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I tested the proposed TLS algorithm on a popular SEP inversion application,
the Hyperbolic Radon Transform (HRT)
Guitton (2000b); Lumley et al. (1995); Nichols (1994).
Figures and compare the results of the
TLS, LS, and DLS methods, for 10 and 150 CG iterations, respectively.
The results of the HRT tests are inconclusive. After 10 iterations, the results
from the three methods are almost indistinguishable. After 50, the DLS model
looks ``best,'' i.e., most interpretable by a human for picking velocities. However,
the TLS residual error is the whitest, the best balanced, and contains no correlated
energy-the very criteria which Guitton (2000a) uses to define
optimality.

**hrtcomp.10
**

Figure 4 Left panel: Input data. Right-top:
Envelope of estimated slowness model for LS, TLS, and DLS methods after 10 iterations.
Right-bottom: Residual error for LS, TLS, and DLS solutions.

**hrtcomp.50
**

Figure 5 Left panel: Input data. Right-top:
Envelope of estimated slowness model for LS, TLS, and DLS methods after 50 iterations.
Right-bottom: Residual error for LS, TLS, and DLS solutions.

** Next:** Conclusions and Discussion
** Up:** Brown: Total least-squares
** Previous:** Least-Squares Deconvolution Tests
Stanford Exploration Project

11/11/2002