Noise Reduction of Seismic Signal via Empirical Mode Decomposition

Abstract

This paper developed a denoising method termed f-x empirical-mode decomposition (EMD) predictive filtering. In this new method, we first applied EMD to each frequency slice in the f-x domain and obtained several intrinsic mode functions (IMFs). Then, an autoregressive model was applied to the sum of the first few IMFs to predict the useful steeper events. Finally, the predicted events were added to the sum of the remaining IMFs. This process improved the prediction precision by using an EMD-based dip filter to reduce the dip components before f-x predictive filtering. A synthetic data example is provided to show the performance of presented method. Introduction Random noise attenuation played an important role in seismic signal processing. Canales (1984) first uses f-x predictive filtering to attenuate random noise [1]. Since then, continuous efforts have been made to improve the predictive precision or to modify the conventional version to meet better the requirements set by various applications [2][3]. When the subsurface is extremely complex, f-x predictive filtering doesn’t yield good results because of the large number of dip components that need to be predicted. Huang et al. propose a new signal processing method that uses empirical mode decomposition (EMD) to prepare stable input for the Hilbert transform. The essence of EMD is to stabilize a nonstationary signal. That is, to decompose a signal into a series of intrinsic mode functions (IMFs) [4]. Each IMF has a relatively local constant frequency. The frequency of each IMF decreases according to the separation sequence of each IMF. EMD is a breakthrough in the analysis of linear and stable spectra. It adaptively separates nonlinear and nonstationary signals, which are features of seismic data, into different frequency ranges. Bekara and van der Baan apply f-x EMD to attenuation of random and coherent noise with good results [5]. For the purpose of random noise attenuation, the f-x domain EMD method can only be applied on NMO-corrected or poststack seismic data. With profiles containing dipping events, these methods will suppress some of the useful energy. In this paper, we present a new approach, termed f-x empirical mode decomposition predictive filtering (EMDPF) that combines f-x EMD and f-x predictive filtering. This new noise attenuation methodology can adapt to more complex seismic profiles than f-x EMD, and preserve more useful energy than f-x predictive filtering. The f-x EMDPF uses an EMD-based dip filter to reduce the dip components for the subsequent predictive filtering to improve the predictive precision. Predictive Filtering in Frequency-Space Domain Let s(t, h) (h=1,2,...,H) be the signal of trace and h and H be the number of traces. If the slope of a linear event with constant amplitude in a seismic section is λ, then ) 1 , ( ) 1 , ( x h t s h t s ∆ λ − = + , (1) where x ∆ denotes the trace interval. Eq. 1 an be transformed into the frequency domain to give x fh i e f s h f s ∆ λ π 2 ) 1 , ( ) 1 , ( − = + . (2) International Conference on Applied Science and Engineering Innovation (ASEI 2015) © 2015. The authors Published by Atlantis Press 16 For a specific frequency f0, from Eq. 2, we can obtain a linear recursion that is given by ) , ( ) 1 , ( ) 1 , ( 0 0 0 h f s f a h f s = + , (3) where x f i e f a ∆ λ π 0 2 0 ) 1 , ( − = . This recursion is a first order difference equation, also known as an autoregressive (AR) model of order 1. Similarly, superposition of p linear events in the t-x domain can be represented by an AR model of order p as the following equation: ) 1 , ( ) , ( ) 1 , ( ) 2 , ( ) , ( ) 1 , ( ) 1 , ( 0 0 0 0 0 0 0 p h f s p f a h f s f a h f s f a h f s − + + + − + = +  , (4) where ) , , 2 , 1 )( , ( 0 p h h f a  = denotes the predictive error filter, with a length of p. The prediction error energy ) ( 0 f E is given by the following equation: