Wave‐equation extrapolation‐based multiple attenuation: 2-D filtering in the f-k domain

Geophysics ◽  
1994 ◽  
Vol 59 (9) ◽  
pp. 1377-1391 ◽  
Author(s):  
Binzhong Zhou ◽  
Stewart A. Greenhalgh
Keyword(s):  
Wave Equation ◽  
Prior Information ◽  
Original Data ◽  
Conventional Technique ◽  
Nonlinear Filter ◽  
Extrapolation Method ◽  
Multiple Model ◽  
Numerical Examples ◽  
Multiple Attenuation

A new nonlinear filter for wave‐equation extrapolation‐based multiple suppression is designed in the f-k domain. The realization of the new filter in the f-k domain is an extension of the conventional f-k dip filter. However, the new demultiple filter is superior to the conventional f-k dip filter in the sense that the multiple reject zones are determined automatically (based on the information of the input original data and the multiple model traces obtained by the wave‐extrapolation method) rather than by prior information on multiple moveout (dip) range. Therefore, it can easily cope with situations such as aliasing and the mixture of energy from multiples and primaries in the same quadrant. The new filter is smooth on the boundary of the reject area. Numerical examples demonstrate that the new filter is equivalent to the conventional f-k dip filter in multiple suppression for simple situations. However, when the multiples and primaries are mixed in the same quadrant and have only slight difference in dip, the new filter offers significant advantages over the conventional technique.

Multiple Suppression By a Wave-equation Extrapolation Method

1991 ◽  
Vol 22 (2) ◽  
pp. 481-483 ◽  
Author(s):  
B. Zhou ◽  
S. A. Greenhalgh
Keyword(s):  
Wave Equation ◽  
Extrapolation Method

scholarly journals Nonnegativity Preserving Interpolation byC1Bivariate Rational Spline Surface

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Xingxuan Peng ◽  
Zhihong Li ◽  
Qian Sun
Keyword(s):  
Sufficient Conditions ◽  
Rational Interpolation ◽  
Original Data ◽  
Interpolation Spline ◽  
Numerical Examples ◽  
Rational Spline ◽  
Spline Surface ◽  
Rectangular Grids

This paper is concerned with the nonnegativity preserving interpolation of data on rectangular grids. The function is a kind of bivariate rational interpolation spline with parameters, which isC1in the whole interpolation region. Sufficient conditions are derived on coefficients in the rational spline to ensure that the surfaces are always nonnegative if the original data are nonnegative. The gradients at the data sites are modified if necessary to ensure that the nonnegativity conditions are fulfilled. Some numerical examples are illustrated in the end of this paper.

scholarly journals Improving adaptive subtraction in seismic multiple attenuation

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. V59-V67 ◽  
Author(s):  
Shoudong Huo ◽  
Yanghua Wang
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Primary Energy ◽  
Multiple Models ◽  
Multiple Model ◽  
Data Set ◽  
Multiple Attenuation ◽  
Matching Filter ◽  
Theoretical Analyses ◽  
Different Order

In seismic multiple attenuation, once the multiple models have been built, the effectiveness of the processing depends on the subtraction step. Usually the primary energy is partially attenuated during the adaptive subtraction if an [Formula: see text]-norm matching filter is used to solve a least-squares problem. The expanded multichannel matching (EMCM) filter generally is effective, but conservative parameters adopted to preserve the primary could lead to some remaining multiples. We have managed to improve the multiple attenuation result through an iterative application of the EMCM filter to accumulate the effect of subtraction. A Butterworth-type masking filter based on the multiple model can be used to preserve most of the primary energy prior to subtraction, and then subtraction can be performed on the remaining part to better suppress the multiples without affecting the primaries. Meanwhile, subtraction can be performed according to the orders of the multiples, as a single subtraction window usually covers different-order multiples with different amplitudes. Theoretical analyses, and synthetic and real seismic data set demonstrations, proved that a combination of these three strategies is effective in improving the adaptive subtraction during seismic multiple attenuation.

Classification and Space Cluster for Visualizing GeoInformation

2019 ◽  
Vol 15 (1) ◽  
pp. 19-38
Author(s):  
Toshihiro Osaragi
Keyword(s):  
Spatial Data ◽  
Spatial Clustering ◽  
Effective Means ◽  
Information Criterion ◽  
Original Data ◽  
Spatial Clusters ◽  
Clustering Method ◽  
Numerical Examples ◽  
Loss Of Information ◽  
Tokyo Metropolitan Area

It is necessary to classify numerical values of spatial data when representing them on a map so that, visually, it can be as clearly understood as possible. Inevitably some loss of information from the original data occurs in the process of this classification. A gate loss of information might lead to a misunderstanding of the nature of original data. At the same time, when we understand the spatial distribution of attribute values, forming spatial clusters is regarded as an effective means, in which values can be regarded as statistically equivalent and distribute continuous in the same patches. In this study, a classification method for organizing spatial data is proposed, in which any loss of information is minimized. Also, a spatial clustering method based on Akaike's Information Criterion is proposed. Some numerical examples of their applications are shown using actual spatial data for the Tokyo metropolitan area.

scholarly journals Approximation to Hadamard Derivative via the Finite Part Integral

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 983 ◽  
Author(s):  
Chuntao Yin ◽  
Changpin Li ◽  
Qinsheng Bi
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Numerical Methods ◽  
Three Dimensional ◽  
Cylindrical Wave ◽  
Physical Models ◽  
Finite Part ◽  
Numerical Examples ◽  
Crack Problems ◽  
Hadamard Derivative

In 1923, Hadamard encountered a class of integrals with strong singularities when using a particular Green’s function to solve the cylindrical wave equation. He ignored the infinite parts of such integrals after integrating by parts. Such an idea is very practical and useful in many physical models, e.g., the crack problems of both planar and three-dimensional elasticities. In this paper, we present the rectangular and trapezoidal formulas to approximate the Hadamard derivative by the idea of the finite part integral. Then, we apply the proposed numerical methods to the differential equation with the Hadamard derivative. Finally, several numerical examples are displayed to show the effectiveness of the basic idea and technique.

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

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. Q27-Q36 ◽  
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.

scholarly journals A Comparison of Splitting Techniques for 3D Complex Padé Fourier Finite Difference Migration

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Jessé C. Costa ◽  
Débora Mondini ◽  
Jörg Schleicher ◽  
Amélia Novais
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Computational Cost ◽  
Three Dimensional ◽  
Depth Level ◽  
Numerical Examples ◽  
The Cost ◽  
Comparable Quality ◽  
3D Problem ◽  
Dimensional Wave

Three-dimensional wave-equation migration techniques are still quite expensive because of the huge matrices that need to be inverted. Several techniques have been proposed to reduce this cost by splitting the full 3D problem into a sequence of 2D problems. We compare the performance of splitting techniques for stable 3D Fourier finite-difference (FFD) migration techniques in terms of image quality and computational cost. The FFD methods are complex Padé FFD and FFD plus interpolation, and the compared splitting techniques are two- and four-way splitting as well as alternating four-way splitting, that is, splitting into the coordinate directions at one depth and the diagonal directions at the next depth level. From numerical examples in homogeneous and inhomogeneous media, we conclude that, though theoretically less accurate, alternate four-way splitting yields results of comparable quality as full four-way splitting at the cost of two-way splitting.

3D multiple attenuation of OBC converted‐wave data using wave‐equation multiple modeling

2010 ◽  
Author(s):  
Andrew Dawson ◽  
Joffrey Brunellière ◽  
Peter Allan ◽  
Mark Ibram
Keyword(s):  
Wave Equation ◽  
Converted Wave ◽  
Wave Data ◽  
Multiple Attenuation

Deep‐water peg legs and multiples: Emulation and suppression

Geophysics ◽  
1986 ◽  
Vol 51 (12) ◽  
pp. 2177-2184 ◽  
Author(s):  
J. R. Berryhill ◽  
Y. C. Kim
Keyword(s):  
Wave Equation ◽  
Seismic Data ◽  
Water Layer ◽  
Original Data ◽  
Equation Method ◽  
Multiple Reflections ◽  
Step Method ◽  
Arrival Times ◽  
Sea Floor ◽  
Water Bottom

This paper discusses a two‐step method for predicting and attenuating multiple and peg‐leg reflections in unstacked seismic data. In the first step, an (observed) seismic record is extrapolated through a round‐trip traversal of the water layer, thus creating an accurate prediction of all possible multiples. In the second step, the record containing the predicted multiples is compared with and subtracted from the original. The wave‐equation method employed to predict the multiples takes accurate account of sea‐floor topography and so requires a precise water‐bottom profile as part of the input. Information about the subsurface below the sea floor is not required. The arrival times of multiple reflections are reproduced precisely, although the amplitudes are not accurate, and the sea floor is treated as a perfect reflector. The comparison step detects the similarities between the computed multiples and the original data, and estimates a transfer function to equalize the amplitudes and account for any change in waveform caused by the sea‐floor reflector. This two‐step wave‐equation method is effective even for dipping sea floors and dipping subsurface reflectors. It does not depend upon any assumed periodicity in the data or upon any difference in stacking velocity between primaries and multiples. Thus it is complementary to the less specialized methods of multiple suppression.

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