Maximum-likelihood estimation of lithospheric flexural rigidity, initial-loading fraction and load correlation, under isotropy

Abstract

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 view point an estimation problem can be formulated where the knowns are topography and gravityand the principal unknown the elastic flexural rigidity of the lithosphere. In the guise ofan equivalent 'effective elastic thickness', this important, geographically varying, structural parameter has been the subject of many interpretative studies, but preciselyhowwell it is knownor how best it can be found from the data, abundant nonetheless, has remained contentious and unresolved throughout the last few decades of dedicated study. Thepopular 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 fractionand load-correlation factors, respectively. Solving this extremely ill-posed inversion problemleads 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 formamenable 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 betweentheir estimates. We are also able to separately characterize the isotropic spectral shape ofthe 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 behaviour is well matched by an analytical theory with numerous tests for its applicability to real-world data examples. © The Authors 2013. Published by Oxford University Press on behalf of The Royal Astronomical Society.