Institut für Geophysik
Prof. Dr. Christine Thomas

Corrensstraße 24 48149 Münster
Germany

Tel: +49 251 83-33591
Fax: +49 251 83-36100

Slowness and backazimuth

The majority of array seismology methods assume a plane wave arriving at the array. The propagation of seismic waves in a spherical Earth arriving at a seismological array can be described by the incidence angle i and the backazimuth theta (Figure 1). Seismological arrays actually do not measure the incidence angle but the inverse of the apparent horizontal propagation velocity of the wavefront 1/v_app. This parameter is called slowness u and related to the incidence angle via

u = 1/v_app = sin i/v_0,

where v0 is the subsurface wave velocity beneath the array.


The backazimuth theta is the angle of the wavefront arriving at the array between geographical north and the epicentre of the earthquake (Figure 2). Slowness and backazimuth can be combined to the slowness vector

u=(u_x,u_y,u_z)
=(sin theta /v_app, cos theta /v_app, 1/(v_app tan theta))
=u_hor (sin theta, cos theta, 1/tan theta).

Where u_hor = .1/v_app.

Slowness Backazimuth

Figure 1: Definition of the horizontal slowness of an incoming plane wavefront (Lessing, 2014, PhD thesis; after Rost and Thomas, 2002). Figure 2: Definition of the backazimuth of an incoming plane wavefront (Lessing, 2014, PhD thesis; after Rost and Thomas, 2002).

Beamforming


Impressum | © 2008 Institut für Geophysik
Institut für Geophysik
Prof. Dr. Christine Thomas

Corrensstraße 24
· 48149 Münster
Germany

Tel: +49 251 83-33591 · Fax: +49 251 83-36100
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