Computation of the Load Love Number and the Load Green¡?s Function for an Elastic and Spherically Symmetric Earth

Na, Sung-Ho; Baek, Ji-Hye

doi:10.3938/jkps.58.1195

Cited by 20 publications

(13 citation statements)

References 3 publications

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“…Installation and maintenance costs may make increases to the density of the GPS station network of the magnitude required infeasible. Moreover, at spatial scales up to ∼10s of km, near‐surface heterogeneity in rheological properties (e.g., between different rock types) can cause local variations in the solid Earth response to loading (Na & Baek, ; Wang et al, ). A one‐dimensional rheological model such as we use is insufficient to fully describe the Earth elastic response to loading at these fine spatial scales, limiting the benefit from adding stations in regions that are already well instrumented.…”

Section: Discussionmentioning

confidence: 99%

“…We used multiple calls to SPOTL to generate synthetic displacements at each station location for each of the 151 monthly load anomalies. Although we used SPOTL with a specific choice of rheological model (Gutenberg‐Bullen; Agnew, ), the vertical displacement response generated by most one‐dimensional models converges at load distances greater than ∼10 km (Na & Baek, ). Thus, the choice of rheological model is not critical to our analysis.…”

Section: Methodsmentioning

confidence: 99%

“…The land surface depresses in response to hydrologic loading from precipitation and rebounds, when unloading occurs through evaporation or runoff (Dong et al, ). The solid Earth response to loading is largest near a load, but extends beyond the boundaries of the load itself (Na & Baek, ). Therefore, displacement at each GPS station is an integrated response to loading at all distances.…”

Section: Introductionmentioning

confidence: 99%

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Accuracy of Snow Water Equivalent Estimated From GPS Vertical Displacements: A Synthetic Loading Case Study for Western U.S. Mountains

Enzminger

Small

Borsa

2018

Water Resources Research

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GPS monitoring of solid Earth deformation due to surface loading is an independent approach for estimating seasonal changes in terrestrial water storage (TWS). In western United States (WUSA) mountain ranges, snow water equivalent (SWE) is the dominant component of TWS and an essential water resource. While several studies have estimated SWE from GPS‐measured vertical displacements, the error associated with this method remains poorly constrained. We examine the accuracy of SWE estimated from synthetic displacements at 1,395 continuous GPS station locations in the WUSA. Displacement at each station is calculated from the predicted elastic response to variations in SWE from SNODAS and soil moisture from the NLDAS‐2 Noah model. We invert synthetic displacements for TWS, showing that both seasonal accumulation and melt as well as year‐to‐year fluctuations in peak SWE can be estimated from data recorded by the existing GPS network. Because we impose a smoothness constraint in the inversion, recovered TWS exhibits mass leakage from mountain ranges to surrounding areas. This leakage bias is removed via linear rescaling in which the magnitude of the gain factor depends on station distribution and TWS anomaly patterns. The synthetic GPS‐derived estimates reproduce approximately half of the spatial variability (unbiased root mean square error ∼50%) of TWS loading within mountain ranges, a considerable improvement over GRACE. The inclusion of additional simulated GPS stations improves representation of spatial variations. GPS data can be used to estimate mountain‐range‐scale SWE, but effects of soil moisture and other TWS components must first be subtracted from the GPS‐derived load estimates.

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Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Accuracy of Snow Water Equivalent Estimated From GPS Vertical Displacements: A Synthetic Loading Case Study for Western U.S. Mountains

Enzminger

Small

Borsa

2018

Water Resources Research

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“…It was found that a typhoon would result in several millimeters uplift in the Korean peninsula and so in other regions as well. We used the load Green's function calculated for the IASPEI Earth model (Na and Baek, 2011), because the physical properties of the Earth's crust and upper mantle around Korea is closer to that one. Unlike the Yellow Sea and the South China Sea (called 'South Sea' in Korea), the Korea-Japan Sea (called 'East Sea' in Korea) has narrow channels to outer open oceans, therefore, the 'inverted barometer' concept need to be used differently with treating the Korea-Japan Sea as a large lake.…”

Section: Discussionmentioning

confidence: 99%

“…As Farrell summarized in his article, the static deformation of flat Earth under surface loading has been well known pursuit called 'Boussinesq problem. ' Guo et al (2004) computed the load Green's function by using the PREM (Preliminary Earth Model) with some extended mathematical expressions, and Na & Baek (2011) did it by using the IASPEI Earth model and compared with former results. Two other quite elaborate works related are; i) inelastic load Green's function by Pagiatakis (1990), and ii) more realistic boundary condition in atmospheric loading treated by Guo et al (2004).…”

Section: Atmospheric Loading On the Earth's Surfacementioning

confidence: 99%

Effects of Earth's Atmosphere on Terrestrial Reference Frame : A Review

Na¹,

Cho²

2015

Geophysics and Geophysical Exploration

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지구 대기가 지구 기준계에 미치는 영향 : 기존 모델 분석 한국천문연구원Abstract: Displacement of the Earth's surface due to atmospheric loading has been recognized since a century years ago, and its accurate estimation is required in present day geodesy and surveying, particularly in space geodesy. Atmospheric load deformation in continental region can readily be calculated with the given atmospheric pressure field and the load Green's function, and, in near coastal area, approximate model is used for the calculation. The changes in the Earth's atmospheric circulation and the seasonal variation of atmospheric pressure on two hemispheres of the Earth are the each main causes of variation of the Earth's spin angular velocity and polar motion respectively. Wind and atmospheric pressure do the major role in other periodic and non-periodic perturbations of the positions in the Earth's reference frame and variations in the Earth's spin rotational state. In this reviewing study, the developments of related theories and models are summarized along with brief description of phenomena, and the geodetic perturbing effects of a hypothetical typhoon passing Korea are shown as an example. Finally related existing problems and further necessary studies are discussed in general.

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The sensitivity of surface mass loading displacement response to perturbations in the elastic structure of the crust and mantle

et al. 2016

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Surface mass loads generate a rich spectrum of deformation responses in the solid Earth that might be exploited to probe the material properties of the crust and mantle. Here we present a detailed examination of load‐induced surface displacements and their sensitivities to systematic perturbations in elastic Earth structure. We compute Love numbers and displacement load Green's functions (LGFs) by integrating the equations of motion for spheroidal deformation of a radially heterogeneous and self‐gravitating Earth. Sensitivity kernels are derived for individual Love numbers numerically using finite differences and quasi‐analytically using calculus of variations. We then generate sensitivity kernels for displacement LGFs by systematically perturbing the preliminary reference Earth model. We find that displacement LGFs are most sensitive to elastic structural perturbations within 500 km depth from the surface and for short source‐receiver distances. For separate perturbations to the shear modulus, bulk modulus, and density within the crust and mantle, the sensitivity kernels exhibit unique patterns, consistent with the possibility to constrain the parameters independently given a spatially distributed set of sufficiently accurate loading response observations. The sensitivity to density structure, however, is generally weak in comparison to elastic structure. We also examine the sensitivity of surface displacements caused by M2 ocean tidal loading (OTL) to systematic perturbations in the elastic moduli and density. Since OTL‐induced surface displacements are load and site dependent, we focus on high‐resolution profiles across Iceland as a case study. The sensitivity kernels constitute a key element in the formulation of the inverse problem with application to geodetic tomography.

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Computation of the Load Love Number and the Load Green¡?s Function for an Elastic and Spherically Symmetric Earth

Cited by 20 publications

References 3 publications

Accuracy of Snow Water Equivalent Estimated From GPS Vertical Displacements: A Synthetic Loading Case Study for Western U.S. Mountains

Accuracy of Snow Water Equivalent Estimated From GPS Vertical Displacements: A Synthetic Loading Case Study for Western U.S. Mountains

Effects of Earth's Atmosphere on Terrestrial Reference Frame : A Review

The sensitivity of surface mass loading displacement response to perturbations in the elastic structure of the crust and mantle

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