The use of degree variances in satellite gradiometry

Gelderen, Martin van; Koop, R.

doi:10.1007/s001900050101

Cited by 42 publications

(18 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The first regularization matrix N PG serves for the stabilization of the coefficients affected by the polar gap (near‐zonal coefficients), whose entries are

{boldN}_{PG} (i, i) = 1 0^{10} l^{4}, if m < m_{\max} = ⌈ θ_{0} l ⌉

where m is the SH order and l the SH degree of the parameter associated with the position i in the parameter vector x . The maximal order affected by the polar gap [ van Gelderen and Koop , ] is m max and θ 0 is the opening angle of the polar gap in radians (≈0.11 for GOCE).…”

Section: Used Methods and Used Datamentioning

confidence: 99%

“…where m is the SH order and l the SH degree of the parameter associated with the position i in the parameter vector x. The maximal order affected by the polar gap [van Gelderen and Koop, 1997] is m max and 0 is the opening angle of the polar gap in radians (≈ 0.11 for GOCE).…”

Section: Stochastic Prior Informationmentioning

confidence: 99%

“…On the other hand, some combined gravity field models which include GOCE data are available. These either include observations from other satellites such as Challenging Minisatellite Payload [Reigber et al, 2002], GRACE (Gravity Recovery and Climate Experiment) [Tapley et al, 2004], satellites tracked by laser measurements (SLR), or they include additional terrestrial and altimetry observations. These are the official ESA models based on the direct approach [Pail et al, 2011a;Bruinsma et al, 2013Bruinsma et al, , 2014 and the closely related EIGEN series, produced by the same team [Förste et al, 2008;Shako et al, 2014].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

EGM_TIM_RL05: An independent geoid with centimeter accuracy purely based on the GOCE mission

Brockmann

Zehentner

Höck

et al. 2014

Geophysical Research Letters

146

View full text Add to dashboard Cite

After more than 4.5 years in orbit, the Gravity field and steady‐state Ocean Circulation Explorer (GOCE) mission ended with the reentry of the satellite on 11 November 2013. This publication serves as a reference for the fifth gravity field model based on the time‐wise approach (EGM_TIM_RL05), a global model only determined from GOCE observations. Due to its independence of any other gravity data, a consistent and homogeneous set of spherical harmonic coefficients up to degree and order 280 (corresponding to spatial resolution of 71.5 km on ground) is provided including a full covariance matrix characterizing the uncertainties of the model. The associated covariance matrix realistically describes the model quality. It is the first model which is purely based on GOCE including all observations collected during the entire mission. The achieved mean global accuracy is 2.4 cm in terms of geoid heights and 0.7 mGal for gravity anomalies at a spatial resolution of 100 km.

show abstract

“…The first regularization matrix N PG serves for the stabilization of the coefficients affected by the polar gap (near‐zonal coefficients), whose entries are

{boldN}_{PG} (i, i) = 1 0^{10} l^{4}, if m < m_{\max} = ⌈ θ_{0} l ⌉

Section: Used Methods and Used Datamentioning

confidence: 99%

Section: Stochastic Prior Informationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

EGM_TIM_RL05: An independent geoid with centimeter accuracy purely based on the GOCE mission

Brockmann

Zehentner

Höck

et al. 2014

Geophysical Research Letters

146

View full text Add to dashboard Cite

show abstract

“…Nevertheless, we use this example because it is simple and informative, and it has been studied by others before. 14,19 If, for simplicity we assume that both signal and noise have a white power spectrum, the spectral error covariance matrix is…”

Section: Sparsity Of Errors In Approximationmentioning

confidence: 99%

Efficient analysis and representation of geophysical processes using localized spherical basis functions

2009

View full text Add to dashboard Cite

While many geological and geophysical processes such as the melting of icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or the surface displacement remaining after large earthquakes are spatially localized, many of these naturally admit spectral representations, or they may need to be extracted from data collected globally, e.g. by satellites that circumnavigate the Earth. Wavelets are often used to study such nonstationary processes. On the sphere, however, many of the known constructions are somewhat limited. And in particular, the notion of 'dilation' is hard to reconcile with the concept of a geological region with fixed boundaries being responsible for generating the signals to be analyzed. Here, we build on our previous work on localized spherical analysis using an approach that is firmly rooted in spherical harmonics. We construct, by quadratic optimization, a set of bandlimited functions that have the majority of their energy concentrated in an arbitrary subdomain of the unit sphere. The 'spherical Slepian basis' that results provides a convenient way for the analysis and representation of geophysical signals, as we show by example. We highlight the connections to sparsity by showing that many geophysical processes are sparse in the Slepian basis.Keywords: spectral analysis, spherical harmonics, statistical methods, geodesy, inverse theory, satellite geodesy, sparsity, earthquakes, geomagnetism THE SPHERICAL SLEPIAN BASISWe denote the colatitude of a geographical pointr on the unit sphere surface Ω = {r : r = 1} by 0 ≤ θ ≤ π and the longitude by 0 ≤ φ < 2π. We use R to denote a region of Ω, of area A, within which we seek to concentrate a bandlimited function of positionr = (θ, φ). We use orthonormalized real surface spherical harmonics, 1, 2 thus expressing a square-integrable real function f (r) on the surface of the unit sphere asThe Slepian basis for the domain R is the collection of bandlimited functionsMaximizing equation (2) leads to the spectral-domain Hermitian, positive-definite eigenvalue equationbut we may equally well rewrite eq. (3) as a spatial-domain eigenvalue equation:where P l is the Legendre function of integer degree l, which arises in this setting as a consequence of the spherical harmonic addition theorem. 1-3Eq. (4) is a homogeneous Fredholm integral equation of the second kind, with arXiv:0909.5403v1 [physics.geo-ph]

show abstract

“…Since the launch of the CHAllenging Minisatellite Payload mission (CHAMP, Reigber et al, 1998) GPS sensors are not only used as a key tracking system for precise orbit determination (POD) but also for extracting the long wavelength part of the Earth's static gravity field (Reigber et al, 2003). Although current gravity missions such as the Gravity Recovery And Climate Experiment (GRACE, Tapley et al, 2004) and the Gravity field and steady-state Ocean Circulation Explorer (GOCE, Drinkwater et al, 2006) are equipped with other core instruments, they still make use of the GPS high-low Satellite-to-Satellite Tracking (hl-SST) to support the determination of the low degree spherical harmonic (SH) coefficients of the Earth's gravity field. In the case of GOCE these coefficients are even exclusively determined from GPS data as the measurements of the core instrument, the three-axis gravity gradiometer, are band-limited (Pail et al, 2006).…”

Section: Introductionmentioning

confidence: 99%