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Download file# Slides: A better strategy for interpolating gravity and magnetic data

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posted on 02.05.2020, 15:13 authored by Santiago Rubén SolerSantiago Rubén Soler, Leonardo UiedaLeonardo UiedaWe present a new strategy for defining the location of point sources when
applying the equivalent sources technique (EQL) for interpolating gravity and
magnetic data. It consist in reducing the number of sources while keeping the
same accuracy when compared with similar EQL methods. It also reduces the
computation time and memory requirements, both of which have been severe
limiting factors.

The equivalent layer technique (also known as equivalent source, radial basis
functions, or Green’s functions interpolation) is used to predict the value of
gravity and magnetic fields (or transformations thereof) at any point based on
the data gathered on some observation points. It consists in estimating
a source distribution that produces the same field as the one measured and
using this estimate to predict new values. It generally outperforms other
general-purpose 2D interpolators, like the minimum curvature or bi-harmonic
splines, because it takes into account the height of measurements and the fact
that these fields are harmonic functions. Nevertheless, defining a layout for
the source distribution used by the EQL is not trivial and plays an important
role in the quality of the predictions.

The most widely used source distributions are: (a) a regular grid of point
sources and (b) one point source beneath each observation point. We propose
a new source distribution: (c) divide the area into blocks, calculate the
average location of observation points inside each block, and place one point
source beneath each average location. This produces a smaller number of point
sources in comparison with the other source distributions, effectively reducing
the computational load. Traditionally, the source points are located: (i) all
at the same depth or (ii) each source point at a constant relative depth
beneath its corresponding observation point. Besides these two, we also
considered (iii) a variable depth for each source point proportional
to the median distance to its nearest neighbours. The combination of source
distributions and depth configurations leads to seven different source layouts
(the regular grid is only compatible with the constant depth configuration).

We have scored the performance of each configuration by interpolating synthetic
ground and airborne gravity data, and comparing the interpolation against the
true values of the model. The block-averaged source layout (c) with variable
relative depth (iii) produces accurate interpolation results when compared to
the other two, but reducing the computation time and memory requirements.
These results are consistent between ground and airborne survey layouts. Our
conclusions can be extrapolated to other applications of equivalent layers,
such as upward continuation, reduction-to-the-pole, and derivative calculation.
What is more, we expect that these optimizations can benefit similar spatial
prediction problems beyond gravity and magnetic data.

The source code developed for this study is based on the EQL implementation
available in Harmonica (fatiando.org/harmonica), an open-source Python library
for modelling and processing gravity and magnetic data.