneity of the real data, approximation of physical models, measurement errors, and scale changes. The method has been tested, as a feasibility step, on real well data and synthetic seismic data to show reliable propagation of the uncertainty through the three different steps and to compare two statistical approaches: parametric and nonparametric. Application to a real reservoir study (including data from two wells and partially stacked seismic volumes) has provided as a main result the probability densities of petrophysical properties and litho-fluid classes. It demonstrated the applicability of the proposed inversion method.

Poststack Seismic Inversion Using A Patch-based Gaussian Mixture Model

Geophysics ◽  
2021 ◽  
pp. 1-102
Author(s):  
Lingqian Wang ◽  
Hui Zhou ◽  
Hengchang Dai ◽  
Bo Yu ◽  
Wenling Liu ◽  
...  
Keyword(s):  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Acoustic Impedance ◽  
Structural Information ◽  
Gaussian Mixture ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Borehole Data ◽  
Inversion Result ◽  
Band Limited

Seismic inversion is a severely ill-posed problem, because of noise in the observed record, band-limited seismic wavelets, and the discretization of a continuous medium. Regularization techniques can impose certain characteristics on inversion results based on prior information in order to obtain a stable and unique solution. However, it is difficult to find an appropriate regularization to describe the actual subsurface geology. We propose a new acoustic impedance inversion method via a patch-based Gaussian mixture model (GMM), which is designed using available well logs. In this method, firstly, the non-local means (NLM) method estimates acoustic impedance around wells in terms of the similarity of local seismic records. The extrapolated multichannel impedance are then decomposed into impedance patches. Using patched data rather than a window or single trace for training samples to obtain the GMM parameters, which contain local lateral structural information, can provide more impedance structure details and enhance the stability of the inversion result. Next, the expectation maximization (EM) algorithm is used to obtain the GMM parameters from the patched data. Finally, we apply the alternating direction method of multipliers (ADMM) to solve the conventional Bayesian inference illustrating the role of regularization, and construct the objective function using the GMM parameters. Therefore, the inversion results are compliant with the local structural features extracted from the borehole data. Both synthetic and field data tests validate the performance of our proposed method. Compared with other conventional inversion methods, our method shows promise in providing a more accurate and stable inversion result.

Seismic inversion of a carbonate buildup: A case study

2017 ◽  
Vol 5 (4) ◽  
pp. T641-T652 ◽  
Author(s):  
Mark Sams ◽  
Paul Begg ◽  
Timur Manapov
Keyword(s):  
Seismic Data ◽  
Probability Distributions ◽  
Low Frequency ◽  
Rock Physics ◽  
Seismic Inversion ◽  
Accurate Estimation ◽  
Amplitude Analysis ◽  
Simultaneous Inversion ◽  
Band Limited ◽  
Using Data

The information within seismic data is band limited and angle limited. Together with the particular physics and geology of carbonate rocks, this imposes limitations on how accurately we can predict the presence of hydrocarbons in carbonates, map the top carbonate, and characterize the porosity distribution through seismic amplitude analysis. Using data for a carbonate reef from the Nam Con Son Basin, Vietnam, the expectations based on rock-physics analysis are that the presence of gas can be predicted only when the porosity at the top of the carbonate is extremely high ([Formula: see text]), but that a fluid contact is unlikely to be observed in the background of significant porosity variations. Mapping the top of the carbonate (except when the top carbonate porosities are low) or a fluid contact requires accurate estimates of changes in [Formula: see text]. The seismic data do not independently support such an accurate estimation of sharp changes in [Formula: see text]. The standard approach of introducing low-frequency models and applying rock-physics constraints during a simultaneous inversion does not resolve the problems: The results are heavily biased by the well control and the initial interpretation of the top carbonate and fluid contact. A facies-based inversion in which the elastic properties are restricted to values consistent with the facies predicted to be present removes the well bias, but it does not completely obviate the need for a reasonably accurate initial interpretation in terms of prior facies probability distributions. Prestack inversion improves the quality of the facies predictions compared with a poststack inversion.

Approximate computation of the acoustic impedance from seismic data

Geophysics ◽  
1983 ◽  
Vol 48 (10) ◽  
pp. 1351-1358 ◽  
Author(s):  
K. A. Berteussen ◽  
B. Ursin
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Recursive Formula ◽  
Continuous Model ◽  
Low Noise ◽  
Nonlinear Transformation ◽  
Earth Model ◽  
Approximate Computation ◽  
Impedance Function ◽  
Band Limited

The approximate computation of the acoustic impedance from seismic data is usually based on the recursive formula [Formula: see text] where [Formula: see text] is the acoustic impedance in layer number k and [Formula: see text] is the pressure reflection coefficient for the interface between layer k and [Formula: see text]. The above formula is derived from a discrete layered earth model. When we consider a continuous earth model and discretize the results, we obtain the recursive formula [Formula: see text] The two expressions give very similar numerical results. For [Formula: see text], the relative difference is less than 5 percent and this cannot be visually recognized on an acoustic impedance section. The expression for the continuous model is more suitable for understanding the result of the approximate computation of the acoustic impedance function from band‐limited seismic data. The calculated impedance minus the impedance in the top layer is approximately equal to the reflectivity function convolved with the integrated seismic pulse multiplied with twice the impedance in the top layer. For impedance values less than 0.2 in absolute value this is also equal to the acoustic impedance function (minus the acoustic impedance in the top layer) convolved with the seismic pulse. The computation of the acoustic impedance from band‐limited seismic data corresponds to an exponential transformation of the integrated seismic trace. On a band‐limited acoustic impedance section with well‐separated reflectors and low noise level the direction of change in the acoustic impedance can be correctly identified. The effect of additive noise in the seismic data is governed by a nonlinear transformation. Our data examples show that the computation of acoustic impedance becomes unstable when noise is added. In order to avoid the nonlinear transformation of the seismic data, it has been suggested to integrate the seismic data. This results in an estimate of the logarithm of the acoustic impedance. For band‐limited seismic data with noise this gives a band‐limited estimate of the logarithm of the acoustic impedance plus the integrated noise. A disadvantage of this method is that the variance of the integrated noise increases linearly with time.

scholarly journals Seismic inversion by Newtonian machine learning

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. WA185-WA200
Author(s):  
Yuqing Chen ◽  
Gerard T. Schuster
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Wave Equation ◽  
Seismic Data ◽  
Velocity Model ◽  
Seismic Inversion ◽  
Low Rank ◽  
Inversion Method ◽  
Model Parameters ◽  
Latent Space

We present a wave-equation inversion method that inverts skeletonized seismic data for the subsurface velocity model. The skeletonized representation of the seismic traces consists of the low-rank latent-space variables predicted by a well-trained autoencoder neural network. The input to the autoencoder consists of seismic traces, and the implicit function theorem is used to determine the Fréchet derivative, i.e., the perturbation of the skeletonized data with respect to the velocity perturbation. The gradient is computed by migrating the shifted observed traces weighted by the skeletonized data residual, and the final velocity model is the one that best predicts the observed latent-space parameters. We denote this as inversion by Newtonian machine learning (NML) because it inverts for the model parameters by combining the forward and backward modeling of Newtonian wave propagation with the dimensional reduction capability of machine learning. Empirical results suggest that inversion by NML can sometimes mitigate the cycle-skipping problem of conventional full-waveform inversion (FWI). Numerical tests with synthetic and field data demonstrate the success of NML inversion in recovering a low-wavenumber approximation to the subsurface velocity model. The advantage of this method over other skeletonized data methods is that no manual picking of important features is required because the skeletal data are automatically selected by the autoencoder. The disadvantage is that the inverted velocity model has less resolution compared with the FWI result, but it can serve as a good initial model for FWI. Our most significant contribution is that we provide a general framework for using wave-equation inversion to invert skeletal data generated by any type of neural network. In other words, we have combined the deterministic modeling of Newtonian physics and the pattern matching capabilities of machine learning to invert seismic data by NML.

Seismic inversion with adaptive edge-preserving smoothing preconditioning on impedance model

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. R11-R19 ◽  
Author(s):  
Ronghuo Dai ◽  
Cheng Yin ◽  
Nueraili Zaman ◽  
Fanchang Zhang
Keyword(s):  
Seismic Data ◽  
Random Noise ◽  
A Priori ◽  
Window Size ◽  
Seismic Inversion ◽  
Small Scale ◽  
Inversion Method ◽  
Reservoir Prediction ◽  
Edge Preserving ◽  
Impedance Model

Poststack seismic impedance inversion is an effective approach for reservoir prediction. Due to the sensitivity to noise and the oscillation near the bed boundary, Gaussian distribution constrained seismic inversion is unfavorable to delineate the subtle-reservoir and small-scale geologic features. To overcome this shortcoming, we have developed a new method that incorporates a priori knowledge in the seismic inversion through a preconditioning impedance model using the adaptive edge-preserving smoothing (Ad-EPS) filter. The Ad-EPS filter preconditioned impedance model for a blocky solution makes the formation interfaces and geologic edges more precise and sharper in the inverted impedance results and keeps the inversion procedure robust even if random noise exists in the seismic data. Furthermore, compared with the conventional EPS filter, the Ad-EPS filter is able to resolve thick and thin geologic features through window size scanning, which is used to find the best-fitting window size for each sample to be filtered. The results of numerical examples and real seismic data test indicate that our inversion method can suppress noise to obtain a “blocky” inversion result and preserve small geologic features.

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