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Regularized Deconvolution of Local Short-Period Seismograms in the Wavelet Packet Domain

Departamento de Física
Ingeniería de Sistemas y Teoría de la Señal
Escuela Politécnica Superior
Universidad de Alicante
Ap. Correos 99, 03080 Alicante, Spain
(J.J.G.-M., J.R.-H.)
Departamento de Ciencias de la Tierra y del Medio Ambiente
Facultad de Ciencias
Universidad de Alicante
Ap. Correos 99, 03080 Alicante, Spain
(J.G., S.M.)
Centro de Investigación Operativa
Universidad Miguel Hernández
Avda. Ferrocarril, s/n, 03202 Elche, Spain
(F.B.)

Manuscript received 28 May 2003.

Short-period seismographs of the vertical component have a frequency response similar to a bandpass filter with a low cutoff frequency around 1 Hz. This instrument's response distorts in some way the interesting signal that arrives at the sensor. In this case, the aim of the deconvolution is at recover the signal as it arrives at the sensor, since this signal can be very important to the study of source mechanisms, for instance.

In this article we present a new method of regularized inversion based on the wavelet packet transform. This method achieves the deconvolution of the instrument response through the time-frequency information contained in the wavelet packet transform of the signals. Although the instrument response is known (Jáuregui, 1997), the noise and other artifacts in the signal make deconvolution a nontrivial process. As an evaluation method, we first apply it to synthetic signals we generated. In this way, the shape of the whole output signal and the onset time of the first pulse can be compared to the ideal signal. The method is also applied to real signals, specifically to local short-period seismograms registered at the seismic network of the University of Alicante in southeastern Spain. In both cases, the results are compared with the water-level correction method currently used. The comparison shows how the proposed method works better, as it provides, in contrast to the current method, the shape and the onset time of the ideal signal.