STATISTICS and ENERGETICS of the SOLID EARTH PROCESSES: RELIEF, PLATES, EARTH PROCESSES, VOLCANOES G.S. Golitsyn A.M. Obukhov Institute of Atmospheric.

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STATISTICS and ENERGETICS of the SOLID EARTH PROCESSES: RELIEF, PLATES, EARTH PROCESSES, VOLCANOES G.S. Golitsyn A.M. Obukhov Institute of Atmospheric Physics, RAS Moscow, RF

a) b)

Relief Decomposition on spherical harmonics up to number Earth Venus Mars(200 km) Legendre polinomials planetary radius

Spectral dispersion Earth km, km Venus km, km km Relief spectrum for regional transsects,, km Turcotte for 60 trajectories Synthetic spectrum

Dependence of the spectral power density S on wave number k for the synthetic depositional topography. The data points are the average of 50 simulations.

Slope Spectrum white noise in the space m for large scale harmonics of Earth erosion: water flows on slopes and wind decelerates over slopes

Structure function If, then m,km, then m

In vertical motions the whole crust with km is involved The relative dispersion of the potential energy - mean geothermal flux density Myr

Convection In the viscous fluid the rate of energy dissipation/generation of kinetic energy at convection thermal expansion of mantle ms, kgm, m /s K km,m s m s cm yr, stress at core?

Check of the convection velocities in viscous and turbulent regimes

Earthquakes Gutenberg-Richter, 1942, Ishima, 1939 (see Kasahara, 1981) Correlation function of random forces where is the stress minimum correlation time (the free energy of deformation)

Frequency spectrum white noise motion equation, momentum red noise

Flow of events, cumulative frequency mean waiting time (Feller) energy

Examples Tsunami: land slides upon the soil mass Number of lakes, Turcotte, Ryanzhin

Earthquakes again magnitudem = 1 ar Gutenberg-Richter for, for S.S. Grigorian 1988, Rundle 1989 Young modulus, mean slip Seismic moment

Energy of seismic waves (Kanamory 1994) total energy of an event stress dropBar = 4 MPaAki, 1967 length scale Similarity criterium at,the process 2 D 1 D Chile, Sumatra

Scatter plot of observed rupture areas against the theoretical values

The scatterplot of the observed rupture length against the theoretical value

Dimensional analysis: energy dimension, E, time, T seek, by geothermal flux seismic moment similarity criterium at… from global catalogs

at for large

time in years. globally: one quake per year with global geothermal flux effective action coefficient averaged over millenia

volume energy

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