Implications of stress-drop models of earthquakes for the inversion
of stress drop from seismic observations
Pure and Applied Geophysics, 115 (1):
301--316 (Jan 1, 1977)DOI: 10.1007/BF01637111
Abstract
We discuss the inversion of stress drops from seismic observations
on the basis of crack or stress-drop models of earthquake mechanism.
Since a formal inverse problem cannot be posed at present we discuss
implications of solutions to direct problems. We first discuss the
static approximations used to obtain stress drop from seismic moment
and source dimensions. We show that the geometrical effects are quite
significant if only one source dimension has been retrieved from
seismic observations. The effect of variable stress drop is discussed
and we show that the inverted stress drop is not a simple average
of the actual stress drops on the fault. We discuss the energy release
during faulting and show that the apparent stress has a complicated
relation to the stress drop on the fault. We also show that the static
stress drops obtained by seismologists are a lower bound to the actual
dynamic stressdrops on the fault. This may in part explain disagreements
with laboratory results. Finally, we discuss the inversion of source
dimensions from the far-field radiation. We analyse two extreme,
simple dynamical source models, a circular fault and a rectangular
fault and show that geometry has a much more pronounced effect on
radiation than is usually acknowledged.