arXiv subjects

G. M. Molchan

Publications and source records attributed to G. M. Molchan.

4 recordsLinked to original sources

arXiv2019

Gusev's stochastic model for the seismic source: high-frequency behavior in the far zone

This paper discusses local features in the source function that generate in the far zone simultaneously (a) a quadratic decay of the source spectrum and (b) the loss of radiation directivity at high frequencies. A. Gusev drew attention to this problem and suggested that a positive solution can be obtained for earthquake rupture front with a rather complex ("lace") structure. Below we give a theoretical solution of the problem and show that the front structure can be simple enough, but not smooth.

physics.geo-ph↗

arXiv2019

Fractal seismicity and seismic risk

Recently, attempts have been made to take into account the fractal properties of seismicity when mapping the long-term rate of earthquakes. The paper touches upon the theoretical aspects of fractality and provides a critical analysis of its applications to the problems of seismic risk

physics.geo-ph↗

arXiv2010

Shape of Empirical and Synthetic Isoseismals: Comparison for Italian M \le 6 Earthquakes

We present results from a comparative analysis of empirical and synthetic shapes for isoseismals of low intensity (I = IV-VI on the MCS scale) for six Italian earthquakes of ML = 4.5-6. Our modelling of isoseismals is based on a plane stratified earth model and on the dou-ble-couple point source approximation to calculate seismograms in the frequency range f =< 1 Hz. With a minimum of parameter variation we demonstrate that the low intensity isoseismals provide information on source geometry. We strive to avoid subjectivity in isoseismal construc-tions by using the new Diffuse Boundary method, which visualizes isoseismals with their uncer-tainty. Similar results in this direction are known for large earthquakes (ML ~ 6 or greater) with extended sources and for the higher isoseismals (I >= VI on the MM scale). The latter studies disregard the earth structure, use a greater number of parameters, and therefore have greater possibilities for fitting the data than our approach.

physics.geo-ph↗

arXiv2002

Small values of the maximum for the integral of fractional Brownian motion

We consider the integral of fractional Brownian motion (IFBM) and its functionals $ξ_T$ on the intervals $(0,T)$ and $(-T,T)$ of the following types: the maximum $M_T$, the position of the maximum, the occupation time above zero etc. We show how the asymptotics of $P(ξ_T<1)=p_T, T\to \infty$, is related to the Hausdorff dimension of Lagrangian regular points for the inviscid Burgers equation with FBM initial velocity. We produce computational evidence in favor of a power asymptotics for $p_T$. The data do not reject the hypothesis that the exponent $θ$ of the power law is related to the similarity parameter $H$ of fractional Brownian motion as follows: $θ=-(1-H)$ for the interval $(-T,T)$ and $θ=-H(1-H)$ for $(0,T)$. The point 0 is special in that IFBM and its derivative both vanish there.

math.PR↗