本源码研究波动传播的鲁棒去卷积功能。
A robust deconvolution function to study wave propagation.
通过低通滤波和重采样到更高的采样率能够实现去噪，并提高峰值捕获的性能。
Low pass filtering and resampling the input signals to higher sampling rates may help to eliminate noise and improve pick peaking.
本源码中包含了一个具体的演示样例。
function[T,S]=deconvolution(uz1,uz2)
% DECONVOLUTION OF TWO DISCRETE TIME SIGNALS IN FREQUENCY DOMAIN
%
% Deconvolution of two signals is defined in the frequency domain as
%
% S(w,z) = u(z1,w)/u(z2,w)
%
% where u(z1,w) and u(z2,w) are the Fourier spectra of the signal
% recorded at z1 and z2, respectively.
%
% The above equation may become ill-conditioned when the denominator
% approaches zero due to data corrupted by noise. In order to eliminate
% the instability, a regularized format following the Tikhonov
% deconvolution S_e(w) is used (Tikhonov and Arsenin, 1977; Petrovic and
% Parolai, 2016; Wen and Kalkan, 2017):
%
% Syntax:
% [T,S] = deconvolution(uz1,uz2);
%
% Input:
% uz1 = a time vector of signal recorded at location z1
% uz2 = a time vector of signal recorded at location z2
%
% Output:
% T = Time axis of deconvolved waveform (1xn)
% S = Deconvolved waveform (1xn)
%
% for plotting, use plot(T,W);
%
% Acknowledgement:
%
% In preparing this function, I benefitted and inspired from MatLAB codes
% of Dr. Nori Nakata of University of Oklahoma, and Hasan Ulusoy.
%
% References:
%
% Tikhonov, A. N. and Arsenin, V. Y. (1977). Solution of Ill-Posed
% Problems, Wiston/Wiley, Washington, D.C.
%
% Petrovic, B. and Parolai, S. (2016). Joint Deconvolution of Building
% and Downhole Strong-Motion Recordings: Evidence for the Seismic
% Wavefield Being Radiated Back into the Shallow Geological Layers,
% Bull. Seismol. Soc. Am. 106(4), doi: 10.1785/0120150326.
%
% Wen, W. and Kalkan, E. (2017). "System Identification Based on
% Deconvolution and Cross-Correlation?An Application To A Twenty-Story
% Instrumented Building In Anchorage, Alaska", Bulletin of Seismological
% Society of America. ol. 107(2), doi: 10.1785/0120160069.
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDER “AS IS” AND ANY
% EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
% PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER BE LIABLE
% FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
% BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
% WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
% OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
% ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
%
% Written by Dr. Erol Kalkan, P.E. ([email protected])
% Revision:1.0 Date:2016/09/0108:00:00
% Regularization parameter, which is 10 percent of the average of the power
% spectrum of uz2
eps = 0.1;
L = numel(uz1);
% Time vector
T = [-(L/2+1):1:(L/2-2)];
% L-point symmetric Hann window in the column vector W
W = hann(L);
% Multiply input signals, uz1 and uz2, with Hann window and take FFT in
% order to make sure that the ends of signal in frequency domain match up
% while keeping everything reasonably smooth; this greatly diminish
% spectral leakage
uz1f = fft(W.*uz1,L);
uz2f = fft(W.*uz2,L);
% Compute deconvolution
Stmp = real(ifft((uz1f.*conj(uz2f))./(uz2f.conj(uz2f)+epsmean(uz2f.*conj(uz2f)))));
S = [Stmp(L/2:L); Stmp(1:L/2-1)];
return
完整源码下载地址：
http://page5.dfpan.com/fs/4lcj42212291e6cc075/
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