Analysis of prior models for a blocky inversion of seismic AVA data

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. C25-C35 ◽  
Author(s):  
Ulrich Theune ◽  
Ingrid Østgård Jensås ◽  
Jo Eidsvik
Keyword(s):  
Synthetic Data ◽  
Iterative Solution ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Optimization Approach ◽  
Additional Parameter ◽  
Inversion Algorithm ◽  
Borehole Data ◽  
Solution Approach ◽  
Exploration And Production

Resolving thinner layers and focusing layer boundaries better in inverted seismic sections are important challenges in exploration and production seismology to better identify a potential drilling target. Many seismic inversion methods are based on a least-squares optimization approach that can intrinsically lead to unfocused transitions between adjacent layers. A Bayesian seismic amplitude variation with angle (AVA) inversion algorithm forms sharper boundaries between layers when enforcing sparseness in the vertical gradients of the inversion results. The underlying principle is similar to high-resolution processing algorithms and has been adapted from digital-image-sharpening algorithms. We have investigated the Cauchy and Laplace statistical distributions for their potential to improve contrasts betweenlayers. An inversion algorithm is derived statistically from Bayes’ theorem and results in a nonlinear problem that requires an iterative solution approach. Bayesian inversions require knowledge of certain statistical properties of the model we want to invert for. The blocky inversion method requires an additional parameter besides the usual properties for a multivariate covariance matrix, which we can estimate from borehole data. Tests on synthetic and field data show that the blocky inversion algorithm can detect and enhance layer boundaries in seismic inversions by effectively suppressing side lobes. The analysis of the synthetic data suggests that the Laplace constraint performs more reliably, whereas the Cauchy constraint may not find the optimum solution by converging to a local minimum of the cost function and thereby introducing some numerical artifacts.

scholarly journals Multidimensional scaling for the evaluation of a geostatistical seismic elastic inversion methodology

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. M1-M10 ◽  
Author(s):  
Leonardo Azevedo ◽  
Ruben Nunes ◽  
Pedro Correia ◽  
Amílcar Soares ◽  
Luis Guerreiro ◽  
...  
Keyword(s):  
Multidimensional Scaling ◽  
Metric Space ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Inversion ◽  
Inversion Algorithm ◽  
Data Set ◽  
The Real ◽  
Geostatistical Inversion ◽  
Impedance Models

Due to the nature of seismic inversion problems, there are multiple possible solutions that can equally fit the observed seismic data while diverging from the real subsurface model. Consequently, it is important to assess how inverse-impedance models are converging toward the real subsurface model. For this purpose, we evaluated a new methodology to combine the multidimensional scaling (MDS) technique with an iterative geostatistical elastic seismic inversion algorithm. The geostatistical inversion algorithm inverted partial angle stacks directly for acoustic and elastic impedance (AI and EI) models. It was based on a genetic algorithm in which the model perturbation at each iteration was performed recurring to stochastic sequential simulation. To assess the reliability and convergence of the inverted models at each step, the simulated models can be projected in a metric space computed by MDS. This projection allowed distinguishing similar from variable models and assessing the convergence of inverted models toward the real impedance ones. The geostatistical inversion results of a synthetic data set, in which the real AI and EI models are known, were plotted in this metric space along with the known impedance models. We applied the same principle to a real data set using a cross-validation technique. These examples revealed that the MDS is a valuable tool to evaluate the convergence of the inverse methodology and the impedance model variability among each iteration of the inversion process. Particularly for the geostatistical inversion algorithm we evaluated, it retrieves reliable impedance models while still producing a set of simulated models with considerable variability.

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.

scholarly journals Three-Dimensional Induced Polarization Parallel Inversion Using Nonlinear Conjugate Gradients Method

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Huan Ma ◽  
Handong Tan ◽  
Yue Guo
Keyword(s):  
Message Passing ◽  
Message Passing Interface ◽  
Joint Inversion ◽  
Synthetic Data ◽  
Induced Polarization ◽  
Conjugate Gradients ◽  
Processing Unit ◽  
Inversion Algorithm ◽  
Borehole Data ◽  
Surface Borehole

Four kinds of array of induced polarization (IP) methods (surface, borehole-surface, surface-borehole, and borehole-borehole) are widely used in resource exploration. However, due to the presence of large amounts of the sources, it will take much time to complete the inversion. In the paper, a new parallel algorithm is described which uses message passing interface (MPI) and graphics processing unit (GPU) to accelerate 3D inversion of these four methods. The forward finite differential equation is solved by ILU0 preconditioner and the conjugate gradient (CG) solver. The inverse problem is solved by nonlinear conjugate gradients (NLCG) iteration which is used to calculate one forward and two “pseudo-forward” modelings and update the direction, space, and model in turn. Because each source is independent in forward and “pseudo-forward” modelings, multiprocess modes are opened by calling MPI library. The iterative matrix solver within CULA is called in each process. Some tables and synthetic data examples illustrate that this parallel inversion algorithm is effective. Furthermore, we demonstrate that the joint inversion of surface and borehole data produces resistivity and chargeability results are superior to those obtained from inversions of individual surface data.

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.

Refinements to the linear velocity inversion theory

Geophysics ◽  
1984 ◽  
Vol 49 (2) ◽  
pp. 112-118 ◽  
Author(s):  
Frank G. Hagin ◽  
Jack K. Cohen
Keyword(s):  
Synthetic Data ◽  
Scattered Wave ◽  
Scattering Data ◽  
Inversion Method ◽  
Impedance Change ◽  
Inversion Algorithm ◽  
Linear Inversion ◽  
Velocity Inversion ◽  
Linear Algorithm ◽  
Inversion Theory

The linear inversion method presented by Cohen and Bleistein in 1979 gives seriously degraded results when large reflectors are encountered. Obviously there is an irrecoverable loss of information when such a linear algorithm is applied to a nonlinear world. However, in many cases, excellent results can be achieved by suitable postprocessing of the output of the basic linear inversion algorithm. Although a certain degree of helpful postprocessing can be and has been performed by straightforward consideration of the linearization process, we present here a substantially improved postprocessing algorithm. The basis for these improvements is a more accurate scattering model due to Lahlou et al where, among other things, a WKB analysis of the wave equation led to a much more accurate accounting of the geometric spreading of the scattered wave. These notions plus an effective use of traveltime are used in the new algorithm to improve both the estimate of the reflector locations and the estimate of amplitude (velocity or acoustic impedance) change across the reflectors. The basic idea is to insert this idealized scattering data into the original linear algorithm, and then use the result of this computation as a guide in the interpretation of the numerical output of the algorithm. We demonstrate the result of computer implementation of this algorithm on synthetic data, with and without noise, and verify that the postprocessing algorithm produces dramatically improved reflector locations and speed estimates. Moreover, the new algorithm adds only very modest cost to the basic processing, which is, in turn, very competitive in cost to other multidimensional algorithms.

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.

Minimum-structure borehole gravity inversion for mineral exploration: A synthetic modeling study

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. G25-G39 ◽  
Author(s):  
Craig R. W. Mosher ◽  
Colin G. Farquharson
Keyword(s):  
Reference Model ◽  
Mineral Exploration ◽  
Gravity Data ◽  
Synthetic Data ◽  
Density Variation ◽  
Gravity Inversion ◽  
Inversion Algorithm ◽  
Borehole Data ◽  
Text Type ◽  
The Impact

A borehole gravimeter for the diameters of holes typically used in mineral exploration has recently been developed. Investigating how the data from such instruments can contribute to the gravity interpretation procedures used in mineral exploration is therefore appropriate. Here, results are presented from a study in which synthetic data for 3D exploration-relevant earth models were inverted and the impact of borehole data assessed. The inversions were carried out using a minimum-structure procedure that is typical of those commonly used to invert surface gravity data. Examples involving data from a single borehole, from multiple boreholes, and combinations of borehole and surface data, are considered. Also, a range of options for the particulars of the inversion algorithm are investigated, including using a reference model and cell weights to incorporate along-borehole density information, and an [Formula: see text]-type measure of model structure. The selection of examples presented demonstrates what one can and cannot expect to determine about the density variation around and between boreholes when borehole gravity data are inverted using a minimum-structure approach. Specifically, the density variation along a borehole can be accurately determined, even without constraints in the inversion, but this capability decreases dramatically a few tens of meters from a borehole.

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.

Free-surface multiple attenuation for blended data

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. V227-V233
Author(s):  
Jitao Ma ◽  
Xiaohong Chen ◽  
Mrinal K. Sen ◽  
Yaru Xue
Keyword(s):  
Free Surface ◽  
Seismic Data ◽  
Synthetic Data ◽  
Primary Energy ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Crosstalk Noise ◽  
Multiple Attenuation ◽  
Blended Data ◽  
Value Decomposition

Blended data sets are now being acquired because of improved efficiency and reduction in cost compared with conventional seismic data acquisition. We have developed two methods for blended data free-surface multiple attenuation. The first method is based on an extension of surface-related multiple elimination (SRME) theory, in which free-surface multiples of the blended data can be predicted by a multidimensional convolution of the seismic data with the inverse of the blending operator. A least-squares inversion method is used, which indicates that crosstalk noise existed in the prediction result due to the approximate inversion. An adaptive subtraction procedure similar to that used in conventional SRME is then applied to obtain the blended primary — this can damage the energy of primaries. The second method is based on inverse data processing (IDP) theory adapted to blended data. We derived a formula similar to that used in conventional IDP, and we attenuated free-surface multiples by simple muting of the focused points in the inverse data space (IDS). The location of the focused points in the IDS for blended data, which can be calculated, is also related to the blending operator. We chose a singular value decomposition-based inversion algorithm to stabilize the inversion in the IDP method. The advantage of IDP compared with SRME is that, it does not have crosstalk noise and is able to better preserve the primary energy. The outputs of our methods are all blended primaries, and they can be further processed using blended data-based algorithms. Synthetic data examples show that the SRME and IDP algorithms for blended data are successful in attenuating free-surface multiples.

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