the magnitude–frequency relationship.pptx

7/29/2019 THE MAGNITUDE–FREQUENCY RELATIONSHIP.pptx

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THE MAGNITUDE –FREQUENCY

RELATIONSHIP



• 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.



• 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.



• 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



Source parameters



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.



• 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.



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.



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



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.



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



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.



Fault Dimension

Dislocation (Fault Offset)



Stresses



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.

the magnitude–frequency relationship.pptx

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