xiaoping jia, paul johnson*, thomas brunet *permanent address:

1
Xiaoping Jia, Paul Johnson*, Thomas Brunet *Permanent address: Los Alamos National Laboratory, New Mexico, USA Nonlinear Acoustics in Granular Media and Dynamic Earthquake Triggering Nonlinear acoustics Dynamic triggering • Pulse mode experiments 0,3 0,4 0,5 0,6 0,7 0,8 0,9 16500 17000 17500 18000 18500 N o r m a l i z e d a f (Hz) Increasing drive amplitude 0 0,005 0,01 0,015 0 1 2 3 4 5 6 7 1 / Q - 1 / Q o Acoustic strain ε (10 -6 ) 0.071 MPa 0.11 MPa 0.16 MPa 0.21 MPa 0.28 MPa -0,05 -0,04 -0,03 -0,02 -0,01 0 0,01 0 1 2 3 4 5 6 7 Δ E / E 0 Acoustic strain ε (10 -6 ) 0.071 MPa 0.11 MPa 0.16 MPa 0.21 MPa 0.28 MPa f res = V / 2L and Q = f res / Δf E = r V P 2 or G = r V S 2 • Resonance experiments • Fundamental compressional mode • Elastic modulus softening • Hysteretic dissipation • Failure model • Influence of slow dynamics • Self demodulation of a high frequency carrier wave ( Parametric ’array effec’) • Demodulated signal vs input amplitude • Recovery of elastic modulus (slow dynamics) 0,00000,00010,00020,00030,00040,0005 -0,30 -0,15 0,00 0,15 0,30 Time (seconde) 30 kHz -0,50 -0,25 0,00 0,25 0,50 50 kHz -0,1 0,0 0,1 75 kHz -0,030 -0,015 0,000 0,015 0,030 150 kHz -0,008 -0,004 0,000 0,004 0,008 300 kHz 500 kHz -0,008 -0,004 0,000 0,004 0,008 (bead packing under P = 0.30 MPa) (1/Q – 1/Q 0 ) ~ ε ΔE/E 0 ~ ε At low P Hysteretic nonlinearity T L T R t P s = M (ε + ε 2 + ε 3 + S (ε, ε/ t) Constitutive law: 0 50 100 150 0 100 200 300 400 500 100 kHz 300 kHz 500 kHz y = 0,044469 * x^(1,1587) R= 0,99591 y = 0,0087545 * x^(1,5905) R= 0,99864 y = 0,0076759 * x^(1,6101) R= 0,99979 A o u t ( m V ) A in (mV) 0,994 0,995 0,996 0,997 0,998 0,999 1 1,001 100 1000 10000 N o r m a l i z e d r e s o Waiting time (second) 0.28 MPa 0.071 MPa

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Nonlinear Acoustics in Granular Media and Dynamic Earthquake Triggering. Xiaoping Jia, Paul Johnson*, Thomas Brunet *Permanent address: L os A lamos N ational L aboratory, New Mexico, USA. Nonlinear acoustics. • Resonance experiments. • Pulse mode experiments. P. - PowerPoint PPT Presentation

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Page 1: Xiaoping  Jia,  Paul  Johnson*,  Thomas  Brunet *Permanent address:

Xiaoping Jia, Paul Johnson*, Thomas Brunet

*Permanent address: Los Alamos National Laboratory, New Mexico, USA

Nonlinear Acoustics in Granular Media and

Dynamic Earthquake Triggering

Nonlinear Acoustics in Granular Media and

Dynamic Earthquake Triggering

Nonlinear acoustics

Dynamic triggering

• Pulse mode experiments

0,3

0,4

0,5

0,6

0,7

0,8

0,9

16500 17000 17500 18000 18500

Normalized amplitude

f (Hz)

Increasing drive amplitude

0

0,005

0,01

0,015

0 1 2 3 4 5 6 7

1/Q-1/Qo

Acoustic strain ε (10-6)

0.071 MPa

0.11 MPa

0.16 MPa0.21 MPa

0.28 MPa

-0,05

-0,04

-0,03

-0,02

-0,01

0

0,01

0 1 2 3 4 5 6 7

ΔE / E

0

Acoustic strainε (10-6)

0.071 MPa0.11 MPa

0.16 MPa0.21 MPa

0.28 MPa

fres = V / 2L and

Q = fres / Δf

E = VP 2 or G = VS

2

• Resonance experiments

• Fundamental compressional mode

• Elastic modulus softening • Hysteretic dissipation

• Failure model • Influence of slow dynamics

• Self demodulation of a high frequency carrier wave ( Parametric ’array effec’)

• Demodulated signal vs input amplitude

• Recovery of elastic modulus (slow dynamics)

0,0000 0,0001 0,0002 0,0003 0,0004 0,0005-0,30-0,150,000,150,30

Time (seconde)

30 kHz

-0,50-0,250,000,250,50 50 kHz

-0,1

0,0

0,1 75 kHz

-0,030-0,0150,0000,0150,030 150 kHz

-0,008-0,0040,0000,0040,008 300 kHz

500 kHz

-0,008-0,0040,0000,0040,008

(bead packing under P = 0.30 MPa)

(1/Q – 1/Q0) ~ εΔE/E0 ~ εAt low P Hysteretic nonlinearity

T

L

T

R

P

= M (ε + ε2 + ε3 + S (ε, ∂ε/∂t) Constitutive law:

0

50

100

150

0 100 200 300 400 500

100 kHz300 kHz500 kHz

y = 0,044469 * x^(1,1587) R= 0,99591 y = 0,0087545 * x^(1,5905) R= 0,99864 y = 0,0076759 * x^(1,6101) R= 0,99979

Aout

(mV)

Ain

(mV)0,994

0,995

0,996

0,997

0,998

0,999

1

1,001

100 1000 10000

Normalized resonace frequency

Waiting time (second)

0.28 MPa

0.071 MPa