Topography and gravity are geophysical fields whose joint
statistical structure derives from interface-loading processes
modulated by the underlying mechanics of isostatic and flexural
compensation in the shallow lithosphere. Under this dual
statistical-mechanistic viewpoint an estimation problem can be
formulated where the knowns are topography and gravity and the
principal unknown the elastic flexural rigidity of the lithosphere.
In the guise of an equivalent ``effective elastic thickness'', this
important, geographically varying, structural parameter has been the
subject of many interpretative studies, but precisely how well it is
known or how best it can be found from the data, abundant
nonetheless, has remained contentious and unresolved throughout the
last few decades of dedicated study. The popular methods whereby
admittance or coherence, both spectral measures of the relation
between gravity and topography, are inverted for the flexural
rigidity, have revealed themselves to have insufficient power to
independently constrain both it and the additional unknown initial-loading
fraction and load-correlation factors, respectively.
Solving this extremely ill-posed inversion problem leads to
non-uniqueness and is further complicated by practical
considerations such as the choice of regularizing data
tapers to render the analysis sufficiently selective both in the
spatial and spectral domains. Here, we rewrite the problem in a form
amenable to maximum-likelihood estimation theory, which we show
yields unbiased, minimum-variance estimates of flexural rigidity,
initial-loading fraction and load correlation, each of those
separably resolved with little a posteriori correlation
between their estimates. We are also able to separately characterize
the isotropic spectral shape of the initial loading processes. Our
procedure is well-posed and computationally tractable for the
two-interface case. The resulting algorithm is validated by
extensive simulations whose behavior is well matched by an
analytical theory with numerous tests for its applicability to
real-world data examples.
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