STATISTICS and ENERGETICS of the SOLID EARTH PROCESSES: RELIEF, PLATES, EARTH PROCESSES, VOLCANOES - PowerPoint PPT Presentation

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STATISTICS and ENERGETICS of the SOLID EARTH PROCESSES: RELIEF, PLATES, EARTH PROCESSES, VOLCANOES

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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 – PowerPoint PPT presentation

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Title: STATISTICS and ENERGETICS of the SOLID EARTH PROCESSES: RELIEF, PLATES, EARTH PROCESSES, VOLCANOES


1
STATISTICS and ENERGETICS of the SOLID EARTH
PROCESSESRELIEF, PLATES, EARTH PROCESSES,
VOLCANOES
  • G.S. Golitsyn
  • A.M. Obukhov Institute
  • of Atmospheric Physics, RAS
  • Moscow, RF

2
a)
b)
3
Relief
  • Decomposition on spherical harmonics up to number
  • Earth
  • Venus
  • Mars (200 km)
  • Legendre polinomials
  • planetary radius

4
Spectral dispersion
  • Earth km, km
  • Venus km , km km
  • Relief spectrum for regional transsects
  • , , km
  • Turcotte for 60 trajectories
  • Synthetic spectrum

5
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.

6
Slope Spectrum
  • white noise in the space
  • m for large scale harmonics of Earth
  • erosion
  • water flows on slopes
  • and wind decelerates over slopes

7
Structure function
  • If , then
  • m, km, then m

8
  • In vertical motions the whole crust with km
    is involved
  • The relative dispersion of the potential energy
  • - mean geothermal flux density
  • Myr

9
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?

10
Check of the convection velocities in viscous
and turbulent regimes
11
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)

12
  • Frequency spectrum
  • white noise
  • motion equation, momentum
  • red noise

13
Flow of events
  • , cumulative frequency
  • mean waiting time (Feller)
  • energy

14
Examples
  • Tsunami
  • land slides upon the soil mass
  • Number of lakes
  • ,
  • Turcotte, Ryanzhin

15
Earthquakes again
  • magnitude m 1 ar
  • Gutenberg-Richter
  • for , for
  • S.S. Grigorian 1988, Rundle 1989
  • Young modulus, mean slip
  • Seismic moment

16
Energy of seismic waves (Kanamory 1994)
  • total energy of an event
  • stress drop Bar 4 MPa Aki, 1967
  • length scale
  • Similarity criterium
  • at , the process 2 D
  • 1 D
  • Chile , Sumatra

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19
Scatter plot of observed rupture areas against
the theoretical values
20
The scatterplot of the observed rupture length
against the theoretical value
21
Dimensional analysis energy dimension, E, time, T
  • seek , by geothermal flux
  • seismic moment
  • similarity criterium
  • at
  • from global catalogs

22
  • at
  • for large

23
  • time in years.
  • globally one quake per year with
  • global geothermal flux
  • effective action coefficient
  • averaged over millenia

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  • volume energy

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