A shallow earthquake occurs at depth in crust with

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics · Seismology, tectonics and geodynamics

The Solid Earth, Ch The earthquake source: moment tensor, radiation and spectra

Problem

A shallow earthquake occurs at depth

h = 10\,\mathrm{km}

in crust with

v_P = 6.2\,\mathrm{km\,s^{-1}}

. Four teleseismic P arrivals are read, each with its azimuth from the epicentre, its ray parameter

p

(already converted from the arrival distance using a standard travel-time table), and its first-motion polarity. Data: station A, azimuth

45^\circ

p=7.80\,\mathrm{s\,deg^{-1}}

, up (compression); station B, azimuth

135^\circ

p=8.40\,\mathrm{s\,deg^{-1}}

, down (dilatation); station C, azimuth

225^\circ

p=6.95\,\mathrm{s\,deg^{-1}}

, up (compression); station D, azimuth

315^\circ

p=9.10\,\mathrm{s\,deg^{-1}}

, down (dilatation). ((a)) Find the takeoff angle

i_h

(from the downward vertical) at the source for each station, using

\sin i_h = pv_P/r_h

with

r_h

the source radius taken as

6371\,\mathrm{km}

minus the depth, and

p

converted to

\mathrm{s\,rad^{-1}}

using

1\,\mathrm{s\,deg^{-1}} = 57.30\,\mathrm{s\,rad^{-1}}

. ((b)) Give the simplest pair of nodal planes consistent with these polarities, vertical and placed midway between stations of opposite polarity, with their strike and dip, and say whether the mechanism is strike-slip, thrust or normal. Explain why these four polarities alone do not fix the pair uniquely.

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