## Point source radiation in inhomogeneous anisotropic structures

**Ivan Psencik ** **&**
**Telesson Neves Teles**
### Summary

The ray formulae for the radiation from point sources in unbounded
inhomogeneous isotropic as well as anisotropic media consist of two
factors. The first one depends fully on the type and orientation of
the source and on the parameters of the medium at the source. We call
this factor the directivity function. The other factor depends on the
parameters of the medium surrounding the source and this factor is
the well-known geometrical spreading. The displacement vector and the
radiation pattern defined as a modulus of the amplitude of the
displacement vector measured on a unit sphere around the source are
both proportional to the ratio of the directivity function and the
geometrical spreading.

For several reasons it is desirable to separate the two mentioned
factors. For example, there are methods in exploration seismics,
which separate the effects of the geometrical spreading from the
observed wave field (so-called true amplitude concept) and thus
require the proposed separation. The separation has also an important
impact on computer time savings in modeling seismic wave fields
generated by point sources by the ray method. For a given position in
a given model, it is sufficient to calculate the geometrical
spreading only once. A great variety of various types of point
sources with a different orientation can then be calculated at
negligible additional cost.

In numerical examples, we show the effects of anisotropy on the
geometrical spreading, the directivity function and the radiation
pattern. Ray synthetic seismograms due to a point source situated in
an anisotropic medium are also presented and compared with seismograms
for an isotropic medium.

### Whole paper

The reprint is available in
PDF (1742 kB !).

PAGEOPH, **148** (1996), 591-623.

SW3D
- main page of consortium ** Seismic Waves in Complex 3-D Structures **.