Gravity inversion in spherical coordinates using tesseroids
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Gravity inversion in spherical coordinates using tesseroids Leonardo Uieda Valéria C. F. Barbosa
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Leonardo Uieda and Valéria C. F. Barbosa Satellite observations of the gravity field have provided geophysicists with exceptionally dense and uniform coverage of data over vast areas. This enables regional or global scale high resolution geophysical investigations. Techniques like forward modeling and inversion of gravity anomalies are routinely used to investigate large geologic structures, such as large igneous provinces, suture zones, intracratonic basins, and the Moho. Accurately modeling such large structures requires taking the sphericity of the Earth into account. A reasonable approximation is to assume a spherical Earth and use spherical coordinates. In recent years, efforts have been made to advance forward modeling in spherical coordinates using tesseroids, particularly with respect to speed and accuracy. Conversely, traditional space domain inverse modeling methods have not yet been adapted to use spherical coordinates and tesseroids. In the literature there are a range of inversion methods that have been developed for Cartesian coordinates and right rectangular prisms. These include methods for estimating the relief of an interface, like the Moho or the basement of a sedimentary basin. Another category includes methods to estimate the density distribution in a medium. The latter apply many algorithms to solve the inverse problem, ranging from analytic solutions to random search methods as well as systematic search methods. We present an adaptation for tesseroids of the systematic search method of "planting anomalous densities". This method can be used to estimate the geometry of geologic structures. As prior information, it requires knowledge of the approximate densities and positions of the structures. The main advantage of this method is its computational efficiency, requiring little computer memory and processing time. We demonstrate the shortcomings and capabilities of this approach using applications to synthetic and field data. Performing the inversion of gravity and gravity gradient data, simultaneously or separately, is straight forward and requires no changes to the existing algorithm. Such feature makes it ideal for inverting the multicomponent gravity gradient data from the GOCE satellite. An implementation of our adaptation is freely available in the open-source modeling and inversion package Fatiando a Terra (http://www.fatiando.org).
Transcript of Gravity inversion in spherical coordinates using tesseroids
Gravity inversion
in spherical coordinates
using tesseroids
Leonardo Uieda
Valéria C. F. Barbosa
vs
Cartesian Spherical
Existing inversion with tesseroids
(Chaves and Ussami, 2013)
● Geoid height anomalies● Space domain● Regularization:
– Depth-weighted Minimum Volume– Similarity to seismic tomography
AdaptPlanting anomalous densities
(Uieda and Barbosa, 2012)
Planting anomalous densities
● Space domain● Multicomponent: gravity + gradients● Non-conventional inversion
– Growth algorithm– No linear systems– Efficient sensitivity computations
Seed
Synthetics● Possible applications● Advantages● Shortcomings
Lineament with dense rocks (magmatic)
Inspired by Chad lineament model (Braitenberg et al, 2011)
After Braitenberg et al (2011)
After Braitenberg et al (2011)
10ºN
300 kg.m-3
2º
8km
top=1 km
gzz
At 20 km
Seeds
observed predicted
What if height=120 km?
at 120 kmat 20 km
observed predicted
at 120 kmat 20 km
Even higher
height=270 km
at 270 kmat 120 km
observed predicted
at 270 kmat 120 km
Magmatic underplatingInspired by model of the Paraná basin
by Mariani et al (2013)
After Mariani et al (2013)
After Mariani et al (2013)
10º
N 200 kg.m-3
15 km
5º
10ºtop=30 km
gzz at 250 km
Seed
What if I use wrong density?
150 kg.m-3
250 kg.m-3
In conclusion
for tesseroids
Works well
height matters
20km 250km
correct
dense
correct
dense
Future
● Combinations of tensor components
● Dipping sources (subducting plate)
● Real data (open for collaboration)
OPEN SOURCE
fatiando.org
github.com/leouieda/egu2014
Extra
(Hypothetical) Mantle Plume
Inspired by synthetics in Chaves and Ussami (2013)
After Chaves and Ussami (2013)
top=100 km
200 km
700 km
2º
-50 kg.m-3
gzz at 250 km
Seed
Joint gz + gzz?
Same seed
gzgzz
gzz Joint
gzz Joint
single vs joint
