Inversion modelling of ground deformation data: local minimum and volcanic sources shape

Inversion modelling of ground deformation data: local minimum and volcanic sources shape Alessandro Spata XIX Brain Storming Day Dottorato di Ricerca in Ingegneria Elettronica, Automatica e del Controllo di Sistemi Complessi Università degli Studi di Catania STM, 23 Ottobre Giugno 29 Tutor Prof G unnari, Coordinatore L Fortuna, Referente IGV G Puglisi

Ground deformation monitoring Global Positioning System DInSAR data High temporal resolution Puntual measure 3D Low temporal resolution Spatial distributed 1D (Line of Sight) Goal: to take advantage of their complementary nature

+ = Ground Deformation Map Over the Whole Intestigated Area

The concept of the integration of GPS and DInSAR data to obtain 3D ground deformation maps GPS measurements GPS data 3D ground deformation map 3D Displacement vectors 8 6 25 4 2 2 15 42 1 6 418 5 416 49 48 414 47 + DInSAR data LOS ascending 51 52 1 5 = 1 5 42 1 6 5 419 East 418 417 25 2 416 48 orth 5 49 25 2 5 5 Up 51 52 1 5 6 5 1 15 2 6 5 4 1 15 2 25 15 1 5-5 1 15 2 25 15 1 5-5 1 15 2 25 5 4 3 25 3 3 2 3 35-1 -15 3 35-1 -15 3 35 2 35 1 4 45 5 1 15 2 25 3 35 4 4 45 2 4-2 -25 4 45 2 4-2 -25 4 45 2 4 1

t los i D u u u u u u u u u u ] [ ) 3( ) 2( ) 1( 3(2) 2(2) 1(2) 3(1) 2(1) 1(1) = = 1 1 1 1 1 1 ) 1( ) 2( ) 3( ) 2( ) 1( ) 1( ) 3( ) 3( ) 2( ) 1( ) 2( ) 3( ) 3( ) 2( ) 1( 1(1) 2(1) 3(1) 2(1) 1(1) 1(1) 3(1) 3(1) 2(1) 1(1) 2(1) 3(1) 3(1) 2(1) 1(1) P z P y P S S S A [ ][ ] T P z P y P P LOS S S S U U U D,,,, 3 2 1 = Wu A WA A l T T 1 ) ( = T U U U l ] [ 23 13 12 23 23 22 13 12 11 3 2 1 ω ω ω ε ε ε ε ε ε = SISTEM method (Simultaneous and Integrated Strain Tensor Estimation from geodetic and satellite deformation Measurements)

3 ovember 5 December 29, European Space Agency, Roma (Frascati)

16-19 ovembre, 29 - Trieste Mappe di spostamento 3D ad alta risoluzione del terremoto di L'Aquila ottenute applicando il metodo SISTEM all integrazione dei dati GPS e DInSAR (EVISAT e ALOS) Guglielmino F (1), Anzidei M (2), Briole P (3), De Michele M (4), Elias P (5), unnari G (6), Puglisi G (1), Spata A (6) (1) Istituto azionale di Geofisica e Vulcanologia, Sezione di Catania, Catania, Italy (puglisig@ctingvit, +39 95 43581), (2) Istituto azionale di Geofisica e Vulcanologia, Centro azionale Terremoti, Roma, Italy (anzidei@ingvit ) (3) Ecole ormale Superieure, Laboratoire de Geologie, UMR CRS 8538, Paris France (4) French Geological Survey, BRGM, Orleans, France (5) ational Observatory of Athens, Institute of Space Applications and Remote Sensing, Athens,Greece (6) Dipartimento di Ingegneria Elettrica, Elettronica e dei Sistemi, Università degli Studi di Catania, Italy

Inverse Modeling The problem of inverse modelling consists of estimating source geometry from the observed surface displacements Surface displacements d can be related to the source geometry by a function g of the source model parameters m: d = g(m) + ε d: surface displacements g(m): source model m: model parameters

Mogi Model

Finite spherical pressure source Magma bodies often are not deep Implicit in the representation of a magma body by a point dilatation is the assumption that the characteristic dimension of the body is very small compared to its depth (McTigue, 1987)

Closed pipe (Davis and Bonaccorso, 1999)

Tensil dislocation (Okada model, 1985)

The Abruzzo earthquake

Abruzzo Earthquake Dataset Red points are the GSP benchmarks/stations Green stars are the epicenters of earthquakes The red star is the epicenter of the main shock (Mw = 63) Thanks are due to the ESA, which made quickly available these images just after their acquisition in the framework of the Earth Watching project

Abruzzo Earthqhake SISTEM approach results Thanks to the availability of ascending and descending EVISAT data was possible to well constraint the vertical component of the displacements (h ma = 22 cm); the corresponding errors are relatively low ( < ± 1 cm) The W-SE trend is compatible with the surface evidences of the Paganica fault system The East-West component suggests a detral movement of the fault system The corresponding errors are relatively low ( < ± 1 cm) The use of ascending / descending SAR geometry and the low number of GPS points with significant displacements do not allow well constrain the orth-south component; more GPS point are needed

Two Steps Inversion Strategy: Particle Swarm Algorithm (PSO) and Gauss-ewton method PSO is a iterative-heuristic, population-based global search algorithm used for optimization of continuous nonlinear functions It models the social behaviour of bird flocking or fish schooling in the attempt to converge to the global optimum PSO works with a population of interacting particles

PSO Each particle is defined within the contet of a topological neighbourhood Each particle moves in the parameter space with an auto-adaptive velocity whose value depends on the move eperiences of its own and those of its companions Individual knowledge : its best previous position p i =(p i1, p i2,, p id ) Collective knowledge : the swarm best position p g =(p g1, p g2,, p gd ) v ( v + c r p ) + c r ( p )) i+ 1 = C i 1 1( i i 2 2 g i i+ 1 = i + vi+1

The Gauss-ewton method (derivative based)

PSO: to quickly find the valleys Gauss-ewton: to reach the bottom of the valleys

Depth =5144 m, Strike = 132 gradi, Dip = 67 gradi, Length = 1197 m,width = 13 m, Strike-slip = -4 m, Dip-slip = -9 m, Opening = 2 m, Xs = 37487385*1^6, Ys = 46877719*1^6

Inverse Modeling The problem of inverse modelling consists of estimating source geometry from the observed surface displacements Surface displacements d can be related to the source geometry by a function g of the source model parameters m: d = g(m) + ε Problem of local minimum * * *

Local minimum: a bio-inspired approach PSO models the social behaviour of bird flocking searching for food The food never ends!!! Agents remain blocked in a local minima

PSO taking into account that the food ends: a Time-Variant Functional Error J(t,) t J(t,) t 1 J(t,) t 2

), ( t + f = = i i i P O J 1 2 )) ( ( 1 ) ( = = i i i P O t J 1 2 )) ( ( 1 ), ( O i : observed value P i : predicted value Traditional Functional Error Time-Variant Functional Error where f(t,) is a time-variant function modelling the food

Time-Variant Functional (balck) Initial Functional (red) f(t,)

Inverse Modeling The problem of inverse modelling consists of estimating source geometry from the observed surface displacements Surface displacements d can be related to the source geometry by a function g of the source model parameters m: d = g(m) + ε g(m) Function of the source model: FIXED!!! m Model parameters: to be evaluated

Toward a more reliable (real) source shape Bonaccorso et al, 26

A eural etwork based approach to estimate shape source from 3D ground deformation map I 1 O 1 Ground Deformation Map I 2 I n eural et O 2 O m Source Shape

eural etwork Learning I 1 O 1 3D Displacement vectors 25 2 15 1 5 42 1 6 419 418 417 416 48 49 5 51 1 5 52 I 2 I n eural et O 2 O m 12 Input 8 Output

First Results

Input Pattern: 2 Mogi sources

Input Pattern: 2 Mogi sources

Input Pattern: Davis (ellissoidal source)

Okada model (tensile dislocation)

Okada model (tensile dislocation)

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