Point-source Parameters from Noisy Waveforms: Error Estimate by Monte-Carlo Simulation

—?We introduce an approach to estimate the error in the determination of the point-source mechanism and corresponding source-time function by inverting waveform data contaminated by a noise. No a priori assumptions about the statistical characteristics of the noise are needed. The estimate of the confidence region of the retrieved source is constructed as a set of solutions of the inverse problem for individual realizations of noisy data. They are generated from a sample of observed noise by Monte-Carlo simulation: white noise is convolved with the observed noise sample yielding a particular realization of the noise, which is random but retains the spectral characteristics of the observed sample. This approach allows us to consider even the situations where the noise varies from station to station. However, the basic assumption is that the noise is random, thus the method cannot handle systematic errors, e.g., due to mislocation or incorrect model of the medium.¶Synthetic tests with noisy data simulating the configuration of the seismic network in Friuli, NE Italy, show that determination of the source-time function is rather uncertain even with low-noise contamination but that orientation of the mechanism is recovered very well. As an example, local waveforms of a magnitude 3 event from the 1988 Moggio Udinese swarm, Northern Italy, are processed.     

On the product of legender functions as encountered in geodynamics

Résumé On rencontre souvent des produits de fonctions de Legendre en géodésie mathématique, en mécanique céleste et quantique, et en géophysique. Nous donnons les expressions générales des coefficients de la décomposition d'un produit quelconque sur la base des fonctions de Legendre ellesmêmes. Quelques applications immédiates sont envisagées.     

Transmitted waves in the vicinity of the interface beyond the critical point

Summary The space (time) delay of transmitted waves in the vicinity of the interface beyond the critical point is investigated on two-dimensional seismic models of a low velocity channel; results of laboratory experiments are compared with the conclusions of the theory. The effect of the time delay in field measurements is demonstrated by means of two typical geological formations.     

Macroseismic effects of the north-Italian earthquake of May 6th, 1976, on the territory of Czechoslovakia

Summary The method of treatment of the macroseismic data obtained on the territory of the CSSR after the main 1976 Friuli earthquake is described and the preliminary results are confronted with the geologic structure.     

Computation of the potential of a simple inhomogeneous equipotential layer with a given density on a given surface

Summary The potential of a simple equipotential layer, defined by the equation of a surface, on which the layer is spread, and by the density function in the form of harmonic expansions, is expressed with the aid of the parameters of the surface and of the density function. The integral of the product of three Legendre associated functions is treated with the aid of Gaunt's integral [3, 4].