Anisotropic travel-time inversion with error bars: theory
, by Joe Dellinger
In most geophysical inversion problems, there is a bothersome null space which intrudes
into the desired answer. If the space we invert in is visualizeable, like a 2D scalar
velocity field, null-space artifacts may be recognized and ignored. Here I examine the
problem of inverting for anisotropic elastic parameters in a layered medium, where the
interplay of anisotropic elastic constants can create a large null space. Since the space
of elastic parameters is hard to visualize, null-space artifacts are hard to recognize and
can make the results worthless. The solution is to take a probabilistic approach to the
problem, by calculating not only a set of best-fitting elastic constants but also error
bars.
STANFORD