manconi pres

7/30/2019 Manconi Pres

1/19

IIstituto per il RRilevamento

Andrea ManconiAndrea Manconi

EElettromagnetico dell'AAmbiente

Consiglio Nazionale delle RicercheConsiglio Nazionale delle Ricerche

. . .. . .

SSimulatedimulated AAnnealing andnnealing and GGeneticenetic AAlgorithmlgorithmOptimization using COMSOL Multiphysics:Optimization using COMSOL Multiphysics:

Applications to the Analysis of GroundApplications to the Analysis of GroundDeformation in Active Volcanic AreasDeformation in Active Volcanic Areas

Presented at the COMSOL Conference 2009 Milan


2/19

Intro: Volcano geodesy

SA and GA optimization within COMSOL

Application to Tenerife, Canary Islands


3/19

Surface displacementSurface displacement

www.geo.ua.edu/www.geo.ua.edu/

p m za on o ourcep m za on o ourceparametersparametersMain problemsMain problems

ResultsResults

location, volume change, shape, etc.location, volume change, shape, etc.

-- ..

GB, RS, SA, GA...GB, RS, SA, GA...

-- Forward model:Forward model:

Analytical vs. FEMAnalytical vs. FEM


4/19

Optimization with gradientOptimization with gradient--based algorithmsbased algorithms

f(x)Misfit = Modeled vs. Observed

Move down-hill might be trapped in local minima

Solution depends on the initial guess a priori constraints!


5/19

Optimization with Monte Carlo algorithmsOptimization with Monte Carlo algorithms

f(x)Misfit = Modeled vs. Observed

Randomness allows escaping from local minima

Simulated annealing and Genetic Algorithm belong to this class


6/19

Simulated Annealing (Kirkpatrick et al., 1983)Simulated Annealing (Kirkpatrick et al., 1983)

Based on analogy with annealing in metallurgy

Lowering Temp solutions with lower cost are favored

J. Vandekerckhove, (2006)Matlab implementation of SAavailable at http://www.mathworks.com


7/19

Genetic Algorithm (Holland,Genetic Algorithm (Holland, 19751975))

Based on analogy with biological evolution

Best-fit model selection after max generations

K. Burjorjee, (2007)Matlab implementation of GA

http://www.mathworks.com


8/19

Standard forward models in Volcano GeodesyStandard forward models in Volcano Geodesy

Sim lified eometr

Homogeneous half-space

as c ma er a proper es

Complex sources shapes

Heterogeneities

properties


9/19

FEM in Volcano GeodesyFEM in Volcano Geodesy

Comsol

Advantages: Disadvanta es: Complex geometries

Material heterogeneities

Computationally expansive

Poor constraints for

Multi-physics simulation subsurface properties


10/19

Application: Tenerife, Canary IslandsApplication: Tenerife, Canary Islands

Fernandez et al., 2008

Surface deformation from space geodesy (1992-2006)

Interpretation: gravitational loading due to denser core


11/19

A priori information: Density structureA priori information: Density structure

Gottsmann et al., 2008

Micro-gravity measurements

Constrain the inner structure

up a FE model and optimize

for the best distribution ofviscosities explaining the

observed deformation


12/19

COMSOL: Model setupCOMSOL: Model setup

P=0

Incompressible Navier-Stokes

Density is a function

rho(r,z), constrained by theBody load,

Fz=rho r z * *z

eta(r,z) with SA and GA


13/19

Results: Tenerife viscosity structureResults: Tenerife viscosity structure

Lateral heterogeneousvi i i ri i n iv

a better fit of the

deformation data

compared with

homogeneous and/or

layered structure!


14/19

Summary & Future workSummary & Future work

Implementation of optimization using SA and GA withCOMSOL

Possibility to use more complex forward models allows for amore accurate analysis of deformation at volcanoes: exampleof Tenerife

-

Straightforward extension to 3-D models


15/19

Thermal evolution of CF caldera

FEM


16/19

3-D Case: Campi Flegrei caldera

3-D Seismic tomography

Chiarabba et al., 2006


17/19

ComplexitiesComplexities,

Spain

Skaergaard,Greenland


18/19

Satellite geodesy: DInSAR Scenario

www.geology.wisc.edu

22

_

losddl

Centimetric displacements can be measured in over large areas!


19/19

Numerical inversion within FE modelsNumerical inversion within FE models

Implementation of complex shapes,Implementation of complex shapes,

,,effects, multiphysics environmenteffects, multiphysics environment

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