Karhunen Loeve Transform with adaptive dictionary learning for coherent and random noise attenuation in seismic data
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Indian Academy of Sciences Sadhana(0123456789().,-volV)FT3 ](0123456789().,-volV)
Karhunen Loeve Transform with adaptive dictionary learning for coherent and random noise attenuation in seismic data RAMYA JAYAKUMAR1,*
and SOMASUNDARESWARI DHANDAPANI2
1
Department of ECE, Hindusthan College of Engineering and Technology, Coimbatore, India Department of EEE, Adithya Institute of Technology, Coimbatore, India e-mail: [email protected]
2
MS received 6 June 2018; revised 23 July 2020; accepted 16 September 2020 Abstract. Seismic reflection data are used by geologists to identify the best site for oil and gas explorations. The raw seismic image cannot be directly used for explorations because the noises may hinder the primary reflections and result in misinterpretations. In the proposed research work, the denoising method with adaptive dictionary learning is attempted to attenuate the coherent and random noises which affect the seismic reflections. In this method, Karhunen Loeve Transform (KLT) is combined with K-means Singular Value Decomposition (KSVD) to improve the Signal to Noise Ratio (SNR) of the seismic data. The combination of fixed transform using KLT and learning-based dictionary using KSVD remove the redundant data while retaining the necessary data for further interpretations. KLT is applied on the whole seismic image to decorrelate the coefficients and retain the primary reflections. The horizontal events in the seismic image are preserved as they represent the eigen images with large energy. The KSVD is applied to the KLT resultant data, which denoises the patch of data while simultaneously updating the dictionary. The noise is eliminated using local sparsity of the image where mutually overlapping small image blocks are learned to yield the self-adaptive redundant dictionary. It is then used to obtain the sparse representation of the image blocks by eliminating noise. The algorithm is tested for both synthetic and field seismic images, and the results indicate a better reduction of random and coherent noise with the acceptable execution time compared to other denoising algorithms used. The KLT combined with KSVD method decorrelate the seismic data from noise by preserving the primary reflections and discarding the redundant noise. Keywords.
Seismic data; denoising; Karhunen Loeve Transform; K-means Singular Value; Decomposition.
1. Introduction Extraction of nonrenewable resources from the earth by exploration and production companies involves several stages. The reflection method is one of the most successful seismic methods for identifying the reservoirs favorable to the accumulation of oil and gas. The seismic data contains information on seismic source, its signal propagation path and presence of noise at the recording site. Since the waves are propagating through the earth’s sub layers, there might be the possibility for geometrically distorted data and the subsequent noise generation which may corrupt the seismic data. Many a times the primary reflections are not recognized due to th
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