Adaptive focusing window for seismic angle migration

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. S1-S10 ◽  
Author(s):  
Mathias Alerini ◽  
Bjørn Ursin
Keyword(s):  
Synthetic Data ◽  
Main Idea ◽  
Three Dimensions ◽  
User Friendliness ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Migration Operator ◽  
Local Geology ◽  
Original Approach

Kirchhoff migration is based on a continuous integral ranging from minus infinity to plus infinity. The necessary discretization and truncation of this integral introduces noise in the migrated image. The attenuation of this noise has been studied by many authors who propose different strategies. The main idea is to limit the migration operator around the specular point. This means that the specular point must be known before migration and that a criterion exists to determine the size of the migration operator. We propose an original approach to estimate the size of the focusing window, knowing the geologic dip. The approach benefits from the use of prestack depth migration in angle domain, which is recognized as the most artifact-free Kirchhoff-type migration. The main advantages of the method are ease of implementation in an existing angle-migration code (two or three dimensions), user friendliness, ability to take into account multiorientation of the local geology as in faulted regions, and flexibility with respect to the quality of the estimated geologic dip field. Common-image gathers resulting from the method are free from migration noise and can be postprocessed in an easier way. We validate the approach and its possibilities on synthetic data examples with different levels of complexity.

Prestack Gaussian-beam depth migration in anisotropic media

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. S133-S138 ◽  
Author(s):  
Tianfei Zhu ◽  
Samuel H. Gray ◽  
Daoliu Wang
Keyword(s):  
Gaussian Beam ◽  
Ray Tracing ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Elastic Parameters ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Beam Depth ◽  
Dynamic Ray Tracing

Gaussian-beam depth migration is a useful alternative to Kirchhoff and wave-equation migrations. It overcomes the limitations of Kirchhoff migration in imaging multipathing arrivals, while retaining its efficiency and its capability of imaging steep dips with turning waves. Extension of this migration method to anisotropic media has, however, been hampered by the difficulties in traditional kinematic and dynamic ray-tracing systems in inhomogeneous, anisotropic media. Formulated in terms of elastic parameters, the traditional anisotropic ray-tracing systems aredifficult to implement and inefficient for computation, especially for the dynamic ray-tracing system. They may also result inambiguity in specifying elastic parameters for a given medium.To overcome these difficulties, we have reformulated the ray-tracing systems in terms of phase velocity.These reformulated systems are simple and especially useful for general transversely isotropic and weak orthorhombic media, because the phase velocities for these two types of media can be computed with simple analytic expressions. These two types of media also represent the majority of anisotropy observed in sedimentary rocks. Based on these newly developed ray-tracing systems, we have extended prestack Gaussian-beam depth migration to general transversely isotropic media. Test results with synthetic data show that our anisotropic, prestack Gaussian-beam migration is accurate and efficient. It produces images superior to those generated by anisotropic, prestack Kirchhoff migration.

Kirchhoff migration using eikonal equation traveltimes

Geophysics ◽  
1994 ◽  
Vol 59 (5) ◽  
pp. 810-817 ◽  
Author(s):  
Samuel H. Gray ◽  
William P. May
Keyword(s):  
Ray Tracing ◽  
Data Storage ◽  
Eikonal Equation ◽  
Synthetic Data ◽  
Velocity Model ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Regular Grid ◽  
Data Set ◽  
Kirchhoff Migration

The use of ray shooting followed by interpolation of traveltimes onto a regular grid is a popular and robust method for computing diffraction curves for Kirchhoff migration. An alternative to this method is to compute the traveltimes by directly solving the eikonal equation on a regular grid, without computing raypaths. Solving the eikonal equation on such a grid simplifies the problem of interpolating times onto the migration grid, but this method is not well defined at points where two different branches of the traveltime field meet. Also, computational and data storage issues that are relatively unimportant for performance in two dimensions limit the applicability of both schemes in three dimensions. A new implementation of a gridded eikonal equation solver has been designed to address these problems. A 2-D version of this algorithm is tested by using it to generate traveltimes to migrate the Marmousi synthetic data set using the exact velocity model. The results are compared with three other images: an F-X migration (a standard for comparison), a Kirchhoff migration using ray tracing, and a Kirchhoff migration using traveltimes generated by a commonly used eikonal equation solver. The F-X‐migrated image shows the imaging objective more clearly than any of the Kirchhoff migrations, and we advance a heuristic reason to explain this fact. Of the Kirchhoff migrations, the one using ray tracing produces the best image, and the other two are of comparable quality.

3-D Kirchhoff Migration of GPR Data to Image the Inside of a Stone Pagoda

2005 ◽  
Vol 277-279 ◽  
pp. 481-486
Author(s):  
Yun Gyeong Choi ◽  
Jung Hee Suh ◽  
Nu Ree Han ◽  
Ji Hyang Choi ◽  
Young Ho Cha
Keyword(s):  
Field Model ◽  
Synthetic Data ◽  
Outer Wall ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Non Destructive ◽  
Migration Technique ◽  
Stone Pagoda ◽  
Selection Of

We have chosen the GPR method for investigating the inner structure of a stone pagoda in a non-destructive way. The selection of a suitable source frequency of the GPR antenna is the key because the main frequency of its pulse controls the resolution and the depth of the investigation. Through theoretical consideration and numerical simulation, we found that 500 to 800 MHz is suitable for a field model with a foundation part of 3 to 4 m. To image the inner structure we selected 3-D Kirchhoff prestack depth migration technique used in seismic processing. We have used the modified migration algorithm for the source and receiver configurations of common offset GPR data. To verify the scheme, we calculated the synthetic data using the 3-D FDTD algorithm and applied the migration technique to it. Through these experiments, we confirmed that the 3-D Kirchhoff prestack depth migration technique is a very powerful tool to image the inside of a stone pagoda with high resolution. We have also applied the technique to the field data of the foundation of a five-story stone pagoda at Jeongnim temple site in Buyeo City, Korea. Based on the 3-D migrated images, we inferred that the structure of the foundation of this pagoda seemed to be preserved quite well and the thickness of the outer wall was about 0.5 m.

Prestack seismic data enhancement with partial common-reflection-surface (CRS) stack

Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. V49-V58 ◽  
Author(s):  
Mikhail Baykulov ◽  
Dirk Gajewski
Keyword(s):  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Synthetic Data ◽  
Original Data ◽  
Signal To Noise ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Common Reflection Surface ◽  
Noise Ratio

We developed a new partial common-reflection-surface (CRS) stacking method to enhance the quality of sparse low-fold seismic data. For this purpose, we use kinematic wavefield attributes computed during the automatic CRS stack. We apply a multiparameter CRS traveltime formula to compute partial stacked CRS supergathers. Our algorithm allows us to generate NMO-uncorrected gathers without the application of inverse NMO/DMO. Gathers obtained by this approach are regularized and have better signal-to-noise ratio compared with original common-midpoint gathers. Instead of the original data, these improved prestack data can be used in many conventional processing steps, e.g., velocity analysis or prestack depth migration, providing enhanced images and better quality control. We verified the method on 2D synthetic data and applied it to low-fold land data from northern Germany. The synthetic examples show the robustness of the partial CRS stack in the presence of noise. Sparse land data became regularized, and the signal-to-noise ratio of the seismograms increased as a result of the partial CRS stack. Prestack depth migration of the generated partially stacked CRS supergathers produced significantly improved common-image gathers as well as depth-migrated sections.

Fast migration/inversion with multivalued ray fields: Part 2—Applications to the 3D SEG/EAGE salt model

Geophysics ◽  
2004 ◽  
Vol 69 (5) ◽  
pp. 1320-1328 ◽  
Author(s):  
Sheng Xu ◽  
Gilles Lambaré ◽  
Henri Calandra
Keyword(s):  
Three Dimensional ◽  
Velocity Model ◽  
Three Dimensions ◽  
Complex Media ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Convenient Approach ◽  
First Arrival ◽  
Subsalt Imaging ◽  
Lateral Variations

Three‐dimensional prestack depth migration is the convenient approach for seismic imaging in the case of strong lateral variations of the velocity. Because of computing limitations, it has been limited to single‐arrival kinematic Kirchhoff migration until recently. This approach fails in the case of complex media characterized by multiarrival traveltimes. We present numerical strategies for extending in three dimensions first‐arrival kinematic Kirchhoff migration to multiarrival quantitative ray‐based migration (preserved amplitude migration). We rely on wavefront construction in a smooth velocity model to compute the multivalued traveltime and amplitude maps, and the CPU efficiency of migration itself is ensured by efficient and robust interpolation or extrapolation strategies. We present an application to the synthetic 3D SEG/EAGE salt model. Taking into account multiarrivals clearly improves subsalt imaging at the price of quite limited computing costs (a 20% increase in our case, with respect to a preserved‐amplitude single‐arrival migration).

Aperture effects in 2.5D Kirchhoff migration: A geometrical explanation

Geophysics ◽  
2003 ◽  
Vol 68 (5) ◽  
pp. 1673-1684 ◽  
Author(s):  
Thomas Hertweck ◽  
Christoph Jäger ◽  
Alexander Goertz ◽  
Jörg Schleicher
Keyword(s):  
Stationary Phase ◽  
Amplitude Variation ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Strong Amplitude ◽  
Zero Offset ◽  
The Time Domain ◽  
Geometrical Explanation ◽  
Seismic Images

Seismic images obtained by Kirchhoff time or depth migration are always accompanied by some artifacts known as migration noise, migration boundary effects, or diffraction smiles, which may severely affect the quality of the migration result. Most of these undesirable effects are caused by a limited aperture if the algorithms make no special disposition to avoid them. Strong amplitude variation along reflection events may cause similar artifacts. All of these effects can be explained mathematically by means of the method of stationary phase. However, such a purely theoretical explication is not always easily understood by applied geophysicists. A geometrical interpretation of the terms of the stationary‐phase approximation in relation to the diffraction and reflection traveltime curves in the time domain can help to develop a more intuitive understanding of the migration artifacts. A simple numerical experiment for poststack (zero‐offset) data indicates the problem and helps to demonstrate the effects and the methods to avoid them.

Efficient 2.5-D true‐amplitude migration

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 943-950 ◽  
Author(s):  
Joe A. Dellinger ◽  
Samuel H. Gray ◽  
Gary E. Murphy ◽  
John T. Etgen
Keyword(s):  
Seismic Data ◽  
Constant Velocity ◽  
Three Dimensions ◽  
Additional Source ◽  
Standard Methods ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Out Of Plane ◽  
Kirchhoff Method ◽  
Kirchhoff Depth Migration

Kirchhoff depth migration is a widely used algorithm for imaging seismic data in both two and three dimensions. To perform the summation at the heart of the algorithm, standard Kirchhoff migration requires a traveltime map for each source and receiver. True‐amplitude Kirchhoff migration in 2.5-D υ(x, z) media additionally requires maps of amplitudes, out‐of‐plane spreading factors, and takeoff angles; these quantities are necessary for calculating the true‐amplitude weight term in the summation. The increased input/output (I/O) and computational expense of including the true‐amplitude weight term is often not justified by significant improvement in the final muted and stacked image. For this reason, some authors advocate neglecting the weight term in the Kirchhoff summation entirely for most everyday imaging purposes. We demonstrate that for nearly the same expense as ignoring the weight term, a much better solution is possible. We first approximate the true‐amplitude weight term by the weight term for constant‐velocity media; this eliminates the need for additional source and receiver maps. With one small additional approximation, the weight term can then be moved entirely outside the innermost loop of the summation. The resulting Kirchhoff method produces images that are almost as good as for exact true‐amplitude Kirchhoff migration and at almost the same cost as standard methods that do not attempt to preserve amplitudes.

Evaluation of the Academic Setting in Spain 1This study was financed by the University of Oviedo.

1995 ◽  
Vol 11 (2) ◽  
pp. 133-137 ◽  
Author(s):  
Juan Fernández ◽  
Miguel A. Mateo ◽  
José Muñiz
Keyword(s):  
Higher Education ◽  
Decision Making ◽  
Social Climate ◽  
Three Dimensions ◽  
Academic Setting ◽  
Teaching And Research ◽  
Evaluation Questionnaire ◽  
University Teachers ◽  
The University

The conditions are investigated in which Spanish university teachers carry out their teaching and research functions. 655 teachers from the University of Oviedo took part in this study by completing the Academic Setting Evaluation Questionnaire (ASEQ). Of the three dimensions assessed in the ASEQ, Satisfaction received the lowest ratings, Social Climate was rated higher, and Relations with students was rated the highest. These results are similar to those found in two studies carried out in the academic years 1986/87 and 1989/90. Their relevance for higher education is twofold because these data can be used as a complement of those obtained by means of students' opinions, and the crossing of both types of data can facilitate decision making in order to improve the quality of the work (teaching and research) of the university institutions.

scholarly journals G-Tric: generating three-way synthetic datasets with triclustering solutions

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
João Lobo ◽  
Rui Henriques ◽  
Sara C. Madeira
Keyword(s):  
State Of The Art ◽  
Synthetic Data ◽  
Ground Truth ◽  
Real Data ◽  
Three Dimensions ◽  
Additional Advantage ◽  
Urban Dynamics ◽  
Data Generator ◽  
Real World Datasets ◽  
Synthetic Datasets

Abstract Background Three-way data started to gain popularity due to their increasing capacity to describe inherently multivariate and temporal events, such as biological responses, social interactions along time, urban dynamics, or complex geophysical phenomena. Triclustering, subspace clustering of three-way data, enables the discovery of patterns corresponding to data subspaces (triclusters) with values correlated across the three dimensions (observations $$\times$$ × features $$\times$$ × contexts). With increasing number of algorithms being proposed, effectively comparing them with state-of-the-art algorithms is paramount. These comparisons are usually performed using real data, without a known ground-truth, thus limiting the assessments. In this context, we propose a synthetic data generator, G-Tric, allowing the creation of synthetic datasets with configurable properties and the possibility to plant triclusters. The generator is prepared to create datasets resembling real 3-way data from biomedical and social data domains, with the additional advantage of further providing the ground truth (triclustering solution) as output. Results G-Tric can replicate real-world datasets and create new ones that match researchers needs across several properties, including data type (numeric or symbolic), dimensions, and background distribution. Users can tune the patterns and structure that characterize the planted triclusters (subspaces) and how they interact (overlapping). Data quality can also be controlled, by defining the amount of missing, noise or errors. Furthermore, a benchmark of datasets resembling real data is made available, together with the corresponding triclustering solutions (planted triclusters) and generating parameters. Conclusions Triclustering evaluation using G-Tric provides the possibility to combine both intrinsic and extrinsic metrics to compare solutions that produce more reliable analyses. A set of predefined datasets, mimicking widely used three-way data and exploring crucial properties was generated and made available, highlighting G-Tric’s potential to advance triclustering state-of-the-art by easing the process of evaluating the quality of new triclustering approaches.

Simple Index to Assess the Calibration Quality of Safety Performance Functions Based on Multiple Goodness-of-Fit Metrics

2021 ◽  
pp. 036119812110088
Author(s):  
Raul E. Avelar ◽  
Karen Dixon ◽  
Boniphace Kutela ◽  
Sam Klump ◽  
Beth Wemple ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Synthetic Data ◽  
Calibration Procedure ◽  
Safety Performance ◽  
Absolute Deviation ◽  
Data Set ◽  
Safety Database ◽  
Simple Index ◽  
Safety Performance Functions

The calibration of safety performance functions (SPFs) is a mechanism included in the Highway Safety Manual (HSM) to adjust SPFs in the HSM for use in intended jurisdictions. Critically, the quality of the calibration procedure must be assessed before using the calibrated SPFs. Multiple resources to aid practitioners in calibrating SPFs have been developed in the years following the publication of the HSM 1st edition. Similarly, the literature suggests multiple ways to assess the goodness-of-fit (GOF) of a calibrated SPF to a data set from a given jurisdiction. This paper uses the calibration results of multiple intersection SPFs to a large Mississippi safety database to examine the relations between multiple GOF metrics. The goal is to develop a sensible single index that leverages the joint information from multiple GOF metrics to assess overall quality of calibration. A factor analysis applied to the calibration results revealed three underlying factors explaining 76% of the variability in the data. From these results, the authors developed an index and performed a sensitivity analysis. The key metrics were found to be, in descending order: the deviation of the cumulative residual (CURE) plot from the 95% confidence area, the mean absolute deviation, the modified R-squared, and the value of the calibration factor. This paper also presents comparisons between the index and alternative scoring strategies, as well as an effort to verify the results using synthetic data. The developed index is recommended to comprehensively assess the quality of the calibrated intersection SPFs.

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