Limits...
High-resolution local gravity model of the south pole of the Moon from GRAIL extended mission data.

Goossens S, Sabaka TJ, Nicholas JB, Lemoine FG, Rowlands DD, Mazarico E, Neumann GA, Smith DE, Zuber MT - Geophys Res Lett (2014)

Bottom Line: Our solution consists of adjustments with respect to a global model expressed in spherical harmonics.We apply a neighbor-smoothing constraint to our solution.Our local model removes striping present in the global model; it reduces the misfit to the KBRR data and improves correlations with topography to higher degrees than current global models.

View Article: PubMed Central - PubMed

Affiliation: CRESST, University of Maryland Baltimore County Baltimore, Maryland, USA ; NASA Goddard Space Flight Center Greenbelt, Maryland, USA.

ABSTRACT

: We estimated a high-resolution local gravity field model over the south pole of the Moon using data from the Gravity Recovery and Interior Laboratory's extended mission. Our solution consists of adjustments with respect to a global model expressed in spherical harmonics. The adjustments are expressed as gridded gravity anomalies with a resolution of 1/6° by 1/6° (equivalent to that of a degree and order 1080 model in spherical harmonics), covering a cap over the south pole with a radius of 40°. The gravity anomalies have been estimated from a short-arc analysis using only Ka-band range-rate (KBRR) data over the area of interest. We apply a neighbor-smoothing constraint to our solution. Our local model removes striping present in the global model; it reduces the misfit to the KBRR data and improves correlations with topography to higher degrees than current global models.

Key points: We present a high-resolution gravity model of the south pole of the Moon Improved correlations with topography to higher degrees than global models Improved fits to the data and reduced striping that is present in global models.

No MeSH data available.


Related in: MedlinePlus

Maps in stereographic projection centered at the south pole for (a and b) free-air anomalies (up to 50°) and (c and d) Bouguer disturbances (up to 70°S). The local model is shown in Figure 1a, the difference between the local model and GRGM900A is shown in Figure 1b, GRGM900A (l = 7–900) is shown in Figure 1c, and a spherical harmonic transform of the local model (l = 7–900) is shown in Figure 1d.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4459178&req=5

fig01: Maps in stereographic projection centered at the south pole for (a and b) free-air anomalies (up to 50°) and (c and d) Bouguer disturbances (up to 70°S). The local model is shown in Figure 1a, the difference between the local model and GRGM900A is shown in Figure 1b, GRGM900A (l = 7–900) is shown in Figure 1c, and a spherical harmonic transform of the local model (l = 7–900) is shown in Figure 1d.

Mentions: Once the partial derivatives of the data with respect to all parameters are generated, the normal equation system is formed. Due to the size of the problem, we use the supercomputers of the NASA Center for Climate Simulation (NCCS) at NASA GSFC. We apply a neighbor-smoothing constraint to our solutions following Rowlands et al. [2010] and Sabaka et al. [2010]. These spatial constraints are straightforward: each anomaly pair is forced to be equal, but each constraint equation is only given a weight Wc,ij that decreases with increasing distance between the ith and jth anomalies, according to Wc,ij= exp(1 − dij/D) with dij being the distance between the two anomalies (computed from their center points), and D being the correlation distance, which was here set equal to the latitudinal size of each grid cell (which is thus the same for all anomalies because the grid is regular). We discuss these constraints further in section 3. We apply the smoothing constraint to the full anomaly field, i.e., on Δgglobal+Δgadj where Δgglobal is the vector with anomalies corresponding to the global spherical harmonics starting model and Δgadj is the vector with gravity anomalies for the adjustment. We apply the constraint to the full field (not just to the estimated gravity anomaly parameters) because the anomalies from GRGM900A show stripes (cf. Figure S1 in the supporting information). Once the constraint system is formed, it is added to the data system with a scaling factor μ, resulting in the following equation:2where Ais the matrix with the partial derivatives of the data with respect to the parameters, Wd is the data weight matrix, Dis the matrix with partial derivatives of the constraints, Wc the constraint weight matrix with elements Wc,ij as defined above, rd is the vector with data residuals, and rc is the vector with constraint residuals which is expressed as rc=−DΔgglobal. The partial derivatives A and the data residuals rd are evaluated using orbits determined with the global field GRGM900A. The anomalies for the global field are computed from its spherical harmonics expansion. The baseline parameters are not included in Δgadj but are accounted for by a modification of the data weight matrix Wd (by taking into account their Schur complement), following Sabaka et al. [2010]. The baseline parameters are unconstrained and free to adjust.


High-resolution local gravity model of the south pole of the Moon from GRAIL extended mission data.

Goossens S, Sabaka TJ, Nicholas JB, Lemoine FG, Rowlands DD, Mazarico E, Neumann GA, Smith DE, Zuber MT - Geophys Res Lett (2014)

Maps in stereographic projection centered at the south pole for (a and b) free-air anomalies (up to 50°) and (c and d) Bouguer disturbances (up to 70°S). The local model is shown in Figure 1a, the difference between the local model and GRGM900A is shown in Figure 1b, GRGM900A (l = 7–900) is shown in Figure 1c, and a spherical harmonic transform of the local model (l = 7–900) is shown in Figure 1d.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4459178&req=5

fig01: Maps in stereographic projection centered at the south pole for (a and b) free-air anomalies (up to 50°) and (c and d) Bouguer disturbances (up to 70°S). The local model is shown in Figure 1a, the difference between the local model and GRGM900A is shown in Figure 1b, GRGM900A (l = 7–900) is shown in Figure 1c, and a spherical harmonic transform of the local model (l = 7–900) is shown in Figure 1d.
Mentions: Once the partial derivatives of the data with respect to all parameters are generated, the normal equation system is formed. Due to the size of the problem, we use the supercomputers of the NASA Center for Climate Simulation (NCCS) at NASA GSFC. We apply a neighbor-smoothing constraint to our solutions following Rowlands et al. [2010] and Sabaka et al. [2010]. These spatial constraints are straightforward: each anomaly pair is forced to be equal, but each constraint equation is only given a weight Wc,ij that decreases with increasing distance between the ith and jth anomalies, according to Wc,ij= exp(1 − dij/D) with dij being the distance between the two anomalies (computed from their center points), and D being the correlation distance, which was here set equal to the latitudinal size of each grid cell (which is thus the same for all anomalies because the grid is regular). We discuss these constraints further in section 3. We apply the smoothing constraint to the full anomaly field, i.e., on Δgglobal+Δgadj where Δgglobal is the vector with anomalies corresponding to the global spherical harmonics starting model and Δgadj is the vector with gravity anomalies for the adjustment. We apply the constraint to the full field (not just to the estimated gravity anomaly parameters) because the anomalies from GRGM900A show stripes (cf. Figure S1 in the supporting information). Once the constraint system is formed, it is added to the data system with a scaling factor μ, resulting in the following equation:2where Ais the matrix with the partial derivatives of the data with respect to the parameters, Wd is the data weight matrix, Dis the matrix with partial derivatives of the constraints, Wc the constraint weight matrix with elements Wc,ij as defined above, rd is the vector with data residuals, and rc is the vector with constraint residuals which is expressed as rc=−DΔgglobal. The partial derivatives A and the data residuals rd are evaluated using orbits determined with the global field GRGM900A. The anomalies for the global field are computed from its spherical harmonics expansion. The baseline parameters are not included in Δgadj but are accounted for by a modification of the data weight matrix Wd (by taking into account their Schur complement), following Sabaka et al. [2010]. The baseline parameters are unconstrained and free to adjust.

Bottom Line: Our solution consists of adjustments with respect to a global model expressed in spherical harmonics.We apply a neighbor-smoothing constraint to our solution.Our local model removes striping present in the global model; it reduces the misfit to the KBRR data and improves correlations with topography to higher degrees than current global models.

View Article: PubMed Central - PubMed

Affiliation: CRESST, University of Maryland Baltimore County Baltimore, Maryland, USA ; NASA Goddard Space Flight Center Greenbelt, Maryland, USA.

ABSTRACT

: We estimated a high-resolution local gravity field model over the south pole of the Moon using data from the Gravity Recovery and Interior Laboratory's extended mission. Our solution consists of adjustments with respect to a global model expressed in spherical harmonics. The adjustments are expressed as gridded gravity anomalies with a resolution of 1/6° by 1/6° (equivalent to that of a degree and order 1080 model in spherical harmonics), covering a cap over the south pole with a radius of 40°. The gravity anomalies have been estimated from a short-arc analysis using only Ka-band range-rate (KBRR) data over the area of interest. We apply a neighbor-smoothing constraint to our solution. Our local model removes striping present in the global model; it reduces the misfit to the KBRR data and improves correlations with topography to higher degrees than current global models.

Key points: We present a high-resolution gravity model of the south pole of the Moon Improved correlations with topography to higher degrees than global models Improved fits to the data and reduced striping that is present in global models.

No MeSH data available.


Related in: MedlinePlus