1. Determination of 2D shallow S wave velocity
profile using waveform inversion of P-SV
refraction data.
AMROUCHE Mohamed YAMANAKA Hiroaki
Tokyo Institute of Technology
東京工業大学
24 September 2012 LISBOA - PORTUGAL

2. Introduction
During earthquakes most of constructions interact directly with the surface layers,
structural soil irregularities and lateral S wave variations may generated complex
waves that interfere to disturb the expected response of the buildings.
The surface wave exploration became very popular in the last few years. Surface
waves have dispersive features while propagating that can be utilized for the one
dimensional soil exploration of shallow soils.
However, the 1D soil profiling assumes that the propagation medium is horizontally
layered and ignores the lateral variations of layers along the profile.
Also, since most of the surface wave methods are based on the inversion of the
dispersion curves of surface waves, it will be very difficult to invert a two
dimensional profile, and only few authors have attempted to invert a 2D soil using
the Rayleigh waves.
We proposed a new approach based on the direct 2D soil numerical modeling and
the full wave inversion of surface Rayleigh waves time series obtained from
conventional seismic refraction survey to estimate the two dimensional soil profile.
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3. Inversion of Rayleigh waves
STEP02: Source Deconvolution.
Waveform
Deconvolution
STEP01: Acquisition.
2D inverted Soil profile
Soil Modelization
based on the
computed waves
STEP03: Numerical modeling.
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4. Numerical Modeling:
Finite Difference Staggered Grid
Vertical Point Yamada (2000) upgraded 2.5D
P-SV Wave field Vertical component
Source
of receivers
- 4th order Approximation for space.
- 2nd order Approximation for time.
- Non physical boundaries (Clayton, Engquist 1980)
based on J.Virieux 1986
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5. Numerical Modeling: Soil parameterization
To materialize the soil structure, we use the combination of the tomographic cell and
homogeneous layered model proposed by Aoi et al.(1993). This technique allows a better
reconstruction of the geological discontinuities using few number of unknown parameters
and gives the lateral variation at each layer.
The interface of each block can be written as follow:
dx：Interface Depth at location x.
L: Number of basis functions.
Pk：Coefficient determined by inversion.
Cx：Basis Function.
A smoothing factor is implemented between blocks to balance the velocity/depth trade off
during inversion.
7 Blocks
Basis
7 Blocks
Functions
Basement.
Total parameters for inversion:
14 velocities + 14 depths= 28 unknown parameters
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6. Waveforms Deconvolution
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7. Generation of a Random initial Inversion Algorithms
model (2.5D FD computation) The inversion algorithm used in this study
is the Hybrid Heuristic Search Method proposed
Cal. Of Misfit between Obs. and by Yamanaka (2007). This method combines the
Cal. waveforms Genetic Algorithms and Simulated Annealing
Algorithms to obtain an optimal solution.
Selection – Cross over – Mutation
The main goal of inversion is to minimize the
misfit function between the Observed
New Generation: waveforms and the Computed ones.
Calculation of new model The Misfit function can be defined as follows:
Cal. Of Misfit for the present
generation
Change
Temp. Where, Oobs and Ocal are respectively the
observed and the calculated waveforms at each
Optimal model M station along N number of data.
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8. Numerical Experiments
250 m/s 200 m/s 400 m/s
650 m/s 650 m/s
Inversion Parameters: Elasticity parameters:
Number of blocks: 30 Vp/Vs Q ρ
Initial population: 20
Number of generations: 200 Surface layer 1.7 10 1700
Search limits:
Velocity: 150 – 500 (m/s) Basement 2.0 12 1900
Depth: 1 – 5 (m)
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9. Model01: Irregular Model
: Observed Waveforms.
Target : Calculated Waveforms.
Model
250 m/s
650 m/s
251 m/s
650 m/s
Inverted
Model
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10. Noise and Impedance effect
Target Model 7% Noise corrupted
Noise free inversion
inversion
250 m/s 251 m/s 248 m/s
650 m/s 650 m/s 650 m/s
251 m/s
500 m/s 423 m/s
650 m/s 650 m/s
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11. Target
Model02: Lateral velocity variation
Model
200 m/s 400 m/s
Generation 01 Generation 100
650 m/s
Generation 50
210 m/s 406 m/s
650 m/s
Generation 200
Inverted
Model
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12. Empirical inversion: Data acquisition
G3 Rear Parking
Tokyo Institute of Technology Suzukakedai
Campus Yokohama (JAPAN)
Down
stream
Up Survey line
stream
Borehole
10m
Google® map
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13. Empirical inversion: Data inversion
Up Stream inversion
Borehole
Data
200
300
500
420
550
Down Stream inversion
200
300
500
420
550
: Observed Waveforms.
: Inverted Waveforms.
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14. Conclusion
Through this method, we have proved the possibility to reconstruct the 2D soil
profile using the full wave inversion of the time series of surface waves in shallow
soils, using numerical soil modeling.
The numerical model is simulated using a2.5D P-SV waves FD staggered grid.
Deconvolution is used to get rid of the source signature in the wave fors.
The numerical experiments shows that the algorithm is able to reconstruct
complex two dimensional soil structures. The effect of noise can me more
pronounced in soils with low impedance ratio.
An empirical inversion was performed showing acceptable correlation with the
excising bore hole data.
Since this method is not based on the inversion of the dispersion curve, all the
energy of the Rayleigh waves encoded in the signal are inverted.
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15. Thank you for your kind attention!
mohamedamrouche347@hotmail.com