вторник, 13 ноября 2018 г.

Pearson correlation between spatial harmonics of free-air gravity anomaly on the Earth's surface and the Earth's topography is almost 1

Link: https://www.linkedin.com/pulse/pearson-correlation-between-spatial-harmonics-gravity-pechnikov/


We consider Free-air gravity anomaly and ETOPO1 topography in WGM2012 Earth's gravity anomalies datasets (see references below).

There is high correlation (0.80) between topography and free air gravity for small areas only:


For relatively large areas the correlation is low (0.41) but the scatter plot looks strange. Let's decompose in spatial domain the topography and the free air gravity and check the spatial harmonics. Pixel resolution of these datasets is about 3.7km. For spatial band pass pixel-wise filters 1-4px, 4-8px, 8-12px, 12-16px, 16-20px we have spatial scales 3.7-14.8km, and so on.


We see on the pictures above that the correlation between the same spatial harmonics of topography and free air gravity is very high for as small as large areas. In fact we have the same results by all spatial harmonics based methods on topography and free air gravity. For example there is well-known Saxov-Nygaard method where concentric circles mean the spatial harmonics (Saxov, Nygaard, 1953). Also we provide our technology to restoring the density gradient of the geological environment from the high-frequency component of the gravitational field or topography data.

References:

1. WGM2012 global model: WGM2012 Earth's gravity anomalies,

http://bgi.omp.obs-mip.fr/data-products/Grids-and-models/wgm2012

2. Saxov, S., & Nygaard, K. (1953). RESIDUAL ANOMALIES AND DEPTH ESTIMATION. GEOPHYSICS, 18(4), 913–928. doi:10.1190/1.1437945

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(C) Alexey Pechnikov aka MBG, mobigroup.ru