### ASA 124th Meeting New Orleans 1992 October

## 2pAO13. Errors in tomographic imaging of scalar and vector fields from
underdetermined data.

**D. Keith Wilson
**

**
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*Dept. of Appl. Ocean Phys. and Eng., Woods Hole Oceanogr. Inst., Woods
Hole, MA 02543
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*
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The usual error maps computed for underdetermined tomographic images can
be very misleading for two reasons. First, the spatial correlation function of
the actual field usually differs from the correlation function used to solve
the inverse problem. Second, the effect of smoothing by the projections is
neglected. Numerical examples are used to demonstrate these points, and methods
for improving the inverse reconstructions are suggested. Tomographic imaging of
flow fields is also discussed. Although it can be proven that the irrotational
part of the flow that is interior to the array is invisible to the
measurements, this is shown not to be a fundamental impediment for flow
tomography using the methods usually applied by geophysical tomographers,
largely because they assume a priori statistics of the spatial structure.