Source shape estimation and deconvolution of teleseismic bodywaves

Abstract

We consider the deconvolution of a suite of teleseismic recordings of the same event in order to separate source and transmission path phenomena. The assumption of source uniformity may restrict the range of azimuths and distances of the seismograms included in the suite. The source shape is estimated by separately averaging the log amplitude spectra and the phase spectra of the recordings. This method of source estimation uses the redundant source information contained in secondary arrivals. The necessary condition for this estimator to resolve the source wavelet is that the travel times of the various secondary arrivals be evenly distributed with respect to the initial arrivals. The subsequent deconvolution of the seismograms is carried out by spectral division with two modifications. The first is the introduction of a minimum allowable source spectral amplitude termed the waterlevel. This parameter constrains the gain of the deconvolution filter in regions where the seismogram has little or no information, and also trades-off arrival time resolution with arrival amplitude resolution. The second modification, designed to increase the time domain resolution of the deconvolution, is the extension of the frequency range of the transmission path impulse response spectrum beyond the optimal passband (the passband of the seismograms). The justification for the extension lies in the fact that the impulse response of the transmission path is itself a series of impulses which means its spectrum is not band-limited. Thus, the impulse response is best represented by a continuous spectrum rather than one which is set to zero outside the optimal passband. This continuity is achieved by a recursive application of a unit-step prediction operator determined by Burg's maximum entropy algorithm. The envelopes of the deconvolution are used to detect the presence of phase shifted arrivals. IntroductionThis paper examines the problem of the deconvolution of source functions from teleseismic recordings. The first step in any deconvolution process is the estimation of the source time function. The next section of this paper deals with this problem.A standard technique in exploration seismology is to decompose the sowce from the seismogram autocorrelation function. This method assumes that the source is minimum phase and that the impulse sequence behaves like white noise (Robinson 1967). Since neither of these assumptions appeared to be generally valid for teleseismic recordings, the technique was not used. Source estimation by homomorphic transformation has also been suggested (Ulrych 1971), and this method is discussed in some detail. However, the low quefrency assumption of this method was found to not be generally valid, and there is also a problem of phase instabilities with the homomorphic transform itself.Both of the above methods attempt to estimate the source from a single seismogram. We decided that on the basis of a single recording of an event it would be difficult, if not impossible, to devise a general method of estimati...

High‐resolution transition zone structures of the Gorda Slab beneath the western United States: Implication for deep water subduction

“…The spectral division is carried out with the introduction of a minimum allowable source spectral amplitude in order to constrain the gain of deconvolution filter in case the seismogram has little or no information [Clayton and Wiggins, 1976]. The data were hand edited for quality before and after formation of receiver functions.…”

Crust and upper-mantle seismic anisotropy variations from the coast to inland in central and Southern Mexico

“…Then, they deconvolved the vertical component from the horizontal components in the frequency domain. A water level of 0.0001, 0.001, 0.01 and 0.1 was first applied to the spectra of the horizontal components to avoid division by zero and enhancement of noise (Clayton & Wiggins 1976). RFs were filtered with a Gaussian filter before Figure 2.…”

Ultralow-velocity zone geometries resolved by multidimensional waveform modelling

“…We deconvolve the source 463 from the data by using the stacked SKS waveform for epicentral distances less than 464 100° as an estimate of the source wavelet and apply a water-level deconvolution 465 with a k-value equal to 0.2 [Clayton and Wiggins, 1976]. We next grid the data into 466 2.5º by 2.5º geographic bins based on SPdKS inception points (the point where P-467 diffraction initiates on the CMB) for all source and receiver regions containing at 468 least one 5º by 5º square with a minimum 100 inception points (Figure 8, 9, 10).…”