Determination of the signature of a dynamite source using source
scaling. Part 1: Theory
Geophysics, 58 (8):
1174--1182 (Aug 1, 1993)DOI: 10.1190/1.1443501
Abstract
It is normally impossible to measure the source signature in land
seismic data acquisition with a dynamite source, because it is normally
impossible to separate the incident field from the scattered field.
Nevertheless, in any serious attempt to invert the seismic data,
it is essential to know the source signature; for the dynamite source
this is the volume injection function. The problem can be solved
by using two different shots at each shot point and relating the
source signatures by the source scaling law, which follows from the
invariance of the medium parameters with the size of the charge.
The volume injection function of the larger shot is an amplified
and stretched version of that of the smaller shot, the amplification
factor being equal to the ratio of the charge masses and the time
stretch factor being equal to the cube-root of this ratio. At a given
receiver, the response to one shot is a convolution of the source
signature with the impulse response of the earth, plus noise. The
two shots and the scaling law give three independent equations relating
the three unknowns: the two source signatures and the impulse response
of the earth (plus noise). This theory may be put at risk in a physical
experiment which requires a third shot at the same shot point, using
a known mass of dynamite, different from the first two. The resulting
shot record should be different from the first two and, apart from
the noise, should be predictable from them.