Gravity inversion in spherical coordinates using tesseroids

Post on 19-Jun-2015

245 views 1 download

Preview:

Click to see full reader

Tags:

description

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

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)

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)

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

single vs joint

Gravity inversion in spherical coordinates using tesseroids

Science

Transcript of Gravity inversion in spherical coordinates using tesseroids

Spherical Coordinates

EElleeccttrroommaaggnneettiicc TThheeoorryythegateacademy.com/files/wppdf/Electromagnetics.pdf · SL. No Cartesian Coordinates Cylindrical Coordinates Spherical Coordinates (a) Differential

Verification of Conduction Heat Transfer Equation in Spherical Coordinates

Matrix Method for Coordinates Transformationbrayebrookobservatory.org/BrayObsWebSite/BOOKS/matrix_method_r… · Matrix Method for Coordinates Transformation ... spherical trigonometry

Inversion of spherical means and the wave equation in even ...rakesh/RESEARCH/even-inversion.pdf · Inversion of spherical means and the wave equation in even dimensions. David Finch

14.3 Change of Variables, Polar Coordinates The equation for this surface is ρ= sinφ *cos(2θ) (in spherical coordinates)

10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates) Use cylindrical coordinates to represent surfaces in space Use spherical coordinates.

Inversion Formulas for Spherical Means in Constant ... · Inversion Formulas for Spherical Means in Constant Curvature Spaces Yu. Antipov, R. Estrada, B. Rubin (LSU) Workshop on Geometric

14.6 triple integrals in cylindrical and spherical coordinates

Chapter 15 – Multiple Integrals 15.9 Triple Integrals in Spherical Coordinates 1 Objectives: Use equations to convert rectangular coordinates to spherical.

Spherical coordinates - BU

3D#morphological#reconstruction## … · 2014. 8. 19. · PROJECTION PLANE COORDINATES spherical CTYPEia projection PVi_ma NATIVE SPHERICAL COORDINATES spherical coordinate CRVALia

Cylindrical and Spherical Coordinates System

Spherical Coordinates - MATH 311, Calculus IIIbanach.millersville.edu/~bob/math311/Spherical/main.pdf · Spherical Coordinates MATH 311, Calculus III J. Robert Buchanan Department

PDEs in Spherical and Circular Coordinates

4.1 Schr odinger Equation in Spherical Coordinates

Connection to Laplacian in spherical coordinates (Chapter 13)schellin/teaching/phz3113_2011/... · 2011-04-11 · Connection to Laplacian in spherical coordinates (Chapter 13) We

Math 213 - Triple Integrals in Spherical Coordinatesperry/213-f19-perry/_assets/lectures/lec_27_15_8.… · Learning Goals Spherical Coordinates Triple Integrals in Spherical Coordinates

Triple Integrals in Cylindrical and Spherical Coordinates · MTH 254 LESSON 20. TRIPLE INTEGRALS IN CYLINDRICAL AND SPHERICAL COORDINATES 20.3 Applications of Triple Integrals Example

Path Integrals in Polar and Spherical Coordinates