Antialiasing methods in Kirchhoff migration

Geophysics ◽  
1999 ◽  
Vol 64 (6) ◽  
pp. 1783-1792 ◽  
Author(s):  
Ray Abma ◽  
James Sun ◽  
Nick Bernitsas
Keyword(s):  
Cost Effective ◽  
Setup Time ◽  
Spatial Derivative ◽  
Kirchhoff Migration ◽  
Migration Operator ◽  
Computational Environment ◽  
Time Migration ◽  
Corrected Expression ◽  
Simple Operator ◽  
Previous Approximation

This paper addresses some practical aspects of antialiasing in Kirchhoff migration. We show that the effective trace spacing related to the aliasing‐frequency limits for directions between the in‐line and cross‐line directions is smaller than values previously used and that the frequency limits for antialiasing may be increased. We present a corrected expression for the migration operator spatial derivative for 3-D time migration that avoids the overfiltering at nonzero offsets produced by a previous approximation. Simple operator truncation is shown to reduce aliasing noise; it is inexpensive but may lead to errors in interpretation. Triangle filtering and Gray’s method both produce similar results, but the relative costs of these two methods will vary with the size of the migration and the computational environment. Gray’s method takes more setup time for each input trace than does triangle filtering, but Gray’s method might be more cost effective when each input trace contributes to a large number of output traces.

Surface-offset gathers from elastic reverse time migration and velocity analysis

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. S47-S64
Author(s):  
Yang Zhao ◽  
Tao Liu ◽  
Xueyi Jia ◽  
Hongwei Liu ◽  
Zhiguang Xue ◽  
...  
Keyword(s):  
Velocity Ratio ◽  
Computational Cost ◽  
Cost Effective ◽  
Velocity Estimation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
The Common ◽  
Wave Decomposition

Angle-domain common-image gathers (ADCIGs) from elastic reverse time migration (ERTM) are valuable tools for seismic elastic velocity estimation. Traditional ADCIGs are based on the concept of common-offset domains, but common-shot domain implementations are often favored for computational cost considerations. Surface-offset gathers (SOGs) built from common-offset migration may serve as an alternative to the common-shot ADCIGs. We have developed a theoretical kinematic framework between these two domains, and we determined that the common SOG gives an alternative measurement of kinematic correctness in the presence of incorrect velocity. Specifically, we exploit analytical expressions for the image misposition between these two domains, with respect to the traveltime perturbation caused by velocity errors. Four formulations of the PP and PS residual moveout functions are derived and provide insightful information of the velocity error, angle, and PS velocity ratio contained in ERTM gathers. The analytical solutions are validated with homogeneous examples with a series of varied parameters. We found that the SOGs may perform in the way of simplicity and linearity as an alternative to the common-shot migration. To make a full comparison with ADCIGs, we have developed a cost-effective workflow of ERTM SOGs. A fast vector P- and S-wave decomposition can be obtained via spatial gradients at selected time steps. A selected ERTM imaging condition is then modified in which the migration is done by offset groups between each source and receiver pair for each P- and S-wave decomposition. Two synthetic (marine and land) examples are used to demonstrate the feasibility of our methods.

A cost-effective scheme for reverse time migration angle gathers

2016 ◽  
Author(s):  
Qiang Fu ◽  
Arthur Weglein ◽  
Faqi Liu ◽  
Scott Morton ◽  
Marion King
Keyword(s):  
Cost Effective ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Effective Scheme

An effective imaging condition for reverse-time migration using wavefield decomposition

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. S29-S39 ◽  
Author(s):  
Faqi Liu ◽  
Guanquan Zhang ◽  
Scott A. Morton ◽  
Jacques P. Leveille
Keyword(s):  
Low Frequency ◽  
Real Data ◽  
Cost Effective ◽  
High Amplitude ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Velocity Models ◽  
Time Migration ◽  
Computationally Intensive

Reverse-time migration (RTM) exhibits great superiority over other imaging algorithms in handling steeply dipping structures and complicated velocity models. However, low-frequency, high-amplitude noises commonly seen in a typical RTM image have been one of the major concerns because they can seriously contaminate the signals in the image if they are not handled properly. We propose a new imaging condition to effectively and efficiently eliminate these specific noises from the image. The method works by first decomposing the source and receiver wavefields to their one-way propagation components, followed by applying a correlation-based imaging condition to the appropriate combinations of the decomposed wavefields. We first give the physical explanation of the principle of such noises in the conventional RTM image. Then we provide the detailed mathematical theory for the new imaging condition. Finally, we propose an efficient scheme for its numerical implementation. It replaces the computationally intensive decomposition with the cost-effective Hilbert transform, which significantly improves the efficiency of the imaging condition. Applications to various synthetic and real data sets demonstrate that this new imaging condition can effectively remove the undesired low-frequency noises in the image.

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.

A prestack residual time migration operator

Geophysics ◽  
1996 ◽  
Vol 61 (2) ◽  
pp. 605-607 ◽  
Author(s):  
Robert H. Stolt
Keyword(s):  
Constant Velocity ◽  
Square Root ◽  
Core Concept ◽  
Residual Time ◽  
The Core ◽  
Migration Operator ◽  
Time Migration ◽  
The Difference

Larner and Beasley (1987) present cascaded migration as a way to increase the power and effectiveness of relatively simple migration methods. In particular, f-k migration (Stolt, 1978) can be made to accommodate a depth‐dependent velocity as a cascade of constant‐velocity migrations. The core concept is that data which have been migrated with an approximate velocity can be effectively migrated to their true velocity by migrating with a velocity that is equal to the square root of the difference between the squares of the true and approximate velocities.

Design of Products for an Agile Manufacturing Environment

1994 ◽  
Author(s):  
Andrew Kusiak ◽  
Chang-Xue Feng
Keyword(s):  
Concurrent Engineering ◽  
Cost Effective ◽  
Setup Time ◽  
Agile Manufacturing ◽  
Manufacturing Companies ◽  
Basic Principles ◽  
Design And Manufacturing ◽  
Feature Based ◽  
Lot Sizes ◽  
Feature Based Design

Abstract Many manufacturing companies have been striving to reduce setup times in order to produce smaller lot sizes and to obtain quicker responses to frequently changing market demands. This paper focuses on the reduction of setup time by design improvements of products. Based on the basic principles of setups and concepts from concurrent engineering, rules for design of products at the feature level are presented. Examples and computational results illustrate that the inter-lot setups and in-lot setups can be reduced by the feature-based design rules. The proposed approach for setup reduction appears to be more cost effective than optimizing the processes and operations where the product designs have been fixed. This research intends to bridge the gap between engineering design and manufacturing.

Hybrid migration: A cost‐effective 3-D depth‐imaging technique

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 568-576 ◽  
Author(s):  
Young C. Kim ◽  
Worth B. Hurt, ◽  
Louis J. Maher ◽  
Patrick J. Starich
Keyword(s):  
Model Building ◽  
Cost Effective ◽  
Velocity Model ◽  
Depth Image ◽  
Hybrid Technique ◽  
Prestack Depth Migration ◽  
Depth Imaging ◽  
Depth Migration ◽  
Time Migration ◽  
Prestack Time Migration

The transformation of surface seismic data into a subsurface image can be separated into two components—focusing and positioning. Focusing is associated with ensuring the data from different offsets are contributing constructively to the same event. Positioning involves the transformation of the focused events into a depth image consistent with a given velocity model. In prestack depth migration, both of these operations are achieved simultaneously; however, for 3-D data, the cost is significant. Prestack time migration is much more economical and focuses events well even in the presence of moderate velocity variations, but suffers from mispositioning problems. Hybrid migration is a cost‐effective depth‐imaging approach that uses prestack time migration for focusing; inverse migration for the removal of positioning errors; and poststack depth migration for proper positioning. When lateral velocity changes are moderate, the hybrid technique can generate a depth image that is consistent with a velocity field. For very complex structures that require prestack depth migration, the results of the hybrid technique can be used to create a starting velocity model, thereby reducing the number of iterations for velocity model building.

Vertical seismic profile Kirchhoff migration with structure dip constraint

2015 ◽  
Vol 3 (3) ◽  
pp. SW51-SW56
Author(s):  
Xiaomin Zhao ◽  
Shengwen Jin
Keyword(s):  
Seismic Profile ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Vertical Seismic Profile ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Time Migration ◽  
Migration Imaging ◽  
Imaging Result ◽  
Borehole Seismic

Prestack Kirchhoff depth migration is commonly used in borehole seismic imaging, where there is uneven illumination due to the limitations of the source-receiver geometry. A new vertical seismic profile (VSP) migration/imaging workflow has been established that incorporates the structure-dip information derived from a newly developed structure tensor analysis into the existing VSP Kirchhoff migration/imaging technique. This allows us to better image the structures in the vicinity of a borehole and the far-field dipping events away from the borehole. We tested the workflow with the HESS salt model. The results were compared with those from reverse time migration, which found that Kirchhoff migration combined with structure-dip information not only reduced ambiguities of the imaging result but also allowed for imaging dip structures (e.g., fault) in the far region from the borehole. This allows for imaging dip structures and provides a useful extension of existing VSP imaging capabilities using Kirchhoff migration.

scholarly journals Simultaneous time imaging, velocity estimation, and multiple suppression using local event slopes

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA65-WCA73 ◽  
Author(s):  
Dennis Cooke ◽  
Andrej Bóna ◽  
Benn Hansen
Keyword(s):  
Temporal Frequency ◽  
Synthetic Data ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Data Set ◽  
Image Domain ◽  
Kirchhoff Migration ◽  
Time Migration ◽  
Prestack Time Migration ◽  
Input Formula

Starting with the double-square-root equation we derive expressions for a velocity-independent prestack time migration and for the associated migration velocity. We then use that velocity to identify multiples and suppress them as part of the imaging step. To describe our algorithm, workflow, and products, we use the terms velocity-independent and oriented. While velocity-independent imaging does not require an input migration velocity, it does require input [Formula: see text]-values (also called local event slopes) measured in both the shot and receiver domains. There are many possible methods of calculating these required input [Formula: see text]-values, perhaps the simplest is to compute the ratio of instantaneous spatial frequency to instantaneous temporal frequency. Using a synthetic data set rich in multiples, we test the oriented algorithm and generate migrated prestack gathers, the oriented migration velocity field, and stacked migrations. We use oriented migration velocities for prestack multiple suppression. Without this multiple suppression step, the velocity-independent migration is inferior to a conventional Kirchhoff migration because the oriented migration will flatten primaries and multiples alike in the common image domain. With this multiple suppression step, the velocity-independent are very similar to a Kirchhoff migration generated using the known migration velocity of this test data set.

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