Noncausal spatial prediction filtering for random noise reduction on 3-D poststack data

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1641-1653 ◽  
Author(s):  
Necati Gülünay
Keyword(s):  
Noise Reduction ◽  
Spectral Properties ◽  
Temporal Frequency ◽  
Random Noise ◽  
Spatial Prediction ◽  
Noise Attenuation ◽  
Ratio Data ◽  
Spatial Dimensions ◽  
Prediction Filter ◽  
Better Than

A common practice in random noise reduction for 2-D data is to use pseudononcausal (PNC) 1-D prediction filters at each temporal frequency. A 1-D PNC filter is a filter that is forced to be two sided by placing a conjugate‐reversed version of a 1-D causal filter in front of itself with a zero between the two. For 3-D data, a similar practice is to solve for two 2-D (causal) one‐quadrant filters at each frequency slice. A 2-D PNC filter is formed by putting a conjugate flipped version of each quadrant filter in a quadrant opposite itself. The center sample of a 2-D PNC filter is zero. This paper suggests the use of 1-D and 2-D noncausal (NC) prediction filters instead of PNC filters for random noise attenuation, where an NC filter is a two‐sided filter solved from one set of normal equations. The number of negative and positive lags in the NC filter is the same. The center sample of the filter is zero. The NC prediction filters are more center loaded than PNC filters. They are conjugate symmetric as PNC filters. Also, NC filters are less sensitive than PNC filters to the size of the gate used in their derivation. They can handle amplitude variations along dip directions better than PNC filters. While a PNC prediction filter suppresses more random noise, it damages more signal. On the other hand, NC prediction filters preserve more of the signal and reject less noise for the same total filter length. For high S/N ratio data, a 2-D NC prediction filter preserves geologic features that do not vary in one of the spatial dimensions. In‐line and cross‐line vertical faults are also well preserved with such filters. When faults are obliquely oriented, the filter coefficients adapt to the fault. Spectral properties of PNC and NC filters are very similar.

Adaptive prediction filtering in t-x-y domain for random noise attenuation using regularized nonstationary autoregression

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. V13-V21 ◽  
Author(s):  
Yang Liu ◽  
Ning Liu ◽  
Cai Liu
Keyword(s):  
Dimensional Space ◽  
Random Noise ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Noise Attenuation ◽  
Random Noise Attenuation ◽  
Frequency Space ◽  
Adaptive Prediction ◽  
Time Space ◽  
Prediction Filter

Many natural phenomena, including geologic events and geophysical data, are fundamentally nonstationary. They may exhibit stationarity on a short timescale but eventually alter their behavior in time and space. We developed a 2D [Formula: see text] adaptive prediction filter (APF) and further extended this to a 3D [Formula: see text] version for random noise attenuation based on regularized nonstationary autoregression (RNA). Instead of patching, a popular method for handling nonstationarity, we obtained smoothly nonstationary APF coefficients by solving a global regularized least-squares problem. We used shaping regularization to control the smoothness of the coefficients of APF. Three-dimensional space-noncausal [Formula: see text] APF uses neighboring traces around the target traces in the 3D seismic cube to predict noise-free signal, so it provided more accurate prediction results than the 2D version. In comparison with other denoising methods, such as frequency-space deconvolution, time-space prediction filter, and frequency-space RNA, we tested the feasibility of our method in reducing seismic random noise on three synthetic data sets. Results of applying the proposed method to seismic field data demonstrated that nonstationary [Formula: see text] APF was effective in practice.

Lateral prediction for noise attenuation by t-x and f-x techniques

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1887-1896 ◽  
Author(s):  
Ray Abma ◽  
Jon Claerbout
Keyword(s):  
Random Noise ◽  
High Amplitude ◽  
Noise Attenuation ◽  
Space Domain ◽  
Frequency Space ◽  
Amplitude Noise ◽  
Time Space ◽  
Domain Prediction ◽  
Prediction Techniques ◽  
Prediction Filter

Attenuating random noise with a prediction filter in the time‐space domain generally produces results similar to those of predictions done in the frequency‐space domain. However, in the presence of moderate‐ to high‐amplitude noise, time‐space or t-x prediction passes less random noise than does frequency‐space, or f-x prediction. The f-x prediction may also produce false events in the presence of parallel events where t-x prediction does not. These advantages of t-x prediction are the result of its ability to control the length of the prediction filter in time. An f-x prediction produces an effective t-x domain filter that is as long in time as the input data. Gulunay’s f-x domain prediction tends to bias the predictions toward the traces nearest the output trace, allowing somewhat more noise to be passed, but this bias may be overcome by modifying the system of equations used to calculate the filter. The 3-D extension to the 2-D t-x and f-x prediction techniques allows improved noise attenuation because more samples are used in the predictions, and the requirement that events be strictly linear is relaxed.

Multicomponent f-x seismic random noise attenuation via vector autoregressive operators

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. V91-V99 ◽  
Author(s):  
Mostafa Naghizadeh ◽  
Mauricio Sacchi
Keyword(s):  
Temporal Frequency ◽  
Random Noise ◽  
Real Data ◽  
Var Model ◽  
Model Parameters ◽  
Prediction Errors ◽  
Noise Attenuation ◽  
Vector Autoregressive ◽  
Random Noise Attenuation ◽  
Frequency Space

We propose an extension of the traditional frequency-space ([Formula: see text]) random noise attenuation method to three-component seismic records. For this purpose, we develop a three-component vector autoregressive (VAR) model in the [Formula: see text] domain that is applied to the multicomponent spatial samples of each individual temporal frequency. VAR model parameters are estimated using the least-squares minimization of forward and backward prediction errors. VAR modeling effectively identifies the potential coherencies between various components of a multicomponent signal. We use the squared coherence spectrum of VAR models as an indicator to determine these coherencies. Synthetic and real data examples are provided to show the effectiveness of the proposed method.

Seismic trace interpolation in the F-X domain

Geophysics ◽  
1991 ◽  
Vol 56 (6) ◽  
pp. 785-794 ◽  
Author(s):  
S. Spitz
Keyword(s):  
Interpolation Method ◽  
Random Noise ◽  
A Priori ◽  
Effective Means ◽  
Linear Equations ◽  
Real Data ◽  
Spatial Prediction ◽  
Data Set ◽  
Spatial Interval ◽  
Prediction Filter

Interpolation of seismic traces is an effective means of improving migration when the data set exhibits spatial aliasing. A major difficulty of standard interpolation methods is that they depend on the degree of reliability with which the various geological events can be separated. In this respect, a multichannel interpolation method is described which requires neither a priori knowledge of the directions of lateral coherence of the events, nor estimation of these directions. The method is based on the fact that linear events present in a section made of equally spaced traces may be interpolated exactly, regardless of the original spatial interval, without any attempt to determine their true dips. The predictability of linear events in the f-x domain allows the missing traces to be expressed as the output of a linear system, the input of which consists of the recorded traces. The interpolation operator is obtained by solving a set of linear equations whose coefficients depend only on the spectrum of the spatial prediction filter defined by the recorded traces. Synthetic examples show that this method is insensitive to random noise and that it correctly handles curvatures and lateral amplitude variations. Assessment of the method with a real data set shows that the interpolation yields an improved migrated section.

Deep learning for denoising

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. V333-V350 ◽  
Author(s):  
Siwei Yu ◽  
Jianwei Ma ◽  
Wenlong Wang
Keyword(s):  
Neural Network ◽  
Deep Learning ◽  
Graphics Processing Unit ◽  
Random Noise ◽  
Stochastic Gradient Descent ◽  
Processing Unit ◽  
Noise Attenuation ◽  
Optimal Parameters ◽  
Training Set ◽  
Unknown Variance

Compared with traditional seismic noise attenuation algorithms that depend on signal models and their corresponding prior assumptions, removing noise with a deep neural network is trained based on a large training set in which the inputs are the raw data sets and the corresponding outputs are the desired clean data. After the completion of training, the deep-learning (DL) method achieves adaptive denoising with no requirements of (1) accurate modelings of the signal and noise or (2) optimal parameters tuning. We call this intelligent denoising. We have used a convolutional neural network (CNN) as the basic tool for DL. In random and linear noise attenuation, the training set is generated with artificially added noise. In the multiple attenuation step, the training set is generated with the acoustic wave equation. The stochastic gradient descent is used to solve the optimal parameters for the CNN. The runtime of DL on a graphics processing unit for denoising has the same order as the [Formula: see text]-[Formula: see text] deconvolution method. Synthetic and field results indicate the potential applications of DL in automatic attenuation of random noise (with unknown variance), linear noise, and multiples.

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