Seismic data denoising through multiscale and sparsity-promoting dictionary learning

What is it about?

Seismic methods are widely used to explore the Earth’s subsurface in order to measure the underground rock properties. However, the acquired seismic data are usually corrupted by noise and/or partially muted by missing (lost) traces due to device malfunctions or other constraints. In this work, we developed a new method to enhance the corrupted seismic signals by removing the noise and interpolating the missing traces. We develop a new seismic denoising and interpolation algorithm to enhance the seismic signals based on a machine learning approach called dictionary learning. We take a bunch of patches from the corrupted seismic data as a training set and then establish a multivariate least square objective function with sparsity constraints for dictionary learning as well as data enhancement. By minimizing this objective function iteratively, we can train a set of signal atoms called dictionary to represent the seismic data patches with the correspondingly calculated sparse coefficients. After the objective function does not further reduce its value, a dictionary that captures the intrinsic structure of the seismic data on both time and space domains has been obtained, and meanwhile, the data enhancement has been accomplished by recovering data patches from their sparse coefficients with the help of the learned dictionary and then tiling all the enhanced data patches in an overlapping manner. There are some other seismic data enhancement methods using traditional sparse transform methods. These methods use predefined models and hence lack the adaptability of varying data structures. Unlike these methods, our method is a data-driven machine learning approach that exploits the underlying sparse structure of the input training data. Previously, such a machine learning approach has to trade the computational complexity for data representation flexibility. In our method, we further define the dictionary as a multiplication of a model-based base dictionary (such as a multi-scale transform like the wavelet transform) and an adaptive but sparse matrix. This approach, called “double-sparsity dictionary learning”, further reduces the number of dictionary parameters required for learning in order to strike a good balance among complexity, flexibility and performance. Experiment results on the test seismic data indicate that our method has achieved the best data enhancement performance comparing to the other traditional methods.

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Why is it important?

Seismic method is used to explore the properties of the Earth’s subsurface before actual drilling commences. Therefore, it is an important task and has been widely used by oil/gas and energy companies to estimate the potential production of a hydrocarbon/coal/mineral reservoir. It is also used to understand geology for engineering and environmental surveys. However, the quality of acquired seismic data is poor due to the noise and missing (lost) traces and this may negatively affect the analysis and interpretation process. We develop a novel and efficient transform method based on the machine learning approach to capture the most useful information of the seismic data within a sparse set of coefficients and use them for data enhancement. Such a technique is particularly useful in the signal processing area as it compresses the large amount of data to a very small set. Not only our research has practical values in seismic data processing for oil/gas and energy industry, it is also beneficial to other signal processing areas such as the enhancement and compression of image and video, computer vision, exploration geophysics, remote sensing, audio analysis, document analysis, etc., as long as a field that involves useful data mixed with useless noise. This method has led to further endeavors in these areas.