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7/29/2019 THE MAGNITUDE–FREQUENCY RELATIONSHIP.pptx
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THE MAGNITUDE –FREQUENCY
RELATIONSHIP
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• The frequency-magnitude relation is a widelyaccepted concept in seismology.
• In general small earthquakes are more frequentthan large earthquakes.
• It describes the number of earthquakes expected
of each size, or magnitude, in a given area.• The frequency of earthquake occurrence as a
function of magnitude is represented byGutenberg and Richter (1941) relation:
log10 N = a – bM
• where N is the cumulative number of earthquakes of magnitude M or greater, and a
and b are numerical constants.
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• The constant a represents the seismic level of
activity.
• It is not an independent quantity. It depends
upon the largest magnitude in the given group of
earthquakes and on the constant b.
• The constant b describes the rate of increase of
earthquakes as magnitude decreases.
• b-values are usually within the range of 0.5-1.5.
• This range corresponds to an increase in numberof earthquakes 4 to 16 times for each decrease of
magnitude by one unit.
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• The relation equally holds good for a aftershocksequence.
•For a given sample of earthquake magnitudedata, if we plot log10 N versus M, the b-value canbe estimated from the slope of the log-linearrelation, the least-square fit line.
• Gutenberg and Richter obtained the magnitudefrequencies of shallow, intermediate and deepearthquakes for the whole world and gave the
following values of b; – Shallow shocks b = 0 . 9 0 ± 0.02
– Intermediate shocks b = 1.2 ± 0.2
– Deep shocks b = 1.2 ± 0.2
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Source parameters
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Macroseismic intensity
• The effect of a seismic source may be
characterized by its macroseismic intensity, I.
• Intensity describes the strength of shaking in
terms of human perception, damage to
buildings and other structures, as well as
changes in the surrounding environment.
• I depends on the distance from the source and
the soil conditions.
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• From an analysis of the areal distribution of
felt reports and damage one can estimate the
epicentral intensity Io in the source area as
well as the source depth, h.
• There exist empirical relationships between Io
and other instrumentally determined
measures of the earthquake size such as themagnitude and ground acceleration.
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Magnitude
• Magnitude is a logarithmic measure of the size
of an earthquake or explosion based on
instrumental measurements.
• The magnitude concept was first proposed by
Richter (1935).
• Magnitudes are derived from ground motion
amplitudes and periods or from signal
duration measured from instrumental records.
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Seismic Energy
• With empirical energy-magnitude relationshipsthe seismic energy, ES radiated by the seismicsource as seismic waves can be estimated.
• Common relationships are those given byGutenberg and Richter (1954, 1956) between ES and the surface-wave magnitude, MS and thebody-wave magnitude, MB:
log ES = 11.8 + 1.5 Ms
and
log ES = 5.8 + 2.4 MB
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Seismic Moment
•Another quantitative measure of the size andstrength of a seismic shear source is the scalarseismic moment Mo
– with µ - rigidity or shear modulus of the medium,
– - average final displacement after the rupture,
– A - the surface area of the rupture.
• Mo is a measure of the irreversible inelastic
deformation in the rupture area.
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Seismic source spectrum
• In a homogeneous half-space Mo can be determinedfrom the spectra of seismic waves observed at theEarth's surface by using the relationship:
• d - hypocentral distance between the event and theseismic station;
•
ρ - average density of the rock and• vp,s - velocity of the P or S waves around the source;
• - a factor correcting the observed seismicamplitudes for the influence of the radiation pattern of
the seismic source, which is different for P and S waves
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Orientation of the fault plane and the
fault slip
• Assuming that the earthquake rupture occurs
along a planar fault surface the orientation of
this plane in space can be described by three
angles: strike ф, dip δ and the direction of slip
on the fault by the rake angle λ.
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Fault Dimension
Dislocation (Fault Offset)
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Stresses
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Rupture Mode and Rupture Speed
• Unilateral, Bilateral, Radial.
• Directivity
– Directivity is an effect of fault rupture where the
ground motion from the earthquake is more
intense in the direction of the rupture propagation
than it is in any of the other directions from the
earthquake source.
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