English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

With the goal to improve the signal/noise ratio and obtain great information to the reservoir characterization, the decomposition called Singular Spectrum Analysis (SSA) and the other one named as Frequency-timing has shown to be very useful to create images with high quality resolution. To decompose into singular values, it works with a single trace named by Porsani et al. (2017) as filtering with iteractive resource Singular Spectrum Analysis (RI-SSA), which allows to obtain a timing correlation of the events, producing images without the unwelcome noising. Afterwards, the chosen method to decompose was the frequency-timing suggested by Zoukaneri and Porsani (2015) who called it Wigner-Ville Maximum Entropy Method (ME-MAM), which involves the maximum entrophy concept from Burg to get a high resolution power spectrum. Introduction Coherent noise attenuation is an important issue in seismic data processing. Several filtering methods has been developed over the years and most of them use a multichannel approach, often leading to poor results due to spatial aliasing. To overcome this, we used the so-called Iteractive Recursive Singular Spectrum Analysis (RI-SSA) introduced by Porsani et al. (2017) to decompose each trace in a shot gather using only the time correlation of the events within it (Silva, 2015). The RI-SSA method was able to separate the signal components more consistently when compared to the well-known Singular Spectrum Analysis (SSA), since the latter mixes the high and low frequency components (Harris and Yuan, 2010). To generate the seismic attributes (Taner et al., 1994) on the RI-SSA filtered stacked section we use the maximum entropy method (Burg, 1967) to estimate a high resolution spectrum, avoiding the crossed terms. This method, called the Maximum Entropy of Wigner-Ville method (MEMWV) by Zoukaneri and Porsani (2015), is based on the estimation of a linear prediction operator and on the estimation and extension of the autocorrelation function. After calculating the autocorrelation coefficients, one can generate the Kernel terms of the Wigner-Ville Maximum Entropy, which generate the maximum entropy spectrum when applied to the Fourier transform. Theory Singular Spectrum Analysis (SSA) In SSA, we first create a Toeplitz matrix D using the operator J{.}, which is applied to the each trace d = [d(1), ...,d(M)]T, as in eq. 1. D is often called the trajectory matrix (Harris and Yuan, 2010). J{d}= D =  d(1) 0 · · · 0N .. d(1) . . . .. d(M) .. . . . 0 0 d(M) .. d(1) .. .. . . . 0M+N−1 0 · · · d(M)  (1) Then we calculate the singular value decomposition of D, given by D = UΣVT = N ∑ i=1 σiuivi = N ∑ i=1 D̃i, (2) where U = [u1 . . . uN] is a (M+N−1)× (M+N−1) matrix containing the left singular vectors, V = [v1 . . . vN] is a N × N matrix with the right singular vectors and Σ = diag(σ1 σ2 . . . σN) is a matrix of the singular values, where σ1 ≥ σ2 ≥ ·· · ≥ σN ≥ 0 (Golub and Van Loan, 2012). The matrix D could be seen as a sum of unitary matrices (uivi ) weighted by the respective singular values, named as eigenimages (Freire, 1986). The seismic trace can be reconstructed applying the inverse operator J−1 {.} in D̃. This inverse operator (eq. 3) includes the displacement adjustement and trace average. d = N ∑ i=1 d̃i = N ∑ i=1 J−1 { D̃i } (3) In order to validate the decomposition, a synthetic trace (Tary et al., 2014) with five components was used. It consists of two harmonic signals of 15 Hz and 35 Hz (s1 and s2), a harmonic signal modulated by frequency around 65 Hz (s3), a sweep between 15 Hz and 158 Hz (s4), and a Morlet wavelet with center frequency 113 Hz (s5). The related equations can be seen in Figure 1. Note that the trace is the sum of the five components. Using the algorithm 1, it was possible to decompose the synthetic signal into 15 components (Figure 2), and combine them to generate similar components Figure 3, in order to restore the components that generated the synthetic trace (Figure 1). Sixteenth International Congress of The Brazilian Geophysical Society COHERENT NOISE FILTERING USING THE RI-SSA ALGORITHM 2 0 2 4 6 8 10 Time (s) s1(t) = 0.8 cos(30πt) s2(t) = 0.6 cos(70πt) s3(t) = 0.7 cos(130πt + 5 sin(2πt)) s4 = sin ( 8π100 log(100) ) s5 = 3e−1250(t−2) 2 cos(710(t − 2)) Synthetic data = ∑5 j=1 sj(t) Figure 1: The five components s1(t), s2(t), s3(t), s4(t), s5(t) and the resulting synthetic signal. Algorithm 1: SSA Generate the matrix of the displaced data, with the J, D operator Calculate the first eigenvalues and eigenvectors Calculate the first eigenimage Generate the filtered trace using the J inverse operator Recursivo Iterativo Singular Spectrum Analysis (RI-SSA) Figure 11 shows the result of the SSA; note that it is not possible to properly separate the high and low energies using this technique, leaving a considerable part of the ground roll behind. Thus, to overcome this limitation, Porsani et al. (2018) added to the SSA method the recursion and iteration to properly decode and separate a signal into high and low energy components using three loops. In the internal loop, the high energy component of the signal is calculated by recursion in the number of rows in the trajectory matrix, using only the first eigenvalues and eigenvectors, which correspond to the highest energy component. The result is subtracted from the input signal in the second loop and the process is repeated. This provides an estimate of the low-energy part of the signal. In the external loop, this low energy signal is subtracted from the input signal and the result is output as a signal component. The entire procedure is then repeated with the low energy component as the new input signal. The procedure starts with the search for input data and is repeated until the K signal components have been estimated. Algorithm 2 illustrates this procedute: 0 2 4 6 8 10 Time (s) Component 1 Component 10 Component 11 Component 12 Component 13 Component 14 Component 15 Error Restored signal Original signal Figure 2: Decomposition of the synthetic signal (Figure 1) using the SSA algorithm 0 2 4 6 8 10 Time(s) Components: 1-2 Components: 3-6 Components 7-12 Components 13-15 Error Restored signal Figure 3: Sum of similar components of Figure 2 Figure 4 shows the result of the synthetic trace decomposition (Figure 1) using the RI-SSA algorithm; note that it was possible to accurately separate the low and high frequency components, which means this method is better Sixteenth International Congress of The Brazilian Geophysical Society BATISTA, PORSANI 3 Algorithm 2: RI-SSA d̂0 = d DO k = 1,...,K (Loop components) N = max{1,K− k+1} d̂0 = dk DO j = 1,..., J (Iterative loop) d̃0 = d̂ 0 j−1 DO τ = 1, ...,N (Recursive loop) • Creats Matrix Dτ from d̃τ−1 • Calculates uτ ,vτ ,στ • Computes and updates d̃τ−1 END DO d̂ j = d̂ j−1− d̃N (Update d̂ j ) END DO Output x̂k = dk− d̂ j Components dk+1− d̂ j END DO The signal decomposition is: d = ∑k=1 xk + d̂ j

Filtering and Obtaining Attributes in Seismic Data Using the SSA Method