Two representations of the fan filter

Geophysics ◽  
1982 ◽  
Vol 47 (6) ◽  
pp. 957-959 ◽  
Author(s):  
Steve T. Hildebrand
Keyword(s):  
Seismic Data ◽  
Noise Suppression ◽  
Apparent Velocity ◽  
Two Dimensional ◽  
Velocity Filter ◽  
Slant Stacking

The fan filter is a two‐dimensional (2-D) velocity filter that removes low apparent velocity events from seismic data. The convolutional representation was derived by Embree et al (1963) and by Fail and Grau (1963). Treitel et al (1967) extended the representation to include a recursive realization. Its basic use includes migration dip suppression, multiple suppression, slant stacking, and noise suppression in stacking.

Coherent noise in marine seismic data

Geophysics ◽  
1983 ◽  
Vol 48 (7) ◽  
pp. 854-886 ◽  
Author(s):  
Ken Larner ◽  
Ron Chambers ◽  
Mai Yang ◽  
Walt Lynn ◽  
Willon Wai
Keyword(s):  
Seismic Data ◽  
Noise Suppression ◽  
Seismic Source ◽  
Coherent Noise ◽  
Critical Data ◽  
Predictive Deconvolution ◽  
Scattered Energy ◽  
Marine Seismic ◽  
The Many ◽  
Water Bottom

Despite significant advances in marine streamer design, seismic data are often plagued by coherent noise having approximately linear moveout across stacked sections. With an understanding of the characteristics that distinguish such noise from signal, we can decide which noise‐suppression techniques to use and at what stages to apply them in acquisition and processing. Three general mechanisms that might produce such noise patterns on stacked sections are examined: direct and trapped waves that propagate outward from the seismic source, cable motion caused by the tugging action of the boat and tail buoy, and scattered energy from irregularities in the water bottom and sub‐bottom. Depending upon the mechanism, entirely different noise patterns can be observed on shot profiles and common‐midpoint (CMP) gathers; these patterns can be diagnostic of the dominant mechanism in a given set of data. Field data from Canada and Alaska suggest that the dominant noise is from waves scattered within the shallow sub‐buttom. This type of noise, while not obvious on the shot records, is actually enhanced by CMP stacking. Moreover, this noise is not confined to marine data; it can be as strong as surface wave noise on stacked land seismic data as well. Of the many processing tools available, moveout filtering is best for suppressing the noise while preserving signal. Since the scattered noise does not exhibit a linear moveout pattern on CMP‐sorted gathers, moveout filtering must be applied either to traces within shot records and common‐receiver gathers or to stacked traces. Our data example demonstrates that although it is more costly, moveout filtering of the unstacked data is particularly effective because it conditions the data for the critical data‐dependent processing steps of predictive deconvolution and velocity analysis.

A STUDY OF TWO‐DIMENSIONAL HEAD WAVES IN FLUID AND SOLID SYSTEMS

Geophysics ◽  
1963 ◽  
Vol 28 (4) ◽  
pp. 563-581 ◽  
Author(s):  
John W. Dunkin
Keyword(s):  
Half Space ◽  
Vertical Displacement ◽  
Point Of View ◽  
Head Wave ◽  
Apparent Velocity ◽  
Two Dimensional ◽  
Multiple Reflections ◽  
Transient Wave ◽  
Line Load ◽  
Head Waves

The problem of transient wave propagation in a three‐layered, fluid or solid half‐plane is investigated with the point of view of determining the effect of refracting bed thickness on the character of the two‐dimensional head wave. The “ray‐theory” technique is used to obtain exact expressions for the vertical displacement at the surface caused by an impulsive line load. The impulsive solutions are convolved with a time function having the shape of one cycle of a sinusoid. The multiple reflections in the refracting bed are found to affect the head wave significantly. For thin refracting beds in the fluid half‐space the character of the head wave can be completely altered by the strong multiple reflections. In the solid half‐space the weaker multiple reflections affect both the rate of decay of the amplitude of the head wave with distance and the apparent velocity of the head wave by changing its shape. A comparison is made of the results for the solid half‐space with previously published results of model experiments.

Application of complex-trace analysis to seismic data for random-noise suppression and temporal resolution improvement

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. V79-V86 ◽  
Author(s):  
Hakan Karsli ◽  
Derman Dondurur ◽  
Günay Çifçi
Keyword(s):  
Seismic Data ◽  
Trace Analysis ◽  
Noise Suppression ◽  
Single Channel ◽  
Random Noise ◽  
Synthetic Data ◽  
Low Frequency ◽  
Bright Spot ◽  
Phase Information ◽  
Resolution Improvement

Time-dependent amplitude and phase information of stacked seismic data are processed independently using complex trace analysis in order to facilitate interpretation by improving resolution and decreasing random noise. We represent seismic traces using their envelopes and instantaneous phases obtained by the Hilbert transform. The proposed method reduces the amplitudes of the low-frequency components of the envelope, while preserving the phase information. Several tests are performed in order to investigate the behavior of the present method for resolution improvement and noise suppression. Applications on both 1D and 2D synthetic data show that the method is capable of reducing the amplitudes and temporal widths of the side lobes of the input wavelets, and hence, the spectral bandwidth of the input seismic data is enhanced, resulting in an improvement in the signal-to-noise ratio. The bright-spot anomalies observed on the stacked sections become clearer because the output seismic traces have a simplified appearance allowing an easier data interpretation. We recommend applying this simple signal processing for signal enhancement prior to interpretation, especially for single channel and low-fold seismic data.

Non-stationary predictive filtering for seismic random noise suppression - A tutorial

Geophysics ◽  
2021 ◽  
pp. 1-79 ◽  
Author(s):  
Hang Wang ◽  
Wei Chen ◽  
Weilin Huang ◽  
Shaohuan Zu ◽  
Xingye Liu ◽  
...  
Keyword(s):  
Seismic Data ◽  
Space Dimension ◽  
Noise Suppression ◽  
Random Noise ◽  
Spatial Dimension ◽  
Seismic Data Processing ◽  
Filtering Method ◽  
Time Space ◽  
Stationary Version ◽  
Predictive Filtering

Predictive filtering in the frequency domain is one of the most widely used denoising algorithms in the seismic data processing workflow. Predictive filtering is based on the assumption of linear/planar events in the time-space domain. In traditional predictive filtering method, the predictive filter is fixed across the spatial dimension, which cannot deal with the spatial variation of seismic data well. To handle the curving events, the predictive filter is either applied in local windows or extended to a non-stationary version. The regularized non-stationary autoregression (RNAR) method can be treated as a non-stationary extension of the traditional predictive filtering, where the predictive filter coefficients are variable in different space locations. The highly under-determined inverse problem is solved by shaping regularization with a smoothness constraint in space. We further extend the RNAR method to a more general case, where we can apply more constraints to the filter coefficients according to the features of seismic data. First, apart from the smoothness in space, we also apply a smoothing constraint in frequency, considering the coherency of the coefficients in the frequency dimension. Secondly, we apply a frequency dependent smoothing radius along the space dimension to better take advantage of the non-stationarity of seismic data in the frequency axis, and to better deal with noise. The proposed method is validated via several synthetic and field data examples.

Desert low-frequency noise suppression by using adaptive DnCNNs based on the determination of high-order statistic

2019 ◽  
Vol 219 (2) ◽  
pp. 1281-1299 ◽  
Author(s):  
X T Dong ◽  
Y Li ◽  
B J Yang
Keyword(s):  
Order Statistic ◽  
Seismic Data ◽  
Noise Suppression ◽  
Random Noise ◽  
Low Frequency ◽  
High Order ◽  
Frequency Noise ◽  
Low Frequency Noise ◽  
High Order Statistic ◽  
Adaptive Noise

SUMMARY The importance of low-frequency seismic data has been already recognized by geophysicists. However, there are still a number of obstacles that must be overcome for events recovery and noise suppression in low-frequency seismic data. The most difficult one is how to increase the signal-to-noise ratio (SNR) at low frequencies. Desert seismic data are a kind of typical low-frequency seismic data. In desert seismic data, the energy of low-frequency noise (including surface wave and random noise) is strong, which largely reduces the SNR of desert seismic data. Moreover, the low-frequency noise is non-stationary and non-Gaussian. In addition, compared with seismic data in other regions, the spectrum overlaps between effective signals and noise is more serious in desert seismic data. These all bring enormous difficulties to the denoising of desert seismic data and subsequent exploration work including geological structure interpretation and forecast of reservoir fluid. In order to solve this technological issue, feed-forward denoising convolutional neural networks (DnCNNs) are introduced into desert seismic data denoising. The local perception and weight sharing of DnCNNs make it very suitable for signal processing. However, this network is initially used to suppress Gaussian white noise in noisy image. For the sake of making DnCNNs suitable for desert seismic data denoising, comprehensive corrections including network parameter optimization and adaptive noise set construction are made to DnCNNs. On the one hand, through the optimization of denoising parameters, the most suitable network parameters (convolution kernel、patch size and network depth) for desert seismic denoising are selected; on the other hand, based on the judgement of high-order statistic, the low-frequency noise of processed desert seismic data is used to construct the adaptive noise set, so as to achieve the adaptive and automatic noise reduction. Several synthetic and actual data examples with different levels of noise demonstrate the effectiveness and robustness of the adaptive DnCNNs in suppressing low-frequency noise and preserving effective signals.

Noise suppression in 2D and 3D seismic data with data-driven sifting algorithms

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. V1-V10
Author(s):  
Julián L. Gómez ◽  
Danilo R. Velis ◽  
Juan I. Sabbione
Keyword(s):  
Seismic Data ◽  
Noise Suppression ◽  
Department Of Energy ◽  
Time Slice ◽  
3D Seismic ◽  
Coherent Noise ◽  
Data Set ◽  
Amplitude Data ◽  
3D Volume ◽  
2D And 3D

We have developed an empirical-mode decomposition (EMD) algorithm for effective suppression of random and coherent noise in 2D and 3D seismic amplitude data. Unlike other EMD-based methods for seismic data processing, our approach does not involve the time direction in the computation of the signal envelopes needed for the iterative sifting process. Instead, we apply the sifting algorithm spatially in the inline-crossline plane. At each time slice, we calculate the upper and lower signal envelopes by means of a filter whose length is adapted dynamically at each sifting iteration according to the spatial distribution of the extrema. The denoising of a 3D volume is achieved by removing the most oscillating modes of each time slice from the noisy data. We determine the performance of the algorithm by using three public-domain poststack field data sets: one 2D line of the well-known Alaska 2D data set, available from the US Geological Survey; a subset of the Penobscot 3D volume acquired offshore by the Nova Scotia Department of Energy, Canada; and a subset of the Stratton 3D land data from South Texas, available from the Bureau of Economic Geology at the University of Texas at Austin. The results indicate that random and coherent noise, such as footprint signatures, can be mitigated satisfactorily, enhancing the reflectors with negligible signal leakage in most cases. Our method, called empirical-mode filtering (EMF), yields improved results compared to other 2D and 3D techniques, such as [Formula: see text] EMD filter, [Formula: see text] deconvolution, and [Formula: see text]-[Formula: see text]-[Formula: see text] adaptive prediction filtering. EMF exploits the flexibility of EMD on seismic data and is presented as an efficient and easy-to-apply alternative for denoising seismic data with mild to moderate structural complexity.

Physical Wavelet Frame Denoising

Geophysics ◽  
2003 ◽  
Vol 68 (1) ◽  
pp. 225-231 ◽  
Author(s):  
Rongfeng Zhang ◽  
Tadeusz J. Ulrych
Keyword(s):  
Seismic Data ◽  
Noise Suppression ◽  
Real Data ◽  
Wavelet Denoising ◽  
Seismic Signals ◽  
Wavelet Frame ◽  
New Approach ◽  
Design And Implementation ◽  
Ground Roll ◽  
Acoustic Processing

This paper deals with the design and implementation of a new wavelet frame for noise suppression based on the character of seismic data. In general, wavelet denoising methods widely used in image and acoustic processing use well‐known conventional wavelets which, although versatile, are often not optimal for seismic data. The new approach, physical wavelet frame denoising uses a wavelet frame that takes into account the characteristics of seismic data both in time and space. Synthetic and real data tests show that the approach is effective even for seismic signals contaminated by strong noise which may be random or coherent, such as ground roll or air waves.

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