On the robustness of estimates of mechanical anisotropy in the continental lithosphere: A North American case study and global reanalysis

Abstract

Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Earth and Planetary Science Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractLithospheric strength variations both influence and are influenced by many tectonic processes, including orogenesis and rifting cycles. The long, complex, and highly anisotropic histories of the continental lithosphere might lead to a natural expectation of widespread mechanical anisotropy. Anisotropy in the coherence between topography and gravity anomalies is indeed often observed, but whether it corresponds to an elastic thickness that is anisotropic remains in question. If coherence is used to estimate flexural strength of the lithosphere, the null-hypothesis of elastic isotropy can only be rejected when there is significant anisotropy in both the coherence and the elastic strengths derived from it, and if interference from anisotropy in the data themselves can be plausibly excluded. We consider coherence estimates made using multitaper and wavelet methods, from which estimates of effective elastic thickness are derived. We develop a series of statistical and geophysical tests for anisotropy, and specifically evaluate the potential for spurious results with synthetically generated data. Our primary case study, the North American continent, does not exhibit meaningful anisotropy in its mechanical strength. Similarly, a global reanalysis of continental gravity and topography using multitaper methods produces only scant evidence for lithospheric flexural anisotropy.

Slepian Spatial-Spectral Concentration Problem on the Sphere: Analytical Formulation for Limited Colatitude–Longitude Spatial Region

“…Once K is computed using (31), the eigenvalue decomposition of K yields the Slepian basis for the region for a given band-limit L. We note that the equivalence between (10) and the formulation in (31) depends on the partition of the region R into M number of rotated limited colatitude-longitude regions. The chosen partitioning of R using an optimal tiling of rotated limited colatitude-longitude regions is the field of finite-element analysis [42], [43] and is beyond the scope of the current work.…”

“…Another useful regions on the sphere is the limited colatitudelongitude region, defined as a Cartesian product of a range of colatitudes and longitudes. For example, limited colatitudelongitude regions appear in the following applications: the cosmic microwave background radiation observed from earth is approximately seen within a limited colatitude-longitude region [29], [30], often a signal of interest in geophysics such as magnetic or gravitational potential are considered between lines of co-latitude and longitude [31], the projection of a rectangular sound source in acoustics or light source in optics on the sphere forms a limited colatitude-longitude region on the sphere [32] and a limited colatitude-longitude region is used to describe possible angles of arrival in communications [33], [34]. As the limited colatitude-longitude region is widely applicable, it would be useful to have an analytical formulation for solving the Slepian problem in this region.…”