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.

Three‐dimensional gravity inversion using simulated annealing: Constraints on the diapiric roots of allochthonous salt structures

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1438-1449 ◽  
Author(s):  
Seiichi Nagihara ◽  
Stuart A. Hall
Keyword(s):  
Simulated Annealing ◽  
Gulf Of Mexico ◽  
Gravity Data ◽  
A Priori ◽  
Gravity Inversion ◽  
Inversion Method ◽  
A Priori Information ◽  
Final Density ◽  
Smoothing Effects ◽  
Priori Information

In the northern continental slope of the Gulf of Mexico, large oil and gas reservoirs are often found beneath sheetlike, allochthonous salt structures that are laterally extensive. Some of these salt structures retain their diapiric feeders or roots beneath them. These hidden roots are difficult to image seismically. In this study, we develop a method to locate and constrain the geometry of such roots through 3‐D inverse modeling of the gravity anomalies observed over the salt structures. This inversion method utilizes a priori information such as the upper surface topography of the salt, which can be delineated by a limited coverage of 2‐D seismic data; the sediment compaction curve in the region; and the continuity of the salt body. The inversion computation is based on the simulated annealing (SA) global optimization algorithm. The SA‐based gravity inversion has some advantages over the approach based on damped least‐squares inversion. It is computationally efficient, can solve underdetermined inverse problems, can more easily implement complex a priori information, and does not introduce smoothing effects in the final density structure model. We test this inversion method using synthetic gravity data for a type of salt geometry that is common among the allochthonous salt structures in the Gulf of Mexico and show that it is highly effective in constraining the diapiric root. We also show that carrying out multiple inversion runs helps reduce the uncertainty in the final density model.

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.

Optimal time‐domain beamforming with simulated annealing including application of a priori information

1990 ◽  
Vol 88 (4) ◽  
pp. 1802-1810 ◽  
Author(s):  
W. A. Kuperman ◽  
Michael D. Collins ◽  
John S. Perkins ◽  
N. R. Davis
Keyword(s):  
Simulated Annealing ◽  
Time Domain ◽  
A Priori ◽  
Optimal Time ◽  
A Priori Information ◽  
Priori Information

Joint interpretation and uncertainty analysis of petrophysical properties in unconventional shale reservoirs

2015 ◽  
Vol 3 (1) ◽  
pp. SA33-SA49 ◽  
Author(s):  
Qinshan Yang ◽  
Carlos Torres-Verdín
Keyword(s):  
Joint Inversion ◽  
A Priori ◽  
Estimation Method ◽  
Monte Carlo Algorithm ◽  
Posteriori Probability ◽  
Inversion Method ◽  
A Posteriori ◽  
A Priori Information ◽  
Core Data ◽  
Priori Information

Interpretation of hydrocarbon-bearing shale is subject to great uncertainty because of pervasive heterogeneity, thin beds, and incomplete and uncertain knowledge of saturation-porosity-resistivity models. We developed a stochastic joint-inversion method specifically developed to address the quantitative petrophysical interpretation of hydrocarbon-bearing shale. The method was based on the rapid and interactive numerical simulation of resistivity and nuclear logs. Instead of property values themselves, the estimation method delivered the a posteriori probability of each property. The Markov-chain Monte Carlo algorithm was used to sample the model space to quantify the a posteriori distribution of formation properties. Additionally, the new interpretation method allows the use of fit-for-purpose statistical correlations between water saturation, salt concentration, porosity, and electrical resistivity to implement uncertain, non-Archie resistivity models derived from core data, including those affected by total organic carbon (TOC). In the case of underdetermined estimation problems, i.e., when the number of measurements was lower than the number of unknowns, the use of a priori information enabled plausible results within prespecified petrophysical and compositional bounds. The developed stochastic interpretation technique was successfully verified with data acquired in the Barnett and Haynesville Shales. Core data (including X-ray diffraction data) were combined into a priori information for interpretation of nuclear and resistivity logs. Results consisted of mineral concentrations, TOC, and porosity together with their uncertainty. Eighty percent of the core data was located within the 95% credible interval of estimated mineral/fluid concentrations.

BAYESIAN METHODS IN THE EVALUATION OF SCATTERING DATA

2006 ◽  
Vol 15 (02) ◽  
pp. 354-361
Author(s):  
H. J. KRAPPE
Keyword(s):  
Elastic Scattering ◽  
Bayesian Methods ◽  
Optical Model ◽  
A Priori ◽  
Scattering Data ◽  
Model Parameters ◽  
A Priori Information ◽  
Model Independent ◽  
Priori Information

It is shown how a priori information can be introduced in an optimal way to extract optical-model parameters in a model-independent way from incomplete elastic scattering data.

scholarly journals Aircraft Turbine Engine Automatic Control Based on Adaptive Dynamic Models

2020 ◽  
Vol 2020 (4) ◽  
pp. 61-70
Author(s):  
Sergiy Yepifanov
Keyword(s):  
Automatic Control ◽  
Thermodynamic Model ◽  
Dynamic Models ◽  
A Priori ◽  
Static Model ◽  
Measuring System ◽  
Model Parameters ◽  
A Priori Information ◽  
Static Models ◽  
Priori Information

AbstractOne of the most perspective development directions of the aircraft engine is the application of adaptive digital automatic control systems (ACS). The significant element of the adaptation is the correction of mathematical models of both engine and its executive, measuring devices. These models help to solve tasks of control and are a combination of static models and dynamic models, as static models describe relations between parameters at steady-state modes, and dynamic ones characterize deviations of the parameters from static values.The work considers problems of the models’ correction using parametric identification methods. It is shown that the main problem of the precise engine simulation is the correction of the static model. A robust procedure that is based on a wide application of a priori information about performances of the engine and its measuring system is proposed for this purpose. One of many variants of this procedure provides an application of the non-linear thermodynamic model of the working process and estimation of individual corrections to the engine components’ characteristics with further substitution of the thermodynamic model by approximating on-board static model. Physically grounded estimates are obtained based on a priori information setting about the estimated parameters and engine performances, using fuzzy sets.Executive devices (actuators) and the most inertial temperature sensors require correction to their dynamic models. Researches showed, in case that the data for identification are collected during regular operation of ACS, the estimates of dynamic model parameters can be strongly correlated that reasons inadmissible errors.The reason is inside the substantial limitations on transients’ intensity that contain regular algorithms of acceleration/deceleration control. Therefore, test actions on the engine are required. Their character and minimum composition are determined using the derived relations between errors in model coefficients, measurement process, and control action parameters.

Should blood transport kinetics be modeled in metabolic processes?

1984 ◽  
Vol 247 (5) ◽  
pp. R895-R900
Author(s):  
G. Belforte ◽  
B. Bona ◽  
G. Molino
Keyword(s):  
A Priori ◽  
Model Parameters ◽  
Physiological System ◽  
A Priori Information ◽  
Design Task ◽  
Single Compartment ◽  
Priori Information ◽  
Blood Transport ◽  
Insight Into ◽  
Drug Kinetics

We analyze the interaction between blood transport phenomena and uptake processes when drug kinetics are studied with compartmental models. Relevant advantages in the physiological interpretation of the model parameters are obtained when blood transport is explicitly included in the model. This is done by aggregating into a single compartment all the blood spaces where no exchange with extravascular spaces takes place and separating into different blood compartments those spaces where some uptake and/or return occurs. The proposed strategy extensively uses all available a priori information about the physiological system, instead of considering only the information available in the measurements. This modeling approach has three main advantages: it provides greater insight into the identified quantities; it allows the introduction of quantitative a priori information; and it facilitates the experiment design task.

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