Null-space and statistical significance of first-arrival traveltime inversion

Details Null-space and statistical significance of first-arrival traveltime inversion Null-space and statistical significance of first-arrival traveltime inversion

Mar 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004geoji.156..549m&link_type=abstract

Geophysical Journal International, Volume 156, Issue 3, pp. 549-554.

Astronomy and Astrophysics

Astronomy

First-Arrival Traveltimes, Iasp91, Inversion, Model Uncertainty, Monte Carlo

Scientific paper

The strong uncertainty inherent in the traveltime inversion of first arrivals from surface sources is usually removed by using a priori constraints or regularization. This leads to the null-space (data-independent model variability) being inadequately sampled, and consequently, model uncertainties may be underestimated in traditional (such as checkerboard) resolution tests. To measure the full null-space model uncertainties, we use unconstrained Monte Carlo inversion and examine the statistics of the resulting model ensembles. In an application to 1-D first-arrival traveltime inversion, the τ-p method is used to build a set of models that are equivalent to the IASP91 model within small, ~0.02 per cent, time deviations. The resulting velocity variances are much larger, ~2-3 per cent within the regions above the mantle discontinuities, and are interpreted as being due to the null-space. Depth-variant depth averaging is required for constraining the velocities within meaningful bounds, and the averaging scalelength could also be used as a measure of depth resolution. Velocity variances show structure-dependent, negative correlation with the depth-averaging scalelength. Neither the smoothest (Herglotz-Wiechert) nor the mean velocity-depth functions reproduce the discontinuities in the IASP91 model; however, the discontinuities can be identified by the increased null-space velocity (co-)variances. Although derived for a 1-D case, the above conclusions also relate to higher dimensions.

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