Stable depth extrapolation of seismic wavefields by a Neumann series

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 2063-2071 ◽  
Author(s):  
Andrzej Kostecki ◽  
Anna Półchłopek
Keyword(s):  
Low Frequency ◽  
Computation Time ◽  
Neumann Series ◽  
Complex Structures ◽  
Lateral Heterogeneity ◽  
Frequency Filter ◽  
Geological Structures ◽  
Depth Migration ◽  
Frequency Space ◽  
Lateral Variations

Several migration methods fail to work when applied to complex geological structures with strong lateral heterogeneity. The generalized migration in the frequency‐wavenumber (f-k) domain based on a convolution with a slowness- (inverse of velocity) dependent operator is capable of downward continuation of wavefield in media with strong vertical and lateral variations of velocity. Unfortunately, this method, as presented in the literature, is potentially unstable. We propose a new, stable extrapolator based on the solution of the integral Fredholm equation, which describes a one‐way wave equation in the form of a Neumann series. The resulting algorithm of depth migration is implemented in both the frequency‐wavenumber (f-k) and frequency‐space (f-x) domains and takes into account arbitrary lateral gradients of velocity, using a low‐frequency filter (in x-f domain) that is the sum of the power series. The computation time of depth migration by a Neumann series is slightly longer than for split‐step Fourier migration. The examples presented suggest that the depth migration by Neumann’s series method can be used to map complex structures with strong lateral gradients of velocity.

Extended local Rytov Fourier migration method

Geophysics ◽  
1999 ◽  
Vol 64 (5) ◽  
pp. 1535-1545 ◽  
Author(s):  
Lian‐Jie Huang ◽  
Michael C. Fehler ◽  
Peter M. Roberts ◽  
Charles C. Burch
Keyword(s):  
Phase Changes ◽  
Fast Fourier Transform Algorithm ◽  
Scalar Wave ◽  
Depth Migration ◽  
Frequency Space ◽  
Rytov Approximation ◽  
Migration Method ◽  
The Stability ◽  
Wavefield Extrapolation ◽  
Lateral Variations

We develop a novel depth‐migration method termed the extended local Rytov Fourier (ELRF) migration method. It is based on the scalar wave equation and a local application of the Rytov approximation within each extrapolation interval. Wavefields are Fourier transformed back and forth between the frequency‐space and frequency‐wavenumber domains during wavefield extrapolation. The lateral slowness variations are taken into account in the frequency‐space domain. The method is efficient due to the use of a fast Fourier transform algorithm. Under the small angle approximation, the ELRF method leads to the split‐step Fourier (SSF) method that is unconditionally stable. The ELRF method and the extended local Born Fourier (ELBF) method that we previously developed can handle wider propagation angles than the SSF method and account for the phase and amplitude changes due to the lateral variations of slowness, whereas the SSF method only accounts for the phase changes. The stability of the ELRF method is controlled more easily than that of the ELBF method.

Fast acquisition aperture correction in prestack depth migration using beamlet decomposition

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. S67-S74 ◽  
Author(s):  
Jun Cao ◽  
Ru-Shan Wu
Keyword(s):  
Wave Equation ◽  
Correction Factor ◽  
Computing Time ◽  
Computation Time ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Wavenumber Domain ◽  
Amplitude Correction ◽  
Local Wavenumber ◽  
Local Angle

Wave-equation-based acquisition aperture correction in the local angle domain can improve image amplitude significantly in prestack depth migration. However, its original implementation is inefficient because the wavefield decomposition uses the local slant stack (LSS), which is demanding computationally. We propose a faster method to obtain the image and amplitude correction factor in the local angle domain using beamlet decomposition in the local wavenumber domain. For a given frequency, the image matrix in the local wavenumber domain for all shots can be calculated efficiently. We then transform the shot-summed image matrix from the local wavenumber domain to the local angle domain (LAD). The LAD amplitude correction factor can be obtained with a similar strategy. Having a calculated image and correction factor, one can apply similar acquisition aperture corrections to the original LSS-based method. For the new implementation, we compare the accuracy and efficiency of two beamlet decompositions: Gabor-Daubechies frame (GDF) and local exponential frame (LEF). With both decompositions, our method produces results similar to the original LSS-based method. However, our method can be more than twice as fast as LSS and cost only twice the computation time of traditional one-way wave-equation-based migrations. The results from GDF decomposition are superior to those from LEF decomposition in terms of artifacts, although GDF requires a little more computing time.

The Low Frequency Space Array (LFSA)

1988 ◽  
pp. 459-460 ◽  
Author(s):  
K. W. Weiler ◽  
B. K. Dennisonz ◽  
K. J. Johnston ◽  
R. S. Simon ◽  
J. H. Spencer ◽  
...  
Keyword(s):  
Low Frequency ◽  
Frequency Space

Velocity estimation in laterally varying media

Geophysics ◽  
1982 ◽  
Vol 47 (6) ◽  
pp. 884-897 ◽  
Author(s):  
Walter S. Lynn ◽  
Jon F. Claerbout
Keyword(s):  
Taylor Series Expansion ◽  
Velocity Estimation ◽  
Lateral Resolution ◽  
Velocity Variation ◽  
Lateral Velocity ◽  
Depth Migration ◽  
Derivative Term ◽  
Fourth Derivative ◽  
Zero Offset ◽  
Lateral Variations

In areas of large lateral variations in velocity, stacking velocities computed on the basis of hyperbolic moveout can differ substantially from the actual root mean square (rms) velocities. This paper addresses the problem of obtaining rms or migration velocities from stacking velocities in such areas. The first‐order difference between the stacking and the vertical rms velocities due to lateral variations in velocity are shown to be related to the second lateral derivative of the rms slowness [Formula: see text]. Approximations leading to this relation are straight raypaths and that the vertical rms slowness to a given interface can be expressed as a second‐order Taylor series expansion in the midpoint direction. Under these approximations, the effect of the first lateral derivative of the slowness on the traveltime is negligible. The linearization of the equation relating the stacking and true velocities results in a set of equations whose inversion is unstable. Stability is achieved, however, by adding a nonphysical fourth derivative term which affects only the higher spatial wavenumbers, those beyond the lateral resolution of the lateral derivative method (LDM). Thus, given the stacking velocities and the zero‐offset traveltime to a given event as a function of midpoint, the LDM provides an estimate of the true vertical rms velocity to that event with a lateral resolution of about two mute zones or cable lengths. The LDM is applicable when lateral variations of velocity greater than 2 percent occur over the mute zone. At variations of 30 percent or greater, the internal assumptions of the LDM begin to break down. Synthetic models designed to test the LDM when the different assumptions are violated show that, in all cases, the results are not seriously affected. A test of the LDM on field data having a lateral velocity variation caused by sea floor topography gives a result which is supported by depth migration.

scholarly journals Nonlinear kernels, dominance, and envirotyping data increase the accuracy of genome-based prediction in multi-environment trials

Heredity ◽  
2020 ◽  
Vol 126 (1) ◽  
pp. 92-106 ◽  
Author(s):  
Germano Costa-Neto ◽  
Roberto Fritsche-Neto ◽  
José Crossa
Keyword(s):  
Kernel Methods ◽  
Large Scale ◽  
Additive Model ◽  
Computation Time ◽  
Reaction Norm ◽  
Model Complexity ◽  
Gaussian Kernel ◽  
Environment Interaction ◽  
Complex Structures ◽  
Processing Times

AbstractModern whole-genome prediction (WGP) frameworks that focus on multi-environment trials (MET) integrate large-scale genomics, phenomics, and envirotyping data. However, the more complex the statistical model, the longer the computational processing times, which do not always result in accuracy gains. We investigated the use of new kernel methods and modeling structures involving genomics and nongenomic sources of variation in two MET maize data sets. Five WGP models were considered, advancing in complexity from a main-effect additive model (A) to more complex structures, including dominance deviations (D), genotype × environment interaction (AE and DE), and the reaction-norm model using environmental covariables (W) and their interaction with A and D (AW + DW). A combination of those models built with three different kernel methods, Gaussian kernel (GK), Deep kernel (DK), and the benchmark genomic best linear-unbiased predictor (GBLUP/GB), was tested under three prediction scenarios: newly developed hybrids (CV1), sparse MET conditions (CV2), and new environments (CV0). GK and DK outperformed GB in prediction accuracy and reduction of computation time (~up to 20%) under all model–kernel scenarios. GK was more efficient in capturing the variation due to A + AE and D + DE effects and translated it into accuracy gains (~up to 85% compared with GB). DK provided more consistent predictions, even for more complex structures such as W + AW + DW. Our results suggest that DK and GK are more efficient in translating model complexity into accuracy, and more suitable for including dominance and reaction-norm effects in a biologically accurate and faster way.

scholarly journals AmpliCI: a high-resolution model-based approach for denoising Illumina amplicon data

2020 ◽  
Author(s):  
Xiyu Peng ◽  
Karin S Dorman
Keyword(s):  
Sequence Similarity ◽  
Low Frequency ◽  
Computation Time ◽  
Amplicon Sequencing ◽  
Supplementary Information ◽  
Quality Information ◽  
Model Based ◽  
Main Challenge ◽  
Sequencing Quality ◽  
Resolution Model

Abstract Motivation Next-generation amplicon sequencing is a powerful tool for investigating microbial communities. A main challenge is to distinguish true biological variants from errors caused by amplification and sequencing. In traditional analyses, such errors are eliminated by clustering reads within a sequence similarity threshold, usually 97%, and constructing operational taxonomic units, but the arbitrary threshold leads to low resolution and high false-positive rates. Recently developed ‘denoising’ methods have proven able to resolve single-nucleotide amplicon variants, but they still miss low-frequency sequences, especially those near more frequent sequences, because they ignore the sequencing quality information. Results We introduce AmpliCI, a reference-free, model-based method for rapidly resolving the number, abundance and identity of error-free sequences in massive Illumina amplicon datasets. AmpliCI considers the quality information and allows the data, not an arbitrary threshold or an external database, to drive conclusions. AmpliCI estimates a finite mixture model, using a greedy strategy to gradually select error-free sequences and approximately maximize the likelihood. AmpliCI has better performance than three popular denoising methods, with acceptable computation time and memory usage. Availability and implementation Source code is available at https://github.com/DormanLab/AmpliCI. Supplementary information Supplementary material are available at Bioinformatics online.

A New Capacitance Multiplier Structure with High Multiplication Factor for Ultra-Low-Frequency Filter in Biomedical Applications

2019 ◽  
Vol 29 (07) ◽  
pp. 2050109
Author(s):  
Yan Li ◽  
Yong Liang Li
Keyword(s):  
Biomedical Applications ◽  
Low Frequency ◽  
Multiplication Factor ◽  
Frequency Filter ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Physiological Signal ◽  
Wide Range ◽  
Low Pass ◽  
Capacitance Multiplier

A novel capacitance multiplier is proposed to implement an ultra-low-frequency filter for physiological signal processing in biomedical applications. With the proposed multiplier, a simple first-order low-pass filter achieves a [Formula: see text]3-dB frequency of 33.4[Formula: see text]μHz with a 1-pF capacitance and a 20[Formula: see text]k[Formula: see text] resistance. This corresponds to a multiplication factor of as large as [Formula: see text]. By changing the controlling terminal, the [Formula: see text]3-dB frequency can be tuned in a wide range of 33.4[Formula: see text]μHz–6.3[Formula: see text]kHz.

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