2-D Bayesian deconvolution

Geophysics ◽  
1991 ◽  
Vol 56 (12) ◽  
pp. 2008-2018 ◽  
Author(s):  
Marc Lavielle
Keyword(s):  
Objective Function ◽  
Seismic Data ◽  
Layer Structure ◽  
A Priori ◽  
A Priori Information ◽  
The Earth ◽  
Markov Random ◽  
Posteriori Distribution ◽  
A Posteriori Distribution ◽  
Priori Information

Inverse problems can be solved in different ways. One way is to define natural criteria of good recovery and build an objective function to be minimized. If, instead, we prefer a Bayesian approach, inversion can be formulated as an estimation problem where a priori information is introduced and the a posteriori distribution of the unobserved variables is maximized. When this distribution is a Gibbs distribution, these two methods are equivalent. Furthermore, global optimization of the objective function can be performed with a Monte Carlo technique, in spite of the presence of numerous local minima. Application to multitrace deconvolution is proposed. In traditional 1-D deconvolution, a set of uni‐dimensional processes models the seismic data, while a Markov random field is used for 2-D deconvolution. In fact, the introduction of a neighborhood system permits one to model the layer structure that exists in the earth and to obtain solutions that present lateral coherency. Moreover, optimization of an appropriated objective function by simulated annealing allows one to control the fit with the input data as well as the spatial distribution of the reflectors. Extension to 3-D deconvolution is straightforward.

scholarly journals A method of combining coherence-constrained sparse coding and dictionary learning for denoising

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. V137-V148 ◽  
Author(s):  
Pierre Turquais ◽  
Endrias G. Asgedom ◽  
Walter Söllner
Keyword(s):  
Dictionary Learning ◽  
Seismic Data ◽  
Random Noise ◽  
A Priori ◽  
Seismic Signal ◽  
Noise Variance ◽  
A Priori Information ◽  
Seismic Section ◽  
Learned Dictionary ◽  
Priori Information

We have addressed the seismic data denoising problem, in which the noise is random and has an unknown spatiotemporally varying variance. In seismic data processing, random noise is often attenuated using transform-based methods. The success of these methods in denoising depends on the ability of the transform to efficiently describe the signal features in the data. Fixed transforms (e.g., wavelets, curvelets) do not adapt to the data and might fail to efficiently describe complex morphologies in the seismic data. Alternatively, dictionary learning methods adapt to the local morphology of the data and provide state-of-the-art denoising results. However, conventional denoising by dictionary learning requires a priori information on the noise variance, and it encounters difficulties when applied for denoising seismic data in which the noise variance is varying in space or time. We have developed a coherence-constrained dictionary learning (CDL) method for denoising that does not require any a priori information related to the signal or noise. To denoise a given window of a seismic section using CDL, overlapping small 2D patches are extracted and a dictionary of patch-sized signals is trained to learn the elementary features embedded in the seismic signal. For each patch, using the learned dictionary, a sparse optimization problem is solved, and a sparse approximation of the patch is computed to attenuate the random noise. Unlike conventional dictionary learning, the sparsity of the approximation is constrained based on coherence such that it does not need a priori noise variance or signal sparsity information and is still optimal to filter out Gaussian random noise. The denoising performance of the CDL method is validated using synthetic and field data examples, and it is compared with the K-SVD and FX-Decon denoising. We found that CDL gives better denoising results than K-SVD and FX-Decon for removing noise when the variance varies in space or time.

Deep learning spectral enhancement considering features of seismic field data

Geophysics ◽  
2021 ◽  
pp. 1-60
Author(s):  
Yonggyu Choi ◽  
Yeonghwa Jo ◽  
Soon Jee Seol ◽  
Joongmoo Byun ◽  
Young Kim
Keyword(s):  
Machine Learning ◽  
Seismic Data ◽  
Input Data ◽  
Field Data ◽  
A Priori ◽  
Resolution Enhancement ◽  
Training Data ◽  
A Priori Information ◽  
Spectral Enhancement ◽  
Priori Information

The resolution of seismic data dictates the ability to identify individual features or details in a given image, and the temporal (vertical) resolution is a function of the frequency content of a signal. To improve thin-bed resolution, broadening of the frequency spectrum is required; this has been one of the major objectives in seismic data processing. Recently, many researchers have proposed machine learning based resolution enhancement and showed their applicability. However, since the performance of machine learning depends on what the model has learned, output from training data with features different from the target field data may be poor. Thus, we present a machine learning based spectral enhancement technique considering features of seismic field data. We used a convolutional U-Net model, which preserves the temporal connectivity and resolution of the input data, and generated numerous synthetic input traces and their corresponding spectrally broadened traces for training the model. A priori information from field data, such as the estimated source wavelet and reflectivity distribution, was considered when generating the input data for complementing the field features. Using synthetic tests and field post-stack seismic data examples, we showed that the trained model with a priori information outperforms the models trained without a priori information in terms of the accuracy of enhanced signals. In addition, our new spectral enhancing method was verified through the application to the high-cut filtered data and its promising features were presented through the comparison with well log data.

On data-independent multicomponent interpolators and the use of priors for optimal reconstruction and 3D up/down separation of pressure wavefields

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. WB39-WB51 ◽  
Author(s):  
Kemal Özdemir ◽  
Ali Özbek ◽  
Dirk-Jan van Manen ◽  
Massimiliano Vassallo
Keyword(s):  
Particle Motion ◽  
Seismic Data ◽  
A Priori ◽  
Sparse Sampling ◽  
Effective Bandwidth ◽  
A Priori Information ◽  
Sampling Theorems ◽  
Multichannel Sampling ◽  
Priori Information ◽  
Seismic Wavefield

In marine acquisition, the interference between the upgoing and downgoing wavefields introduces a receiver ghost which reduces the effective bandwidth of the seismic wavefield. A two-component streamer provides means for removing the receiver ghost by measuring pressure and vertical particle velocity. However, due to nonuniform and relatively sparse sampling in the crossline direction, the seismic data are usually severely aliased in the crossline direction and the deghosting may not be feasible in a true 3D sense. A true multicomponent streamer measures all components of the particle motion wavefield in addition to the pressure wavefield. This enables solving the 3D deghosting and crossline reconstruction problems simultaneously, without making assumptions on the wavefield or the subsurface. We havedeveloped two data-independent algorithms suited for multicomponent acquisition. The first algorithm reconstructs the total pressure wavefield in the crossline direction by using the pressure and the crossline component of particle motion simultaneously. The second algorithm reconstructs the upgoing pressure wavefield by using the pressure, the crossline, and the vertical components of particle motion simultaneously. Both algorithms are optimal in the minimum-mean-squares-error sense and are ideally suited for a small number of irregularly spaced samples, as is common in towed marine acquisition. We find that by using the spectrum of the wavefield as a priori information, these algorithms have the potential to overcome higher-order aliasing than what is predicted by multichannel sampling theorems. Such a priori information can be extracted from an unaliased portion of the seismic data in novel and robust manners.

A constrained global inversion method using an overparameterized scheme: Application to poststack seismic data

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 613-626 ◽  
Author(s):  
Xin‐Quan Ma
Keyword(s):  
Simulated Annealing ◽  
Seismic Data ◽  
A Priori ◽  
Constant Thickness ◽  
Inversion Method ◽  
Model Parameters ◽  
A Priori Information ◽  
Initial Model ◽  
Seismic Waveform ◽  
Priori Information

A global optimization algorithm using simulated annealing has advantages over local optimization approaches in that it can escape from being trapped in local minima and it does not require a good initial model and function derivatives to find a global minimum. It is therefore more attractive and suitable for seismic waveform inversion. I adopt an improved version of a simulated annealing algorithm to invert simultaneously for acoustic impedance and layer interfaces from poststack seismic data. The earth’s subsurface is overparameterized by a series of microlayers with constant thickness in two‐way traveltime. The algorithm is constrained using the low‐frequency impedance trend and has been made computationally more efficient using this a priori information as an initial model. A search bound of each parameter, derived directly from the a priori information, reduces the nonuniqueness problem. Application of this technique to synthetic and field data examples helps one recover the true model parameters and reveals good continuity of estimated impedance across a seismic section. This approach has the capability of revealing the high‐resolution detail needed for reservoir characterization when a reliable migrated image is available with good well ties.

3-D HYBRID IMAGING BASED ON GRAVITY MIGRATION AND REGULARIZED FOCUSING INVERSION TO PREDICT THE POYANG BASIN INTERFACE

Geophysics ◽  
2021 ◽  
pp. 1-46
Author(s):  
Zhengwei Xu ◽  
Rui Wang ◽  
Wei Xiong ◽  
Jian Wang ◽  
Dian Wang
Keyword(s):  
High Resolution ◽  
Density Distribution ◽  
Seismic Data ◽  
Sedimentary Basin ◽  
A Priori ◽  
Sedimentary Basins ◽  
Density Contrast ◽  
A Priori Information ◽  
Spatial Direction ◽  
Priori Information

Describing and understanding the basement relief of sedimentary basins is vital for oil and gas exploration. The traditional method to map an interface in each spatial direction is based on three-dimensional (3D) modeling of gravity Bouguer anomalies with variable lateral and vertical density contrasts using a priori information derived from other types of geoscience datasets as constraints (e.g., well and/or seismic data). However, in the pre-exploration stage, vertical gravity, gz, which is sometimes the only available geophysical data, are typically used to recover smooth density contrast distributions under a generic set of constraints. Apparently, the use of the gz component is not sufficient to produce geologically reasonable interpretations with high resolution. To address this, we developed a novel process of hybrid inversion, combining gravity migration and inversion using the same gz dataset, to distinguish the complicated interface between basement and sedimentary basin rocks from a full-space inverted density distribution volume. First, a 3D-migrated model delineating the basic sedimentary basin structure was derived using a focusing gravity iterative migration method, where a priori information is not necessary. Subsequently, under the framework of the regularized focusing conjugate inversion algorithm, a high-resolution density contrast model was inverted for the delineation of the basement boundary by integrating the 3D-migrated density model as a priori information. We examined the method using one synthetic example and a field data case, of which a transformed resolution density matrix was developed from logarithmic space to qualitatively evaluate the practical resolutions. The high resolution of density distribution of Cretaceous basement with clear interface was achieved and verified by limited seismic data and strata markers in limited wells.

3-D inversion of magnetic data

Geophysics ◽  
1996 ◽  
Vol 61 (2) ◽  
pp. 394-408 ◽  
Author(s):  
Yaoguo Li ◽  
Douglas W. Oldenburg
Keyword(s):  
Objective Function ◽  
A Priori ◽  
Magnetic Data ◽  
A Priori Information ◽  
Data Set ◽  
Earth Models ◽  
Priori Information ◽  
Model Region ◽  
D Model ◽  
Physical Realizability

We present a method for inverting surface magnetic data to recover 3-D susceptibility models. To allow the maximum flexibility for the model to represent geologically realistic structures, we discretize the 3-D model region into a set of rectangular cells, each having a constant susceptibility. The number of cells is generally far greater than the number of the data available, and thus we solve an underdetermined problem. Solutions are obtained by minimizing a global objective function composed of the model objective function and data misfit. The algorithm can incorporate a priori information into the model objective function by using one or more appropriate weighting functions. The model for inversion can be either susceptibility or its logarithm. If susceptibility is chosen, a positivity constraint is imposed to reduce the nonuniqueness and to maintain physical realizability. Our algorithm assumes that there is no remanent magnetization and that the magnetic data are produced by induced magnetization only. All minimizations are carried out with a subspace approach where only a small number of search vectors is used at each iteration. This obviates the need to solve a large system of equations directly, and hence earth models with many cells can be solved on a deskside workstation. The algorithm is tested on synthetic examples and on a field data set.

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