Seismic Sources

Seismic Sources 1. Fault Plane Solutions 2. Source parameters

Imtiyaz A. Parvez

C-MMACS, Bangalore

Imtiyaz A. Parvez, C-MMACS

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Fault Plane Solutions • Understanding the effect of the movement on the fault in relation to the polarities of P-waves; • Understanding the presentation of P-wave polarities in an equal angle (Wulff net) or equal area projection (LambertSchmidt net) of the focal sphere; • Constructing a fault-plane solution and the related parameters (P- and T-axes, displacement vector) for a real earthquake; • To discuss the fault-plane solution in relation to the tectonic setting of the epicentral area.

Imtiyaz A. Parvez, C-MMACS

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Data and relationships Before a fault-plane solution for a teleseismic event can be constructed, the following steps must be completed or data be known: A. Interpretation of P-wave first-motion polarities from

seismograms at several stations B. Calculation of epicentral distances and source-to-station azimuths for these stations; C. Calculation of the take-off angles for the seismic P-wave rays leaving the hypocenter towards these stations. This requires the knowledge of the focal depth and of the P-wave velocity at this depth Imtiyaz A. Parvez, C-MMACS

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Take-off angle (AIN) calculations based on strongly biased velocity models might result in inconsistent fault-plane solutions or not permit a proper separation of polarity readings into quadrants at all! STA

AZM (degree)

AIN (degree)

POL

ALI ME2 KAN YAR ERD DEM GIR UNK SAN PEL GUN ESK SOT BA2 MOL YUL ALT GUM GU2 BAS BIN HAR KIZ AKS SUT

40 134 197 48 313 330 301 336 76 327 290 312 318 79 297 67 59 320 320 308 295 24 311 284 295

130 114 112 111 103 102 102 101 62 62 62 62 62 62 62 62 62 62 62 62 62 62 62 62 62

D D D D D D U D U D U U D U U U D U D D U D U D U

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Set up stereonet Place tracing paper or a transparency sheet over the Wulff or Lambert-Schmidt net projection Mark on it the centre and perimeter of the net, as well as the N, E, S and W directions. Pin the marked sheet centre with a needle to the centre of the net.

Imtiyaz A. Parvez, C-MMACS

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Plot each station Mark the azimuth of the station on the perimeter of the transparency and rotate the latter until the tick mark is aligned along an azimuth of 0°, 90°, 180° or 270°. Measure the take-off angle from the centre of the net along this azimuth. This gives the intersection point of the particular P-wave ray with the lower hemisphere. Mark on this position the P-wave polarity with a neat (+) for compression or (-) for dilatation using different colour for better distinction of closely spaced polarities of different sign . Distane d = r x tan (AIN/2) = r x sin ( AIN/2)

Wulff net Lambert-Schmidt net

r radius of the given net Imtiyaz A. Parvez, C-MMACS

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Find a nodal plane By rotating the net over the plotted data try to find a great circle which separates as well as possible the expected quadrants with different first motion signs. This great circle represents the intersection trace of one of the possible fault (respectively nodal) planes with the lower half of the focal sphere (FP1). Find the pole of the first nodal plane, and the second nodal plane Mark point A at the middle of FP1 and find, on the great circle perpendicular to it, the pole P1 of FP1, 90o apart. All great circles, passing this pole are perpendicular to the great circle of FP1. Since the second possible (auxiliary) fault plane (FP2) must be perpendicular to the FP1, it has to pass P1. Find, accordingly, FP2 which again has to separate Imtiyaz areasA.of different Parvez, C-MMACSpolarity.

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Find the pole of the second nodal plane, and the equatorial plane Find the pole P2 for FP2 and delineate the equatorial plane EP. The latter is perpendicular to both FP1 and FP2 , i.e. a great circle through the poles P1 and P2. The intersection point between FP1 and FP2 is the pole of the equatorial plane (P3). Mark P and T axes Mark the position of the pressure and tension axes on the equatorial plane and indicate their direction towards (P) and from the center (T) of the considered net. Their positions on the equatorial plane lie in the centre of the respective dilatational (-) or compressional (+) quadrant, i.e. 45° away from the intersection points of the two fault planes with the equatorial plane. Imtiyaz A. Parvez, C-MMACS

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Find the azimuth of the nodal planes Determine the azimuth (strike direction φ) of both FP1 and FP2. It is the angle measured clockwise against North between the directional vector connecting the centre of the net with the end point of the respective projected fault trace lying towards the right of the net centre.

Find the dip angle of both nodal planes Determine the dip angle δ (against the horizontal) for both FP1 and FP2 by putting their projected traces on a great circle. Measure δ as the difference angle from the outremost great circle Determine the slip direction Slip direction can be obtained by drawing one vector each from the center of the net to the poles P1 and P2 of the nodal planes

Imtiyaz A. Parvez, C-MMACS

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Find the azimuth and plunge of P & T axes The azimuth of the pressure and the tension axes, respectively, is equal to the azimuth of the line connecting the centre of the net through the P and T point with the perimeter of the net. Their plunge is the respective dip angle of these vectors against the horizontal (to be measured as for δ ).

The angles may range between Strike Dip Slip -

0 to 360 0 to 90 -180 to 180

Imtiyaz A. Parvez, C-MMACS

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Imtiyaz A. Parvez, C-MMACS

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Imtiyaz A. Parvez, C-MMACS

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Focal Mechanism by Moment Tensors Solution The concept of moment tensor provides a complete description of equivalent forces of a general seismic point source. A source can be considered a point source if both the distance D of the observer from the source and the wavelength λ are much greater than the linear source dimension. A special case is the shear dislocation along a planar fault which is described by the double couple source model.

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A double couple mechanism assumes that slip occurs on both the fault plane and the auxiliary plane. As a result, the following radiation pattern is obtained.

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The displacement d on the Earth surface at station s can be expressed as a linear combination of time-dependent moment tensor elements Mkj(ξ,t) that are assumed to have the same time dependence convolved (indicated by the star symbol) with the corresponding Green’s functions Gsk,j(x,ξ,t):

ds(x,t) = Mkj (ξ ,t)*G sk,j (x,ξ ,t) Further, if source time history s(t) which describes the time dependence of moment released at the source, is contained in Mkj(ξ,t) and if we assume that all the components of Mkj(ξ,t) have the same time dependence s(t), the above equation can be written as;

ds(x,t) = Mkj [Gsk,j (x,ξ ,t) ∗ s (t)]

Imtiyaz A. Parvez, C-MMACS

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The nine generalized couples representing G sk,j (x,ξ ,t)

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Owing to the symmetry of the moment tensor, the components (x,y), (y,x); (x,z), (z,x) & (y,z), (z,y) will have the same moment tensor representation and same seismic radiation pattern. Finally, for a double-couple source, the cartesian components of the moment tensor can be expressed in terms of strike (φ φ), dip (δ δ) and slip (λ λ) of the shear dislocation source and the scalar seismic Moment(Mo).

Mxx = - Mo(sinδ cosλ sin2φ + sin2δ sinλ sin2φ ) Mxy = Mo(sinδ cosλ cos2φ + 0.5 sin2δ sinλ sin2φ ) Mxz = - Mo(cosδ cosλ cosφ + cos2δ sinλ sinφ ) Myy = Mo(sinδ cosλ sin2φ - sin2δ sinλ cos2φ ) Myz = - Mo(cosδ cosλ sinφ - cos2δ sinλ cosφ ) Mzz = Mo sin2δ sinλ Imtiyaz A. Parvez, C-MMACS

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Some methods of moment tensor inversion Harvard CMT Solution The Harvard group maintains the most extensive catalogue of Centroid moment tensor (CMT) solutions for strong (M>5.0) Earthquakes over the period from 1976 till present. This and quick CMT solutions of recent events can be viewed at http://www.seismology.harvard.edu/projects/CMT

NEIC Fast Moment Tensors This is an effort by the US National Earthquake Information Centre (NEIC) to produce rapid estimates of the seismic moment Tensor for earthquakes with mb>5.7. More information under http://gldss7.cr.usgs.gov/neis/FM/fast_moment.html

Imtiyaz A. Parvez, C-MMACS

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EMSC rapid source parameter determinations The method uses a grid search algorithm to derive within 24 hours after the event fault plane solutions and seismic moment Of earthquakes (M>5.5) in the European Mediterranean area. This Is an initiative of European Mediterranean Seismological Centre and The GEOFON programme at GeoForschungs-Zentrum Potsdam. http://www.emsc-csem.org and http://www.gfz-potsdam.de/pb2/pb24/emsc.html

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Estimation of Source Parameters The physics of the earthquake source indicates that elastic waves recorded within a few wavelengths of an extended source (the near field). The complexity of near field depends on following three components. 1.The first component involves the complex rupturing Process along the fault surface during the occurrence of an earthquake. 2.The second component concerns the effect of intervening medium on the recorded seismic signals. The seismic signals generated at the source travel along the different paths to reach the stations. Therefore, the shape of recorded seismic signal differ considerably in comparison to the signals originating from the source. Imtiyaz A. Parvez, C-MMACS

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3. The final and major component component of the problem is the influence of the recording system. This effect should be removed from the recorded seismic signals in order to obtain the information about the physical processes acting at the earthquake source.

The seismic signal at the station is represented by: Where, AR(t) AT(t) IR(t)

AR(t)=AT(t)*IR(t) relative ground motion true ground motion Instrument response

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In frequency domain, AR(f)=AT(f) IR(f) Therefore, one can obtain the true ground motion In frequency domain as, AT(f)=AR(f) / IR(f) Removal of attenuation effect

Ao ( f ) = AT exp(−πfR / 2QV )

Ao(f) AT(f) V Q

True ground motion at source True ground motion at distance R Velocity quality factor Imtiyaz A. Parvez, C-MMACS

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Relations for estimating the seismic source parameters The long period spectral level Ωo and the corner Frequency fc can be obtained from the body-wave spectra Source parameters 1. Seismic moment (size of the source)

Mo = Mo Rφϕ ρ R

4πρv 3 RΩ 0

Rφϕ

Keilis-Borok, 1959

Seismic moment in dyne-cm Radiation patter (0.63 for strike-slip and 0.51 for normal Density at the source Epicentral distance Imtiyaz A. Parvez, C-MMACS

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2. Stress drop (difference of shear stress in the plane of the fault surface prior to the occurrence of earthquake and after the earthquake)

∆σ = 7 M o / 16.r .10 3

Where,

−6

r = 2.34v / 2πf c

3. Strain drop

∑=

∆σ

µ Imtiyaz A. Parvez, C-MMACS

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4. Energy Released

2π 3 2 E= r ∆σ 3 µn

7π n= 12

5. Apparent stress (The apparent stress is a measure of the stresses in the focal region)

ησ =

µE M0

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