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Santiago Soler

Background

Past research

Gravitational fields in
spherical coordinates

Tesseroids

a.k.a. spherical prisms

Tesseroids' gravitational fields:

$$ V(\mathbf{p}) = G \rho \iiint_V \frac{\kappa}{\left\lVert \mathbf{p} - \mathbf{q} \right\rVert} \text{d} r' \text{d} \lambda' \text{d} \phi' $$

no analytical solution

Tesseroids

a.k.a. spherical prisms

Solution:
Numerical approximations

$$ V(\mathbf{p}) \cong G \rho A \sum\limits_{i=1}^{N_r} \sum\limits_{j=1}^{N_\lambda} \sum\limits_{k=1}^{N_\phi} W_{ijk} \frac{\kappa_{ik}}{\left\lVert \mathbf{p} - \mathbf{q}_{ijk} \right\rVert} $$

Constant density tesseroids

$$ V(\mathbf{p}) = G {\color{#e4564a}{\rho}} \iiint_V \frac{\kappa}{\left\lVert \mathbf{p} - \mathbf{q} \right\rVert} \text{d} r' \text{d} \lambda' \text{d} \phi' $$

Variable density tesseroids

$$ V(\mathbf{p}) = G \iiint_V {\color{#e4564a}{\rho(r')}} \frac{\kappa}{\left\lVert \mathbf{p} - \mathbf{q} \right\rVert} \text{d} r' \text{d} \lambda' \text{d} \phi' $$

Developed new method

  • Gravitational fields of variable density tesseroids
  • Density: continuous function of depth
  • Open-source Python implementation

Developed new method

  • Gravitational fields of variable density tesseroids
  • Density: continuous function of depth
  • Open-source Python implementation

from numba import njit
import harmonica as hm

@njit
def linear_density(radius):
    origin, slope = ...
    return slope * radius  + origin

gravity = hm.tesseroid_gravity(
    coordinates, tesseroids, linear_density, field="g_z"
)

Soler et al. (2019). doi: 10.1093/gji/ggz277

Preprint: 10.31223/osf.io/3548g

Gradient-boosted equivalent sources

Equivalent sources

Equivalent sources

  • Always produce harmonic fields
  • Consider the observation heights

THE PROBLEM

Require too much computational load

  • 200.000 data points
  • + 200.000 equivalent sources
  • = ~300GB RAM

THE SOLUTION

Gradient-boosted equivalent sources

  • Interpolate very large datasets
  • Significant reduction in required memory
  • Open-source Python implementation

THE SOLUTION

Gradient-boosted equivalent sources

  • Interpolate very large datasets
  • Significant reduction in required memory
  • Open-source Python implementation

import verde as vd
import harmonica as hm

eqs = hm.EquivalentSourcesGB(
    depth=depth, damping=damping, window_size=window_size
)
eqs.fit(coordinates, data)

grid_coords = vd.grid_coordinates(
    region, spacing, extra_coords=height
)
grid = eqs.grid(grid_coords)

Gridding +1.7 million gravity data points

Gridding +1.7 million gravity data points

Soler and Uieda (2021). doi: 10.1093/gji/ggab297

Preprint: 10.31223/X58G7C

Open-source software development

The libraries

Verde

Spatial data processing and interpolation with a Machine Learning flavour

Boule

Reference ellipsoids and normal gravity calculations

Harmonica

Processing and modelling potential fields data

Pooch

A friend to download and cache your data

Who we are

Who is using Fatiando?

Research and open-source software

Research and open-source software

Current research

Carbon mineralization

Serpentinization

Carbonation

  • Serpentinized rocks react with CO2
  • Mineralize in carbonated rocks
  • Carbon sequestration with ultramafic rocks

Cutts et al. (2021). doi: 10.1029/2021GC009989

Mitchinson et al., (2020). ISBN: 978-0-88865-470-0

Physical properties

Density and susceptibility change with alteration

Research opportunity:

Geophysical inversion for assessing
carbonation potential

Goals

  • Gravity + magnetic data
  • 3D joint inversions
  • Characterize volume and depth of rocks with carbonation potential

Contact

Muchas gracias | Thank you

Slides: www.santisoler.com/2022-ubc-open-house

These slides are available under a
Creative Commons Attribution 4.0 International License