COMPUTER‐DESIGNED WIENER FILTERS FOR SEISMIC DATA

Geophysics ◽  
1972 ◽  
Vol 37 (2) ◽  
pp. 235-259 ◽  
Author(s):  
John C. Robinson
Keyword(s):  
Seismic Data ◽  
Digital Computer ◽  
Wiener Filter ◽  
Time Dependent ◽  
Special Consideration ◽  
Frequency Content ◽  
Spatial Range ◽  
Wiener Filters ◽  
Data Windows ◽  
Finite Data

This paper is concerned with differences in the frequency content of signal and noise on seismic traces. In order to develop a filter which has applicability over some considerable spatial range, special consideration is given to basic differences in the shape and the frequency content of individual signal and noise wavelets (events) on these traces. Therefore, a so‐called “wavelet” Wiener filter is introduced which suppresses “noise” wavelets and enhances “signal” wavelets; this filter can be contrasted with an ordinary Wiener filter which discriminates between signal and noise on the additional basis of the statistics of the repetition of wavelets along the seismic trace. A technique for the automatic derivation of (wavelet) Wiener filters for seismic data by a digital computer is developed. The filters are time dependent to the extent that independent filters are derived at a sequence of data windows which are specified by the operator; criteria for selecting the window positions are given. The overall technique for the computer derivation of Wiener filters is demonstrated with synthetic and actual seismic data. A discussion of the wavelet Wiener filter and its relation to the ordinary Wiener filter is appended to this paper with a discussion of the effects of finite data windows on the eduction of the wavelet Wiener filter.

THE DETERMINATION OF DIGITAL WIENER FILTERS BY MEANS OF GRADIENT METHODS

Geophysics ◽  
1973 ◽  
Vol 38 (2) ◽  
pp. 310-326 ◽  
Author(s):  
R. J. Wang ◽  
S. Treitel
Keyword(s):  
Seismic Data ◽  
High Speed ◽  
Gradient Methods ◽  
Wiener Filter ◽  
Gradient Algorithm ◽  
Rapid Convergence ◽  
True Solution ◽  
Peripheral Device ◽  
Wiener Filters

The normal equations for the discrete Wiener filter are conventionally solved with Levinson’s algorithm. The resultant solutions are exact except for numerical roundoff. In many instances, approximate rather than exact solutions satisfy seismologists’ requirements. The so‐called “gradient” or “steepest descent” iteration techniques can be used to produce approximate filters at computing speeds significantly higher than those achievable with Levinson’s method. Moreover, gradient schemes are well suited for implementation on a digital computer provided with a floating‐point array processor (i.e., a high‐speed peripheral device designed to carry out a specific set of multiply‐and‐add operations). Levinson’s method (1947) cannot be programmed efficiently for such special‐purpose hardware, and this consideration renders the use of gradient schemes even more attractive. It is, of course, advisable to utilize a gradient algorithm which generally provides rapid convergence to the true solution. The “conjugate‐gradient” method of Hestenes (1956) is one of a family of algorithms having this property. Experimental calculations performed with real seismic data indicate that adequate filter approximations are obtainable at a fraction of the computer cost required for use of Levinson’s algorithm.

scholarly journals Application of the Wiener filter to magnetic profiling in the volcanic environment of Mt. Etna (Italy)

1996 ◽  
Vol 39 (1) ◽  
Author(s):  
C. Del Negro
Keyword(s):  
Synthetic Data ◽  
Wiener Filter ◽  
Magnetic Anomalies ◽  
Fault System ◽  
Volcanic Area ◽  
Wiener Filters ◽  
Mt Etna ◽  
Band Pass ◽  
Magnetic Profile ◽  
Mean Square Error Criterion

The frequency-domain Wiener filtering was applied to magnetic anomalies in the volcanic area of Mt. Etna. This filter, under suitable conditions (additive noise, linear processing and mean-square error criterion), can furnish an effective tool for discriminating the geologic feature of interest (the signal) from the noise. The filter was first tested with synthetic data. Afterwards it was applied to a magnetic profile carried out across the principal fault system of the Mt. Etna volcano, that hosted the dykes feeding both the 1989 and the 1991-93 eruptions. The magnetic anomalies linked to the volcanic section and those linked to the contact between the clay basement and the lava coverage show significant spectral overlap. Thus by estimating the power spectrum of the signal, obtained resolving the forward problem, a least-squares Wiener filter has been designed. In such context, it was possible to verify the effectiveness of Wiener filters, whereas traditional band-pass filtering proved inadequate. In fact, analysis of the noise showed that all the meaningful components of the observed magnetic field were resolved. The results put further constraints on location and geometry of the shallow plumbing system of Mt. Etna.

3-D seismic imaging and seismic attribute analysis of genetic sequences deposited in low‐accommodation conditions

Geophysics ◽  
1996 ◽  
Vol 61 (5) ◽  
pp. 1351-1362 ◽  
Author(s):  
B. A. Hardage ◽  
D. L. Carr ◽  
D. E. Lancaster ◽  
J. L. Simmons ◽  
D. S. Hamilton ◽  
...  
Keyword(s):  
Seismic Data ◽  
Sediment Accumulation ◽  
Gas Reservoirs ◽  
Seismic Attribute ◽  
Gas Field ◽  
Reservoir System ◽  
Depositional Processes ◽  
Genetic Sequences ◽  
Data Windows ◽  
Reservoir Facies

A multidisciplinary team, composed of stratigraphers, petrophysicists, reservoir engineers, and geophysicists, studied a portion of Boonsville gas field in the Fort Worth Basin of North‐Central Texas to determine how modern geophysical, geological, and engineering techniques could be combined to understand the mechanisms by which fluvio‐deltaic depositional processes create reservoir compartmentalization in a low‐ to moderate‐accommodation basin. An extensive database involving well logs, cores, production, and pressure data from 200‐plus wells, [Formula: see text] [Formula: see text] of 3-D seismic data, vertical seismic profiles (VSPs), and checkshots was assembled to support this investigation. The reservoir system we studied was the Bend Conglomerate, a productive series of gas reservoirs composed of Middle Pennsylvanian fluvio‐deltaic clastics 900 to 1300 ft (275 to 400 m) thick in our project area. We were particularly interested in this reservoir system because evidence suggested that many of the sequences in this stratigraphic interval were deposited in low‐accommodation conditions (that is, in an environment where there was limited vertical space available for sediment accumulation), and our objective was to investigate how fluvio‐deltaic reservoirs were compartmentalized by low‐accommodation depositional processes. Using an extensive well log database (200 plus wells) and a core‐calibrated calculation of rock facies derived from these logs, we divided the Bend Conglomerate interval into ten genetic sequences, with each sequence being approximately 100 ft (30 m) thick. We then used local VSP and checkshot control to transform log‐measured depths of each sequence boundary to seismic two‐way time coordinates and identified narrow seismic data windows encompassing each sequence across the [Formula: see text] [Formula: see text] 3-D seismic grid. A series of seismic attributes was calculated in these carefully defined data windows to determine which attributes were reliable indicators of the presence of productive reservoir facies and which attributes could, therefore, reveal distinct reservoir compartments and potentially show where infield wells should be drilled to reach previously uncontacted gas reservoirs. Our best success was the seismic attribute correlations we found in the Upper and Lower Caddo sequences, at the top of the Bend Conglomerate. These sequences were deposited in a low‐accommodation setting, relative to other Boonsville sequences, and we found that reflection amplitude and instantaneous frequency, respectively, were reliable indicators of the areal distribution of reservoir facies in these low‐accommodation sequences.

Laplace-domain full-waveform inversion of seismic data lacking low-frequency information

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. R199-R206 ◽  
Author(s):  
Wansoo Ha ◽  
Changsoo Shin
Keyword(s):  
Seismic Data ◽  
Field Data ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Single Frequency ◽  
Frequency Content ◽  
Laplace Domain ◽  
Frequency Information ◽  
Velocity Models ◽  
Gaussian Source

The lack of the low-frequency information in field data prohibits the time- or frequency-domain waveform inversions from recovering large-scale background velocity models. On the other hand, Laplace-domain waveform inversion is less sensitive to the lack of the low frequencies than conventional inversions. In theory, frequency filtering of the seismic signal in the time domain is equivalent to a constant multiplication of the wavefield in the Laplace domain. Because the constant can be retrieved using the source estimation process, the frequency content of the seismic data does not affect the gradient direction of the Laplace-domain waveform inversion. We obtained inversion results of the frequency-filtered field data acquired in the Gulf of Mexico and two synthetic data sets obtained using a first-derivative Gaussian source wavelet and a single-frequency causal sine function. They demonstrated that Laplace-domain inversion yielded consistent results regardless of the frequency content within the seismic data.

Broadband seismic over/under sources and their designature-deghosting

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. P61-P73 ◽  
Author(s):  
Lasse Amundsen ◽  
Ørjan Pedersen ◽  
Are Osen ◽  
Johan O. A. Robertsson ◽  
Martin Landrø
Keyword(s):  
Seismic Data ◽  
High Frequency ◽  
Low Frequency ◽  
Point Sources ◽  
High Frequency Side ◽  
Frequency Content ◽  
Source Depth ◽  
Deep Sources ◽  
The Cost ◽  
High Frequency Content

The source depth influences the frequency band of seismic data. Due to the source ghost effect, it is advantageous to deploy sources deep to enhance the low-frequency content of seismic data. But, for a given source volume, the bubble period decreases with the source depth, thereby degrading the low-frequency content. At the same time, deep sources reduce the seismic bandwidth. Deploying sources at shallower depths has the opposite effects. A shallow source provides improved high-frequency content at the cost of degraded low-frequency content due to the ghosting effect, whereas the bubble period increases with a lesser source depth, thereby slightly improving the low-frequency content. A solution to the challenge of extending the bandwidth on the low- and high-frequency side is to deploy over/under sources, in which sources are towed at two depths. We have developed a mathematical ghost model for over/under point sources fired in sequential and simultaneous modes, and we have found an inverse model, which on common receiver gathers can jointly perform designature and deghosting of the over/under source measurements. We relate the model for simultaneous mode shooting to recent work on general multidepth level array sources, with previous known solutions. Two numerical examples related to over/under sequential shooting develop the main principles and the viability of the method.

scholarly journals Wiener estimation of the Green’s function

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. W31-W44 ◽  
Author(s):  
Anton Ziolkowski
Keyword(s):  
Green’S Function ◽  
Impulse Response ◽  
Green's Function ◽  
Seismic Data ◽  
Wiener Filter ◽  
Electromagnetic Data ◽  
Transient Electromagnetic ◽  
Marine Seismic ◽  
Measured Response

I consider the problem of finding the impulse response, or Green’s function, from a measured response including noise, given an estimate of the source time function. This process is usually known as signature deconvolution. Classical signature deconvolution provides no measure of the quality of the result and does not separate signal from noise. Recovery of the earth impulse response is here formulated as the calculation of a Wiener filter in which the estimated source signature is the input and the measured response is the desired output. Convolution of this filter with the estimated source signature is the part of the measured response that is correlated with the estimated signature. Subtraction of the correlated part from the measured response yields the estimated noise, or the uncorrelated part. The fraction of energy not contained in this uncorrelated component is defined as the quality of the filter. If the estimated source signature contains errors, the estimated earth impulse response is incomplete, and the estimated noise contains signal, recognizable as trace-to-trace correlation. The method can be applied to many types of geophysical data, including earthquake seismic data, exploration seismic data, and controlled source electromagnetic data; it is illustrated here with examples of marine seismic and marine transient electromagnetic data.

Lattice filtering applications to deconvolution of seismic data

Geophysics ◽  
1983 ◽  
Vol 48 (3) ◽  
pp. 295-310 ◽  
Author(s):  
John C. Robinson
Keyword(s):  
Seismic Data ◽  
Wiener Filter ◽  
Reflection Seismology ◽  
Significant Extent ◽  
Technical Literature ◽  
Lattice Filters ◽  
Effective Implementation ◽  
Deconvolution Technique ◽  
Potential Applications ◽  
Adaptive Abilities

Lattice digital filtering techniques have only recently been exposed to any significant extent through the technical literature, primarily in articles not directly related to reflection seismology. The most basic “all‐zero” lattice filter dates back only around a decade. This paper first reviews current technology in adaptive lattice filtering from the standpoint of seismic deconvolution. An “all‐pole” deconvolution technique is developed next; then a new “pole‐zero” lattice is adapted to seismic deconvolution, and operational methodologies for its effective implementation and stabilization are developed. Some advantages of deconvolution by lattice filtering and other potential applications of lattice filters to seismic data processing are suggested. The adaptive abilities and effectiveness of seismic deconvolution by the three lattice types are tested and compared with stationary Wiener deconvolution. The test data, are realistically nonstationary, thus allowing all three of the adaptive lattice filters to perform favorably in comparison to the nonadaptive or stationary Wiener filter.

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