Numerical study of acoustic wavesaround and inside an underground cavity

CTBTO Young Scientist Research Award 2014

WWTF project 2015

Sofi Esterhazy, Ilaria Perugia, Joachim Schoberl, Gotz Bokelmann

Wave animation

Scattered wave field Zoom

Sofi Esterhazy University of Vienna 2 / 13

Objectives

Contribution to the scientific groundwork for OSI

Numerical investigation

Development of new method for elastic-acoustic problemsImprovement of computational algorithms

Applied investigation

Define characteristics of wave field interactionsImprove and design methods and experiments

Sofi Esterhazy University of Vienna 3 / 13

On-Site Inspection

Launch Pre-Inspection Inspection Post-InspectionRequest of OSI

Equipment - Training/Field tests - OSI Action Plan

Techniques IFE08 IFE14 Techniques IFE08 IFE14

Visual Observations Environmental measurements

Seismological aftershock monitoring Electrical conductivity measurements

Gamma radiation monitoring Air-borne gamma spectroscopy

Magnetic field mapping Active seismic survey

Gravitational field mapping Resonance seismometry

Multi-spectral imaging Drilling

Argon-37 and radioxenonmeasurement

Key: Tested, Partly tested, Not tested

Sofi Esterhazy University of Vienna 4 / 13

Seismic Methods

Subsurface structure after an UNE

(Adushkin

&Spivak,2004)

!"# $"#

Simplified model

2

1

?

Sources:

Passive seismic sources: Body waves, Surface waves, Noise

Active seismic sources: Vibroseis, Explosions

Sofi Esterhazy University of Vienna 5 / 13

Underling physics

Acoustic wave equation in medium 1 2

1

?

Elastic wave equation in medium 2

Focus on compressional waves

Time harmonic cases:

Spherical point source?

Plane wave sources

Sofi Esterhazy University of Vienna 6 / 13

Underling physics

Acoustic wave equation in medium 1 2

1

?

Elastic wave equation in medium 2 Focus on compressional waves

Time harmonic cases:

Spherical point source?

Plane wave sources

Sofi Esterhazy University of Vienna 6 / 13

In/Out Scattering

Separation into the incident and scattered wave field:

p = pinc + pscat

pinc

pscat

Better inside to the wave field interaction

Sofi Esterhazy University of Vienna 7 / 13

Numerical results (1)

Scattered wave field from a plane wavefrom the bottom left with f = 16Hz

Cavity at depth D = 600m and diameter d = 60m

Material parameters:v1 = 300m/s, 1 = 1kg/m

3

v2 = 3000m/s, 2 = 1000kg/m3 Incident wave field

Without Cavity With cavity

Sofi Esterhazy University of Vienna 8 / 13

Numerical results (1)

Scattered wave field from a plane wavefrom the bottom left with f = 16Hz

Cavity at depth D = 600m and diameter d = 60m

Material parameters:v1 = 300m/s, 1 = 1kg/m

3

v2 = 3000m/s, 2 = 1000kg/m3

Netgen/Ngsolve

Automatic 2D/3D adap-tive mesh generator

High-order Finite Element Method Applicable for Heat-flow, Acous-

tics, Elasticity, Navier-Stokes,Maxwell, etc.

Open-source, C++, MPI parallel,Python Plugin

Without Cavity With cavity

Sofi Esterhazy University of Vienna 8 / 13

Numerical Results (2)

Scattering profile

No surface

Total field Scattered field

Geometrywith PML

Plane wave from the bottom with f = 16Hz

Cavity at depth D = 600m and diameter d = 60m

Material parameters:v1 = 3000m/s, 1 = 1000kg/m

3, v2 = 300m/s, 2 = 1kg/m3

kR = 1

Sofi Esterhazy University of Vienna 9 / 13

Numerical Results (2)

Scattering profile

No surface

Total field Scattered field

Zoom

Plane wave from the bottom with f = 16Hz

Cavity at depth D = 600m and diameter d = 60m

Material parameters:v1 = 3000m/s, 1 = 1000kg/m

3, v2 = 300m/s, 2 = 1kg/m3

kR = 1

Sofi Esterhazy University of Vienna 9 / 13

Analytic Approach (Felix M. Schneider)

Express the incident and the scattered wave field by linearcombinations of spherical vectors and solve a system of linearequations

For each index l find the coefficients to match at the boundary r = R

Sofi Esterhazy University of Vienna 10 / 13

Scattering cross sections(Valeri Korneev, Geophys. J. Int. (1993))

S = Ein/Escat . . . Ratio between scattered and incoming energy flow

kR = U/ . . . Ratio between cavity circumference and incident wavelength

Vacuum inclusion Acoustic inclusion

Modeling the cavity as an acoustic inclusion is crucial to resonanceseismometry

Sofi Esterhazy University of Vienna 11 / 13

Summary & Outlook

Project distinguished by the Young Scientists Research Award

Wave propagation with focus on acoustic case

Identification of underlying physics

Investigation of characteristics (analytically and numerically)

Set up of an efficient numerical code

Extension to full elastic wave field

Extension to 3D

Numerical improvement and Post-processing

Incorporation of our findings into the practices of an OSI

Thank you!

Sofi Esterhazy University of Vienna 12 / 13

Summary & Outlook

Project distinguished by the Young Scientists Research Award

Wave propagation with focus on acoustic case

Identification of underlying physics

Investigation of characteristics (analytically and numerically)

Set up of an efficient numerical code

Extension to full elastic wave field

Extension to 3D

Numerical improvement and Post-processing

Incorporation of our findings into the practices of an OSI

Thank you!

Sofi Esterhazy University of Vienna 12 / 13

In/Out Separation

Ansatz p = pinc + pscat

pinc solves

2pinc + k1pinc = (x x0) + rad. cond. for x x0

The remaining unknown pscat is then the solution of

(

1

1pscat

)+

k11

pscat = 0 in 2

(

1

2pscat

)+

k22

pscat =1

2(k1 k2)pinc in 1

pscat = pinc on

+ radiation condition for r

Sofi Esterhazy University of Vienna 12 / 13

Numerical method

High-Order Finite Element Method

Can handle highly complex, irregularly shaped geometriesTends to exponentially increase the accuracy of the computations

Software

Netgen: Automatic 2D/3D tetrahedral adaptive mesh generatorNgsolve: Applicable for Heat-flow, Acoustics, Elasticity,Navier-Stokes, Maxwell, etc.Open-source, C++, MPI parallel, Python Plugin

Hardware

Internal server with 48 coresVienna Scientific Cluster 3 - 140/2020 dual nodes a 8 cores

Sofi Esterhazy University of Vienna 13 / 13

ObjectivesApproachResults