Build Super-resolution Gravity from GGMplus Free-Air Gravity Anomaly (200m) enhanced by SRTM topography (30m)

Important note: we use only cross-platform Open Source Software and Open Datasets for our publications. You can free download the used software and data.

Although we have high-accuracy global gravity model GGMplus suitable for regional analysis, we still require better resolution for local analysis. Below I provide a way to produce super high resolution gravity from the GGMplus gravity model enhanced by spatial spectrum components from SRTM topography 30m.

To start see links below to get the source datasets:

GGMplus (Global Gravity Model plus) is Open Gravity Acceleration dataset at ~200m resolution

NASA Shuttle Radar Topography Mission (SRTM) Version 3.0 Global 1 arc second Data Released over Asia and Australia

There is a significant difference between the gravity and the topography resolution:

Before we can operate with the datasets, we need to check spatial spectrums of the gravity and topography:

For practical usage we just need to know that for the GGMplus 2013 model, short-wavelengths (up to 10 km) of gravity acceleration calculated by the constant value of gravity field gradient and these are inversely proportional to SRTM topography (Hirt et al., 2013). To be exact, we can transfer 0-10km short-wavelengths spatial spectrum components and so WGM2012 Earth's Gravity Anomalies 2-arc-minute resolution (Balmino et al., 2011) is usable too (I use this one for regions where is no GGMplus data available). That's follows from the models basics and it's approved by correlogram above.

Scheme of the topographic potential in the context of global high-resolution gravity field modelling (Rexer, 2017).

And if you want drive deeper see the more detailed explanation I provided before:

The correlation between spatial spectrum components for global gravity models WGM2012 & GGMplus 2013 and global topography models ETOPO1 & SRTM 30

The picture above prove that there is almost 100% correlation between short-wavelength gravity anomalies and short-wavelength topography up to the gravity resolution limit (200m). Consequently, that's possible to transfer short-wavelength topography to gravity spectrum. The transferring spectral range should be up to 500m - 3000m where the correlogram is symmetric and correlation is almost 100%. This operation is easy enough although that's requires using the spectral components normalization. There are a lot of ways to do the normalization and I prefer moment-based (where mean value is a 1st moment of a distribution and standard deviation is a 2nd) approaches. For this processing we can select equality of value for a single cell (200m x 200m) of the gravity to the mean value for corresponding cells of the topography (30m x 30m) for transferred components. This is the resulting gravity with transferred short-wavelength spectral components in range 0-500m:

Also, we can use a more detailed DEM to produce much more detailed gravity. In case when we need to build ~1m gravity an ortho photo images and satellite pictures applicable in case when there is the high correlation between these and the gravity (it should be checked by correlogram as above before the processing). See also correlograms between gradient of an ortho photo images and satellite pictures and a gravity gradient. This works for many areas but it requires more complex processing to restore gravity from the produced super resolution gravity gradient.

And let me say about obvious but very important fact. Some kinds of spatial analysis are not sensitive to absolute values. As the example these are lineament analysis and Saxov-Nigaard method for restoring 3D density model. For them we can use the original topography and ortho-photos and satellite images filtered to remove uncorrelated (to gravity field) spectral components.

Update. I forgot to write about a satellite altimetry which I use together with WGM2012 Earth's Gravity Anomalies to produce a super-resolution gravity on a water surface. See

Using Cryosat-2 satellite altimeter data and Landsat-8 satellite imagery to identify oil and gas promising diapir structures on the Greece offshore

Update. This is the Python 3 source code (Jupyter notebook):

https://github.com/mobigroup/gis-snippets/blob/master/ggmplus2013_v4-super-resolution.ipynb

Update. There is the explanation why and when this approach works:

What in fact mean Bouguer and Free-Air Gravity Anomalies in terms of spatial spectrum?

Balmino, G., Vales, N., Bonvalot, S., & Briais, A. (2011). Spherical harmonic modelling to ultra-high degree of Bouguer and isostatic anomalies. Journal of Geodesy, 86(7), 499–520. doi:10.1007/s00190-011-0533-4

Hirt, C, S.J. Claessens, T. Fecher, M. Kuhn, R. Pail, M. Rexer (2013), New ultra-high resolution picture of 2 Earth's gravity field, Geophysical Research Letters, Vol 40, doi: 10.1002/grl.50838.

Rexer, M., 2017. Spectral Solutions to the Topographic Potential in the context of High-Resolution Global Gravity Field Modelling.