4.2.3.4 Knowledge gained from spherical harmonic models

2005 ◽  
pp. 169-178
Author(s):  
D. Voppel
Keyword(s):  
Spherical Harmonic ◽  
Spherical Harmonic Models

Using isostatic gravity anomalies from spherical harmonic models and elastic plate compensation to interpret the lithosphere of the Bolivian Andes

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. G41-G53 ◽  
Author(s):  
Christopher Jekeli ◽  
Hyo Jin Yang ◽  
Kevin Ahlgren
Keyword(s):  
Spherical Harmonic ◽  
Flexural Rigidity ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Surface Gravity ◽  
Bolivian Andes ◽  
Isostatic Gravity Anomalies ◽  
Isostatic Gravity ◽  
Spherical Harmonic Models ◽  
Surface Gravity Data

We have determined for the Bolivian Andes that the new global gravity models derived from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission may be used directly to study lithospheric structure. Toward this end, we have formulated Bouguer and isostatic gravity anomalies in spherical approximation, rather than in the usual planar approach, using spherical harmonic series consistent with the satellite-derived gravitational models. From the approximate equivalency of topographic masses and surface density layers using the Helmert condensation method we further derived and used isotropic transfer relations between the spherical spectra of topographic loads and elastic spherical shell deflections, where the Airy isostatic compensation is the special case of no flexural rigidity. A numerical comparison of these spherical harmonic models to conventional three-dimensional modeling based on topographic data and newly acquired surface gravity data in Bolivia confirmed their suitability for lithospheric interpretation. Specifically, the relatively high and uniform resolution of the satellite gravitational model (better than 83 km) produces detailed maps of the isostatic anomaly that clearly delineate the flexure of the Brazilian shield that is thrust under the Sub-Andes. Inferred values of the thickness of Airy-type roots and the flexural rigidity of the elastic lithosphere agree reasonably with published results based on seismic and surface gravity data. In addition, a local minimum in the flexural rigidity is evident at the sharp bend of the eastern margins of the Sub-Andes in Bolivia. This feature is consistent with earlier theories for counter rotations about a vertical axis at this minimum, associated with the confluence of the subducted Nazca plate and the Brazilian craton. The GOCE model thus generates high-resolution isostatic anomaly maps that offer additional structural detail not seen as clearly from previous seismic and gravity investigations in this region.

Harmonic analysis of surface instability patterns on colloidal particles

Soft Matter ◽  
2018 ◽  
Vol 14 (17) ◽  
pp. 3387-3396 ◽  
Author(s):  
Tero Kämäräinen ◽  
Mariko Ago ◽  
Jani Seitsonen ◽  
Janne Raula ◽  
Esko I. Kauppinen ◽  
...  
Keyword(s):  
Harmonic Analysis ◽  
Spherical Harmonic ◽  
Colloidal Particles ◽  
Colloidal Particle ◽  
Electron Tomography ◽  
Surface Instability ◽  
Cryo Electron Tomography ◽  
Spherical Harmonic Models ◽  
Topographical Analysis

Spectral topographical analysis of wrinkled and crumpled colloidal particle surfaces utilizing cryo-electron tomography and spherical harmonic models.

High-resolution GRACE Monthly Gravity Field Solutions Expressed as Geopotential Coefficients

2021 ◽  
Author(s):  
Qiujie Chen ◽  
Jürgen Kusche ◽  
Yunzhong Shen ◽  
Xingfu Zhang
Keyword(s):  
High Resolution ◽  
Gravity Field ◽  
Spatial Resolution ◽  
Spherical Harmonic ◽  
Regularization Method ◽  
A Priori ◽  
Spatial Constraints ◽  
Spherical Harmonic Models ◽  
Priori Information ◽  
Geopotential Coefficients

<p>The commonly used filters (e.g. Gaussian smoothing, decorrelation and DDK filtering) applied to GRACE spherical harmonic gravity field solutions generally lead to reduced resolution, signal damping and leakage. This work is dedicated to improving spatial resolution and reducing signal damping by developing a regularization method with spectral constraints to spherical harmonics. Before constructing the spectral constraints, we create spatial constraints over global grids (covering lands, oceans and the boundaries between lands and oceans) from the a priori information of GRACE spherical harmonic models. Since we are solving geopotential coefficients rather than mascon grids, we further transfer the spatial constraints into the spectral domain according to the law of variance-covariance propagation, leading to spectral constraints regarding geopotential coefficients. In our work, the regularization method with spectral constraints was demonstrated to have comparable ability as mascon modelling method to enhance the spatial resolution and signal power besides reducing signal leakage. Applying the presented method with spatial constraints, we produced the first time series of high-resolution gravity field solutions expressed as geopotential coefficients complete to degree and order 180. Our analyses over the global and regional areas show that our high-resolution solutions are in good agreement with CSR and JPL mascon solutions.</p>

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