## On the retrieval of moment tensors from borehole data

**Vaclav Vavrycuk**
### Summary

The complete moment tensors of seismic sources in homogeneous or vertically
inhomogeneous isotropic structures cannot be retrieved using receivers deployed
in one vertical borehole. The complete moment tensors can be retrieved from
amplitudes of P-waves, provided that receivers are deployed in at least three
boreholes. Using amplitudes of P- and S-waves, two boreholes are, in principle,
sufficient. Similar rules also apply to transversely isotropic media with
a vertical axis of symmetry.

In the case of limited observations, the inversion
can be stabilized by imposing the zero-trace constraint on the moment tensors.
However, this constraint is valid only if applied to observations of shear
faulting on planar faults in isotropic media, which produces double-couple
mechanisms. For shear faulting on non-planar faults, for tensile faulting,
and for shear faulting in anisotropic media, the zero-trace constraint is
no longer valid and can distort the retrieved moment tensor and bias
the fault-plane solution.

Numerical modelling simulating the inversion of
the double-couple mechanism from real data reveals that the errors in
the double-couple and non-double-couple percentages of the moment tensors
rapidly decrease with increase in the number of boreholes used. For noisy
P- and S-wave amplitudes with noise of 15% of the top amplitude at each channel
and for a velocity model biased by 10%, the errors in the double-couple
percentage attain 25, 13 and 6% when inverting for the double-couple
mechanism from one, two and three boreholes.

### Whole paper

The reprint is available in
PDF (141 kB).

*Geophysical Prospecting*, **55** (2007), 381-391.

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