AI Coherent Noise Attenuation in Seismic Signal Processing
Noise attenuation is a fundamental step in seismic signal processing that aims to reduce or eliminate unwanted noise from seismic data, thereby enhancing the quality and interpretability of the seismic images. Seismic data often contain various types of noise, such as environmental noise, instrumental noise, and coherent noise (e.g., multiples and surface waves), which can obscure the true geological signals. Effective noise attenuation techniques are essential to distinguish between noise and useful seismic reflections, leading to more accurate subsurface imaging.
Several methods are employed for noise attenuation in seismic data processing. Common techniques include band-pass filtering, which removes frequencies outside the range of interest; adaptive filtering, which dynamically adjusts to the characteristics of the noise; and de-noising algorithms, which specifically target and reduce random noise. Other advanced methods like wavelet transforms and multi-channel filtering can isolate and suppress coherent noise patterns such as multiples and ground roll. By applying these noise attenuation techniques, geoscientists can significantly improve the signal-to-noise ratio of seismic data, resulting in clearer and more reliable images of the Earth's subsurface. This improved data quality is crucial for accurate interpretation and decision-making in oil and gas exploration, earthquake seismology, and other geophysical applications.
Signal Based Noise Attenuation Methods
Band Pass Filtering
Band pas filtering is the simplest method of removing the noise by limiting the frequency range of data. But, both of signal and noise will be attenuated by applying bandpass filtering.
FK Filtering
FK filtering suppresses the coherent noise by applying the 2D Fourier transform. procedure of work is simplified as:
- Takes a 2D seismic matrix as input and returns a denoised 2D matrix.
- Applies 2D FFT (Fast Fourier Transform) to convert data into F-K domain.
- Designs and applies a filter mask to attenuate unwanted coherent noise.
- Uses inverse FFT to reconstruct denoised seismic data.
- Easily adjustable for different types of noise filtering (e.g., notch filters, high-pass, low-pass).
Band Pass Filtering
FK Filtering
KL Filtering
K-L transform makes a principal component analysis which is indeed a mathematical way to determine if a linear transformation of a sample of points in an L-dimensional space exhibits the properties of the sample most clearly along the coordinate axes. Along the new axes, the sample variance is extreme and uncorrelated. Using a cutoff on the spread along each axis, a sample may be reduced in its dimensionality. This way, it can be used to transform independent coordinates into significant and independent ones.
EFFECTIVE PARAMETERS:
1. Noise contaminated region: This region is selected by the user after the data is plotted. As a result, it can differ based on the user judgment.
2. The number of representatives selected eigen images (Ne): The number of eigen images to be eliminated depends on the eigenvalue diagram of data. However, since it is entered by the user, it is somehow dependent on user’s choice.
3. Difference between ground roll and reflectors energies: The K-L transform decomposes the signal and noise into different eigen images based on their energy contents; therefore, the more is the difference between the energies, the better is the separation of signal and noise.
4. Ground roll amplitude change with offset: The ground roll amplitude becomes usually weaker with increasing the offset. As a consequence, there is less energy at far offsets which can result in the presence of ground roll energy at later eigenvalues. Elimination of the corresponding eigenimages suppresses the reflections; therefore, it should be decided whether the ground roll is suppressed or the reflections are preserved.
Wavelet Based NOISE ATTENUATION METHODS
Wavelet Decomposition
The analysis of seismic traces using a wavelet transform decomposes each trace into a set of time-scale wavelet coefficients. The scale can be considered as a frequency range, which can then be analyzed and filtered. The ground roll energy that contaminates the traces in a time limited fashion is represented in higher scales. As a result, a wavelet transform provides a basis for the ground roll and reflection separation suitable for filtering purposes. Moreover, these filters only affect those coefficients that are in the region and contaminated by the ground roll, leaving the other parts of data unaltered.
EFFECTIVE PARAMETERS
1. Mother wavelet (W): Depending on the application of a wavelet transform, different wavelets can be used. However, for the purpose of a signal processing, the Daubechies wavelets and symlets have better results.
2. Decomposition level (Dl): Considering that the number of samples is halved at each level of decomposition, the maximum decomposition level is determined based on the number of the input data samples. The decomposition level can be between 1 and this maximum.
3. Frequency of noise corresponding to scales (Fgr): Each scale represents a certain frequency band. Here, the purpose of WT is to attenuate the ground roll. Therefore, usually the scale corresponding to frequencies lower than 18 is a suitable choice.
4. Noise contaminated region determination (Vgr): The noise contaminated region is determined based on the maximum velocity of the ground roll, time sampling interval, and the receiver stations offset. The filter is only applied to this part of data leaving the other parts unchanged.
5. Time and frequency difference between signal and noise: The WT transforms data from a time domain into a time-scale domain. The more different is the time and the frequency content of the signal and the noise, the better is the filter performance.
Radial BaSED NOISE ATTENUATION METHODS
Radial Trace Filtering
RT transform maps the wave-field amplitudes to coordinates of apparent velocity and travel time. The common shape of an RT path is a fan which can wrap the extended range of velocities in a time-offset domain. This method has the following framework. It uses a combination of noise characteristics such as frequency content and its apparent velocity for attenuation. The RT transform has one main characteristic. It moves the frequency content of the event along the radial path to the low frequency and does not change the frequency content of an event perpendicular to the radial path. Thus, in suppressing the unwanted linear events along the radial paths, using the frequency filtering will be more effective. A general strategy for using this filter involves the following approach. First, the data are transformed to a new domain along the radial paths where the linear components may be stretched. Then, the frequency filtering can be used to filter the undesired components. The data are mapped back into the original domain retaining only the desired information.
The data in an RT domain is a set of traces equal to the number of the radial paths whose samples are amplitudes corresponding to an interpolation of two adjacent sample amplitudes. The RT is a transformation from a time-offset grid to a time-apparent velocity grid. Interpolation is a method used to obtain the RT sample values because the coordinate grids between two domains do not coincide. EFFECTIVE PARAMETERS:
Like the entire seismic processing step, the selection of appropriate values in the parameter setting step of filtering by an RT transform is important to obtain optimum results in a minimum time. The parameters for this filter are:
1. Minimum velocity: The user has to enter the minimum apparent velocity value. An interpolation of the amplitudes along the minimum velocity radial path will be the first trace in an RT domain. To retain the signal using a band-pass filter in an RT domain, this should be equal to the lowest possible velocity (e.g. 1 m/s). To model the ground roll using a low-pass filter in an RT domain, this value should be less than the lowest ground roll velocity.
2. Maximum velocity (Vmax): The user has to enter the maximum velocity value of interest. The amplitudes along the radial path with a maximum velocity will be the last trace in RT domain. To retain the signal this value should be more than the linear velocity of a shallow reflector hyperbola in a far offset. To model the ground roll, this value could be slightly more than the highest ground roll velocity.
Note: The data between the maximum- and the minimum-velocity paths will be preserved in the RT transform. Take care of losing data in the selection of the minimum and maximum velocities in the case of a band-pass filtering approach in an RT domain!
3. Velocity increment (Vinc): The user should enter the appropriate value for the interval of the radial paths. To avoid the spatial aliasing and increasing the effectiveness of the filter, the interval of the radial path should be decreased. Also, the selection of very small velocity increment would make the data too large to be filtered in an optimum time. Therefore, a proper selection is important. The default value is the 1 m/s.
4. Frequency filtering parameters (Flow, Fhigh): The frequency filtering is divided into two types: using a band-pass filter which will filter the stretched events (such as ground roll) and using a low-pass filter which will retain the stretched events.
Selection of proper frequency values for low_cut- low_pass- high_pass- high_cut in the case of a band-pass filter and high_pass- high_cut in the case of a low-pass filter is important. Study of an amplitude spectrum of RT traces will be helpful in the selection of an appropriate frequency.