The applicability of dip moveout/azimuth moveout in the presence of caustics

Reflection seismic data continuation is the computation of data at source and receiver locations that differ from those in the original data, using whatever data are available. We develop a general theory of data continuation in the presence of caustics and illustrate it with three examples: dip moveout (DMO), azimuth moveout (AMO), and offset continuation. This theory does not require knowledge of the reflector positions. We construct the output data set from the input through the composition of three operators: an imaging operator, a modeling operator, and a restriction operator. This results in a single operator that maps directly from the input data to the desired output data. We use the calculus of Fourier integral operators to develop this theory in the presence of caustics. For both DMO and AMO, we compute impulse responses in a constant-velocity model and in a more complicated model in which caustics arise. This analysis reveals errors that can be introduced by assuming, for example, a model with a constant vertical velocity gradient when the true model is laterally heterogeneous. Data continuation uses as input a subset (common offset, common angle) of the available data, which may introduce artifacts in the continued data. One could suppress these artifacts by stacking over a neighborhood of input data (using a small range of offsets or angles, for example). We test data continuation on synthetic data from a model known to generate imaging artifacts. We show that stacking over input scattering angles suppresses artifacts in the continued data.

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Automatic velocity analysis using convolutional neural network and transfer learning

Geophysics ◽

10.1190/geo2018-0870.1 ◽

2019 ◽

Vol 85 (1) ◽

pp. V33-V43 ◽

Cited By ~ 4

Author(s):

Min Jun Park ◽

Mauricio D. Sacchi

Keyword(s):

Neural Network ◽

Convolutional Neural Network ◽

Transfer Learning ◽

Input Data ◽

Synthetic Data ◽

Velocity Model ◽

Training Data ◽

Velocity Analysis ◽

Time Step ◽

Data Set

Velocity analysis can be a time-consuming task when performed manually. Methods have been proposed to automate the process of velocity analysis, which, however, typically requires significant manual effort. We have developed a convolutional neural network (CNN) to estimate stacking velocities directly from the semblance. Our CNN model uses two images as one input data for training. One is an entire semblance (guide image), and the other is a small patch (target image) extracted from the semblance at a specific time step. Labels for each input data set are the root mean square velocities. We generate the training data set using synthetic data. After training the CNN model with synthetic data, we test the trained model with another synthetic data that were not used in the training step. The results indicate that the model can predict a consistent velocity model. We also noticed that when the input data are extremely different from those used for the training, the CNN model will hardly pick the correct velocities. In this case, we adopt transfer learning to update the trained model (base model) with a small portion of the target data to improve the accuracy of the predicted velocity model. A marine data set from the Gulf of Mexico is used for validating our new model. The updated model performed a reasonable velocity analysis in seconds.

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Seismic demigration/migration in the curvelet domain

Geophysics ◽

10.1190/1.2831933 ◽

2008 ◽

Vol 73 (2) ◽

pp. S35-S46 ◽

Cited By ~ 41

Author(s):

Hervé Chauris ◽

Truong Nguyen

Keyword(s):

Input Data ◽

Plane Waves ◽

Synthetic Data ◽

Velocity Model ◽

Local Velocity ◽

Data Set ◽

Migration Operator ◽

Local Plane ◽

Seismic Images

Curvelets can represent local plane waves. They efficiently decompose seismic images and possibly imaging operators. We study how curvelets are distorted after demigration followed by migration in a different velocity model. We show that for small local velocity perturbations, the demigration/migration is reduced to a simple morphing of the initial curvelet. The derivation of the expected curvature of the curvelets shows that it is easier to sparsify the demigration/migration operator than the migration operator. An application on a 2D synthetic data set, generated in a smooth heterogeneous velocity model and with a complex reflectivity, demonstrates the usefulness of curvelets to predict what a migrated image would become in a locally different velocity model without the need for remigrating the full input data set. Curvelets are thus well suited to study the sensitivity of a prestack depth-migrated image with respect to the heterogeneous velocity model used for migration.

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Rapid estimation of earthquake locations using waveform traveltimes

Geophysical Journal International ◽

10.1093/gji/ggz114 ◽

2019 ◽

Vol 217 (3) ◽

pp. 1727-1741 ◽

Cited By ~ 1

Author(s):

D W Vasco ◽

Seiji Nakagawa ◽

Petr Petrov ◽

Greg Newman

Keyword(s):

Standard Error ◽

Random Noise ◽

Grid Point ◽

Synthetic Data ◽

Velocity Model ◽

Source Location ◽

Model Errors ◽

Average Deviation ◽

Origin Time ◽

Data Set

SUMMARY We introduce a new approach for locating earthquakes using arrival times derived from waveforms. The most costly computational step of the algorithm scales as the number of stations in the active seismographic network. In this approach, a variation on existing grid search methods, a series of full waveform simulations are conducted for all receiver locations, with sources positioned successively at each station. The traveltime field over the region of interest is calculated by applying a phase picking algorithm to the numerical wavefields produced from each simulation. An event is located by subtracting the stored traveltime field from the arrival time at each station. This provides a shifted and time-reversed traveltime field for each station. The shifted and time-reversed fields all approach the origin time of the event at the source location. The mean or median value at the source location thus approximates the event origin time. Measures of dispersion about this mean or median time at each grid point, such as the sample standard error and the average deviation, are minimized at the correct source position. Uncertainty in the event position is provided by the contours of standard error defined over the grid. An application of this technique to a synthetic data set indicates that the approach provides stable locations even when the traveltimes are contaminated by additive random noise containing a significant number of outliers and velocity model errors. It is found that the waveform-based method out-performs one based upon the eikonal equation for a velocity model with rapid spatial variations in properties due to layering. A comparison with conventional location algorithms in both a laboratory and field setting demonstrates that the technique performs at least as well as existing techniques.

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Bayesian Classifier for Sparsity-Promoting Feature Selection

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001415500226 ◽

2015 ◽

Vol 29 (06) ◽

pp. 1550022 ◽

Cited By ~ 1

Author(s):

Danlei Xu ◽

Lan Du ◽

Hongwei Liu ◽

Penghui Wang

Keyword(s):

Feature Selection ◽

Synthetic Data ◽

Original Data ◽

Radar Data ◽

Bayesian Classifier ◽

Classification Model ◽

Data Sets ◽

Data Set ◽

Classification Boundary ◽

Nonlinear Mappings

A Bayesian classifier for sparsity-promoting feature selection is developed in this paper, where a set of nonlinear mappings for the original data is performed as a pre-processing step. The linear classification model with such mappings from the original input space to a nonlinear transformation space can not only construct the nonlinear classification boundary, but also realize the feature selection for the original data. A zero-mean Gaussian prior with Gamma precision and a finite approximation of Beta process prior are used to promote sparsity in the utilization of features and nonlinear mappings in our model, respectively. We derive the Variational Bayesian (VB) inference algorithm for the proposed linear classifier. Experimental results based on the synthetic data set, measured radar data set, high-dimensional gene expression data set, and several benchmark data sets demonstrate the aggressive and robust feature selection capability and comparable classification accuracy of our method comparing with some other existing classifiers.

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Tackling cycle skipping in full-waveform inversion with intermediate data

Geophysics ◽

10.1190/geo2018-0096.1 ◽

2019 ◽

Vol 84 (3) ◽

pp. R411-R427 ◽

Cited By ~ 8

Author(s):

Gang Yao ◽

Nuno V. da Silva ◽

Michael Warner ◽

Di Wu ◽

Chenhao Yang

Keyword(s):

Objective Function ◽

Waveform Inversion ◽

Synthetic Data ◽

Velocity Model ◽

Full Waveform Inversion ◽

Data Set ◽

Intermediate Data ◽

Full Waveform ◽

L2 Norm ◽

Recorded Data

Full-waveform inversion (FWI) is a promising technique for recovering the earth models for exploration geophysics and global seismology. FWI is generally formulated as the minimization of an objective function, defined as the L2-norm of the data residuals. The nonconvex nature of this objective function is one of the main obstacles for the successful application of FWI. A key manifestation of this nonconvexity is cycle skipping, which happens if the predicted data are more than half a cycle away from the recorded data. We have developed the concept of intermediate data for tackling cycle skipping. This intermediate data set is created to sit between predicted and recorded data, and it is less than half a cycle away from the predicted data. Inverting the intermediate data rather than the cycle-skipped recorded data can then circumvent cycle skipping. We applied this concept to invert cycle-skipped first arrivals. First, we picked up the first breaks of the predicted data and the recorded data. Second, we linearly scaled down the time difference between the two first breaks of each shot into a series of time shifts, the maximum of which was less than half a cycle, for each trace in this shot. Third, we moved the predicted data with the corresponding time shifts to create the intermediate data. Finally, we inverted the intermediate data rather than the recorded data. Because the intermediate data are not cycle-skipped and contain the traveltime information of the recorded data, FWI with intermediate data updates the background velocity model in the correct direction. Thus, it produces a background velocity model accurate enough for carrying out conventional FWI to rebuild the intermediate- and short-wavelength components of the velocity model. Our numerical examples using synthetic data validate the intermediate-data concept for tackling cycle skipping and demonstrate its effectiveness for the application to first arrivals.

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Transmission compensated primary reflection retrieval in the data domain and consequences for imaging

Geophysics ◽

10.1190/geo2018-0340.1 ◽

2019 ◽

Vol 84 (4) ◽

pp. Q27-Q36 ◽

Cited By ~ 13

Author(s):

Lele Zhang ◽

Jan Thorbecke ◽

Kees Wapenaar ◽

Evert Slob

Keyword(s):

Thin Layer ◽

Time Domain ◽

Velocity Model ◽

Original Data ◽

Transmission Losses ◽

Multiple Reflections ◽

Data Set ◽

Numerical Examples ◽

The One ◽

The Time Domain

We have developed a scheme that retrieves primary reflections in the two-way traveltime domain by filtering the data. The data have their own filter that removes internal multiple reflections, whereas the amplitudes of the retrieved primary reflections are compensated for two-way transmission losses. Application of the filter does not require any model information. It consists of convolutions and correlations of the data with itself. A truncation in the time domain is applied after each convolution or correlation. The retrieved data set can be used as the input to construct a better velocity model than the one that would be obtained by working directly with the original data and to construct an enhanced subsurface image. Two 2D numerical examples indicate the effectiveness of the method. We have studied bandwidth limitations by analyzing the effects of a thin layer. The presence of refracted and scattered waves is a known limitation of the method, and we studied it as well. Our analysis indicates that a thin layer is treated as a more complicated reflector, and internal multiple reflections related to the thin layer are properly removed. We found that the presence of refracted and scattered waves generates artifacts in the retrieved data.

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Automatic, geologic layer-constrained well-seismic tie through blocked dynamic warping

Interpretation ◽

10.1190/int-2016-0160.1 ◽

2017 ◽

Vol 5 (3) ◽

pp. SJ81-SJ90 ◽

Cited By ~ 1

Author(s):

Kainan Wang ◽

Jesse Lomask ◽

Felix Segovia

Keyword(s):

Seismic Data ◽

Oil And Gas ◽

Synthetic Data ◽

Optimal Solution ◽

Velocity Model ◽

Data Set ◽

Oil And Gas Exploration ◽

Interval Velocity ◽

Velocity Changes ◽

Dynamic Warping

Well-log-to-seismic tying is a key step in many interpretation workflows for oil and gas exploration. Synthetic seismic traces from the wells are often manually tied to seismic data; this process can be very time consuming and, in some cases, inaccurate. Automatic methods, such as dynamic time warping (DTW), can match synthetic traces to seismic data. Although these methods are extremely fast, they tend to create interval velocities that are not geologically realistic. We have described the modification of DTW to create a blocked dynamic warping (BDW) method. BDW generates an automatic, optimal well tie that honors geologically consistent velocity constraints. Consequently, it results in updated velocities that are more realistic than other methods. BDW constrains the updated velocity to be constant or linearly variable inside each geologic layer. With an optimal correlation between synthetic seismograms and surface seismic data, this algorithm returns an automatically updated time-depth curve and an updated interval velocity model that still retains the original geologic velocity boundaries. In other words, the algorithm finds the optimal solution for tying the synthetic to the seismic data while restricting the interval velocity changes to coincide with the initial input blocking. We have determined the application of the BDW technique on a synthetic data example and field data set.

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Migration moveout analysis and depth focusing

Geophysics ◽

10.1190/1.1443354 ◽

1993 ◽

Vol 58 (1) ◽

pp. 91-100 ◽

Cited By ~ 52

Author(s):

Claude F. Lafond ◽

Alan R. Levander

Keyword(s):

Heterogeneous Media ◽

A Priori ◽

Complex Structure ◽

Tomographic Reconstruction ◽

Synthetic Data ◽

Real Data ◽

Velocity Model ◽

Velocity Analysis ◽

Data Set ◽

Velocity Models

Prestack depth migration still suffers from the problems associated with building appropriate velocity models. The two main after‐migration, before‐stack velocity analysis techniques currently used, depth focusing and residual moveout correction, have found good use in many applications but have also shown their limitations in the case of very complex structures. To address this issue, we have extended the residual moveout analysis technique to the general case of heterogeneous velocity fields and steep dips, while keeping the algorithm robust enough to be of practical use on real data. Our method is not based on analytic expressions for the moveouts and requires no a priori knowledge of the model, but instead uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections. These corrections are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction. While this approach is more general than existing migration velocity analysis implementations, it is also much more computer intensive and is best used locally around a particularly complex structure. We demonstrate the technique using synthetic data from a model with strong velocity gradients and then apply it to a marine data set to improve the positioning of a major fault.

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Deep generative models in DataSHIELD

BMC Medical Research Methodology ◽

10.1186/s12874-021-01237-6 ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Stefan Lenz ◽

Moritz Hess ◽

Harald Binder

Keyword(s):

Genetic Variant ◽

Small Sample Size ◽

Synthetic Data ◽

Routine Data ◽

Original Data ◽

Generative Models ◽

Small Sample ◽

Generative Adversarial Networks ◽

Artificial Data ◽

Data Set

Abstract Background The best way to calculate statistics from medical data is to use the data of individual patients. In some settings, this data is difficult to obtain due to privacy restrictions. In Germany, for example, it is not possible to pool routine data from different hospitals for research purposes without the consent of the patients. Methods The DataSHIELD software provides an infrastructure and a set of statistical methods for joint, privacy-preserving analyses of distributed data. The contained algorithms are reformulated to work with aggregated data from the participating sites instead of the individual data. If a desired algorithm is not implemented in DataSHIELD or cannot be reformulated in such a way, using artificial data is an alternative. Generating artificial data is possible using so-called generative models, which are able to capture the distribution of given data. Here, we employ deep Boltzmann machines (DBMs) as generative models. For the implementation, we use the package “BoltzmannMachines” from the Julia programming language and wrap it for use with DataSHIELD, which is based on R. Results We present a methodology together with a software implementation that builds on DataSHIELD to create artificial data that preserve complex patterns from distributed individual patient data. Such data sets of artificial patients, which are not linked to real patients, can then be used for joint analyses. As an exemplary application, we conduct a distributed analysis with DBMs on a synthetic data set, which simulates genetic variant data. Patterns from the original data can be recovered in the artificial data using hierarchical clustering of the virtual patients, demonstrating the feasibility of the approach. Additionally, we compare DBMs, variational autoencoders, generative adversarial networks, and multivariate imputation as generative approaches by assessing the utility and disclosure of synthetic data generated from real genetic variant data in a distributed setting with data of a small sample size. Conclusions Our implementation adds to DataSHIELD the ability to generate artificial data that can be used for various analyses, e.g., for pattern recognition with deep learning. This also demonstrates more generally how DataSHIELD can be flexibly extended with advanced algorithms from languages other than R.

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GENERATING BALANCED LEARNING AND TEST SETS FOR FUNCTION APPROXIMATION PROBLEMS

International Journal of Neural Systems ◽

10.1142/s0129065711002791 ◽

2011 ◽

Vol 21 (03) ◽

pp. 247-263 ◽

Cited By ~ 7

Author(s):

J. P. FLORIDO ◽

H. POMARES ◽

I. ROJAS

Keyword(s):

Function Approximation ◽

Nearest Neighbor ◽

Learning Algorithm ◽

Original Data ◽

Input Output ◽

Output Data ◽

Data Set ◽

Out Of Sample ◽

Test Sets ◽

Approximation Problems

In function approximation problems, one of the most common ways to evaluate a learning algorithm consists in partitioning the original data set (input/output data) into two sets: learning, used for building models, and test, applied for genuine out-of-sample evaluation. When the partition into learning and test sets does not take into account the variability and geometry of the original data, it might lead to non-balanced and unrepresentative learning and test sets and, thus, to wrong conclusions in the accuracy of the learning algorithm. How the partitioning is made is therefore a key issue and becomes more important when the data set is small due to the need of reducing the pessimistic effects caused by the removal of instances from the original data set. Thus, in this work, we propose a deterministic data mining approach for a distribution of a data set (input/output data) into two representative and balanced sets of roughly equal size taking the variability of the data set into consideration with the purpose of allowing both a fair evaluation of learning's accuracy and to make reproducible machine learning experiments usually based on random distributions. The sets are generated using a combination of a clustering procedure, especially suited for function approximation problems, and a distribution algorithm which distributes the data set into two sets within each cluster based on a nearest-neighbor approach. In the experiments section, the performance of the proposed methodology is reported in a variety of situations through an ANOVA-based statistical study of the results.

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