Precise identification of onset time for an earthquake is imperative in the right figuring of earthquake's location and different parameters that are utilized for building seismic catalogues. P-wave arrival detection of weak events or micro-earthquakes cannot be precisely determined due to background noise. In this paper, we propose a novel approach based on Modified Laplacian of Gaussian (MLoG) filter to detect the onset time even in the presence of very weak signal-to-noise ratios (SNRs). The proposed algorithm utilizes a denoising-filter algorithm to smooth the background noise. In the proposed algorithm, we employ the MLoG mask to filter the seismic data. Afterward, we apply a Dual-threshold comparator to detect the onset time of the event. The results show that the proposed algorithm can detect the onset time for micro-earthquakes accurately, with SNR of −12 dB. The proposed algorithm achieves an onset time picking accuracy of 93% with a standard deviation error of 0.10 s for 407 field seismic waveforms. Also, we compare the results with short and long time average algorithm (STA/LTA) and the Akaike Information Criterion (AIC), and the proposed algorithm outperforms them.
% Tune sigma, and N according to the application you want to use.
% For smoothing the background noise in DOI:
% The optimum parameters are :
sigma = 2.5;
N = 10;
% Call MLOG and stores the cofficients in Gaussian_1D_2_Diff_Modified
% MLOG
% [Gaussian_1D_2_Diff_Modified]=MLOG(sigma,N);
% For More Scaling dividing by sigma.
Gaussian_1D_2_Diff_Modified\]=MLOG(sigma,N) /sigma;
% Filtering The Input (Denoising the Input Signal)
Output = filter (Gaussian_1D_2_Diff_Modified,1,x);
% Output Squaring
Output = Output.\^2;
% For more smoothing, average movabale window is obatined for m samples
% with k stride (moving by k samples)
% Adjustce m, and k according to the application you want to use.
Output_More_Smoothing = zeros(1,size(x,2));
m = 8;
k = 1;
count = 1;
for j=1:k:(length(Output))-max(\[m k\])
Output_More_Smoothing(count)=(mean(Output(j:j+m-1)));
count = count +1;
end
% Plotting
% Plotting the Cofficients of MLOG.
figure(1)
plot( (1:N), Gaussian_1D_2_Diff_Modified, 'LineWidth',3)
xlabel('Index (n)','FontSize',14,'FontWeight','bold')
ylabel('MLOG Mask Values','FontSize',14,'FontWeight','bold')
title('MLOG MASK','FontSize',14,'FontWeight','bold')
set(gca,'fontsize',12,'FontWeight','bold')
% Plotting Input, Output of MLOG, and Smoothed Output Signal.
figure(2)
subplot(3,1,1),plot(1:length(x),x)
xlabel('Sample Index','FontSize',14,'FontWeight','bold')
ylabel('Count','FontSize',14,'FontWeight','bold')
title('Input Seismic Event','FontSize',14,'FontWeight','bold')
set(gca,'fontsize',12,'FontWeight','bold')
subplot(3,1,2),plot(1:length(Output), Output)
xlabel('Sample Index','FontSize',14,'FontWeight','bold')
ylabel('Count\^2','FontSize',14,'FontWeight','bold')
title('Output Signal of MLOG Filter','FontSize',14,'FontWeight','bold')
set(gca,'fontsize',12,'FontWeight','bold')
subplot(3,1,3),plot(1:length(Output_More_Smoothing), Output_More_Smoothing)
xlabel('Sample Index','FontSize',14,'FontWeight','bold')
ylabel('Count\^2','FontSize',14,'FontWeight','bold')
title('Smoothed Output Signal','FontSize',14,'FontWeight','bold')
set(gca,'fontsize',12,'FontWeight','bold')
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