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