Resonant Excitation of SeismoAcoustic Interface Waves by a Sonic Boom: A Theoretical Approach

1
Resonant Excitation of Seismo-Acoustic Interface
Waves by a Sonic Boom A Theoretical Approach
Oleg A. Godin CIRES, University of Colorado at
Boulder and NOAA/Environmental Technology
Laboratory, Boulder, CO
2
Outline

• Motivation
• Background
• soft marine sediments
• fast and slow seismo-acoustic waves
• Interface waves supported by soft marine
  sediments
• analytic description
• experimental verification
• Application to the sonic boom problem
• reflection coefficient from a sediment half-space
• underwater acoustic field
• example linear profile of shear rigidity in the
  sediment
• Summary
• Future work

3
Evidence of power-law depth-dependence of shear
rigidity in unconsolidated marine sediments
G. M.Bryan and R. D. Stoll, The dynamic shear
modulus of marine sediments, J. Acoust. Soc. Am.
83, 2159-2164 (1988) M. D. Richardson, E. Muzi,
B. Miaschi, and F. Turgutcan, Shear wave velocity
gradients in near-surface marine sediments, in
Shear Waves in Marine Sediments (Kluwer,
Dordrecht, 1991) Pp. 295-304 B. O. Hardin, The
nature of stress-strain behavior for soils, in
Proc. Of the Specialty Conference on Earthquake
Engineering and Soil Dynamics (ASCE, Pasadena,
1978) Pp. 30-90 D. Huns, A. Davis, and J. Pyrah,
Relating in situ shear wave velocity to void
ratio and grain size for unconsolidated marine
sediments, in High Frequency Acoustics in Shallow
Water (SACLANTCEN, La Spezia, Italy, 1997) Pp.
251-258 J. C. Osler, D. M. F. Chapman,
Seismo-acoustic determination of the shear-wave
speed of surficial clay and silt sediments on the
Scotian Shelf, Canadian Acoustics 24, 11-22 (1996)
4
Previous Work
O. A. Godin and D. M. F. Chapman, Shear speed
gradients and ocean seismo-acoustic noise
resonances, J. Acoust. Soc. Am. 106, p.
2367-2382 (1999) O. A. Godin and D. M. F.
Chapman, Dispersion of interface waves in
sediments with power-law shear speed profiles. I
Exact and approximate analytical results, J.
Acoust. Soc. Am. 110, 1890-1907 (2001) D. M. F.
Chapman and O. A. Godin Dispersion of interface
waves in sediments with power-law shear speed
profiles. II Experimental observations and
seismo-acoustic inversions, J. Acoust. Soc. Am.
110, 1908-1916 (2001) F. Desharnais and D.M.F.
Chapman, Underwater measurements and modeling of
a sonic boom, J. Acoust. Soc. Am. 111, 544-553
(2002)
5
Fast and slow waves in sediments
Equations of motion for quasi-plane waves
Wave field representation for slow waves
4-th order wave equation
6
Scaling law for surface waves
Power-law depth-dependence of the shear modulus
Non-dimensional equations of motion
Boundary conditions
The scaling law
7
Benchmark problem ? 1/2
Dispersion relations
- fundamental mode
- main sequence of modes
Displacement and stress fields
8
Approximate dispersion relations
Main sequence modes
Fundamental mode
Effect of finite compressibility (? 1/2)
9
Inversion of experimental data (1)
Eastern Shore, Canada c (22.0 0.2) z 0.608
0.008, 1/R1.6 0.1 J. C. Osler and D. M.
F. Chapman, "Seismo-acoustic determination of
the shear-wave speed of surficial clay and silt
sediments on the Scotian Shelf," Canadian
Acoustics 24, 11-22 (1996)
10
Inversion of experimental data (2)
Strait of Sicily 1/R1.7 (assumed) c
(136.9 1.9) z 0.499 0.008 A. Caiti, T. Akal,
and R. D. Stoll, Estimation of shear wave
velocity in shallow marine sediments, IEEE J.
Ocean. Eng. 19, 58-72 (1994)
11
Inversion of experimental data (3)
Strait of Sicily 1/R1.8 (assumed) c (160.1
1.7) z 0.344 0.006 A. Caiti, T. Akal, and R. D.
Stoll, Estimation of shear wave velocity in
shallow marine sediments, IEEE J. Ocean. Eng.
19, 58-72 (1994)
12
Inversion of experimental data (4)
The Gulf of Mexico. SH wave c (121.5 0.1) z
0.253 0.002 R.D. Stoll and T. Akal,
"Experimental techniques for bottom parameter
inversion in shallow water," in Full Field
Inversion Methods in Ocean and Seismo-Acoustics,
ed. by O. Diachok, A. Caiti, P. Gerstoft, and H.
Schmidt (Kluwer Academic Publishers, Dordrecht,
1995), pp. 311-316.
13
Plane Wave Reflection from Sea Floor
Reflection coefficient
?f , cf
Impedance of inhomogeneous solid half-space
?s , cl , ?, B, l
14
Plane Acoustic Wave Incident on the Ocean
Surface from the Air
Horizontal phase velocity
?a , ca
?f , cf
Vertical component of wave vector in the water
?s , cl , ?, B, l
Acoustic pressure in the water
15
Example Sediment with linear depth-dependence
of shear rigidity
Reflection coefficient from fluid and elastic (ß
0.01, 0.05, and 0.2) seabeds
Assumptions
16
Sonic boom spectra
Hydrophone depths 1, 38, and 75 m below the
ocean surface. Ocean depth 76 m. N-wave
duration 0.225 s.
Fluid seabed
Elastic seabed ß 0.02
17
Sonic boom spectra (continued)
Hydrophone depth 16.5 m. Shear wave
attenuation ß 0.003, 0.01, and 0.1. Ocean
depth 76 m. N-wave duration 0.225 s.
18
Depth-dependence at near-resonant frequencies
f 3.44 Hz
Acoustic pressure underwater for fluid and
elastic (ß 0.003, 0.01, and 0.1) seabeds
19
Depth-dependence away from the resonance
f 3 Hz (solid lines)
f 2 Hz (dashed lines)
Acoustic pressure underwater for fluid and
elastic (ß 0.003, 0.01, and 0.1) seabeds
20
Summary
Unconsolidated marine sediments support strongly
dispersive seismo-acoustic interface waves which
propagate along ocean floor with velocities of
several hundreds meters per second or
less. Shock waves from a supersonic transport
traveling over water can resonantly excite the
seismo-acoustic interface waves leading to a
greatly enhanced penetration of sonic boom energy
into water. An analytic theory originally
developed to model the seismo-acoustic interface
waves in marine sediments is extended to simulate
the shallow-water sound field induced by a shock
wave incident from the air. The frequency at
which resonance between sonic boom and the
interface wave occurs is determined by
geoacoustic parameters of the sediment. Acoustic
pressure at near-resonant frequencies proves very
sensitive to shear wave attenuation. It may be
possible to extract the shear wave attenuation
coefficient in the sediment at low frequencies by
analyzing sonic boom records.