initial-loading fraction, and load correlation, under isotropy

Princeton University

Princeton NJ 08544, USA

University College London

London WC1E 6BT

Reprint | Related work | Software | Figure software | Publications |

## 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 posterioricorrelation 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.

- Figure 01
Synthetic data representing the standard model without initial-load correlation

- Figure 02
Expected values of the
admittance and coherence between Bouguer gravity anomalies
and topography

- Figure 03
Synthetic "topographies" generated from the Matérnrn spectral class

- Figure 04
Synthetic data representing the standard model with initial-load correlation

- Figure 05
The behavior of the quadratic residuals in a recovery simulation for correlated loading

- Figure 06
Recovery statistics of simulations under
uncorrelated loading on a 64x64 grid with 20 km spacing

- Figure 07
Recovery statistics of simulations under
uncorrelated loading on a 128x128 grid with 20 km spacing

- Figure 08
Recovery statistics of simulations under
correlated loading on a 32x32 grid with 20 km spacing

- Figure 09
Recovery statistics of simulations under
uncorrelated loading on a 64x64 grid with 20 km spacing

- Figure 10a
Correlation (normalized covariance) matrices for
the uncorrelated-loading experiments previously reported

- Figure 10b
Correlation (normalized covariance) matrices for
the uncorrelated-loading experiments previously reported

- Figure 11a
Correlation (normalized covariance) matrices for
the correlated-loading experiments previously reported

- Figure 11b
Correlation (normalized covariance) matrices for
the correlated-loading experiments previously reported

- Figure 12a
Admittance and coherence
curves for the uncorrelated-loading experiments previously
reported

- Figure 12b
Admittance and coherence curves for
the uncorrelated-loading experiments previously reported

- Figure 13a
Admittance and coherence
curves for the correlated-loading experiments previously
reported

- Figure 13b
Admittance and coherence curves for
the correlated-loading experiments previously reported

Frederik Simons Last modified: Wed Apr 12 23:06:25 EDT 2023