Introduction of Rayleigh wave. Physical parameter such as P-Wave



Real and synthetic data verifies the wavefield
transformation method described here converts surface waves on a shot gather
directly into images of multi-mode dispersion curves. Pre-existing
multi-channel processing methods require preparation of a shot gather with
exceptionally large number of traces that cover wide range of
source-to-receiver offsets for a reliable separation of different modes.

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This method constructs high-resolution images of
dispersion curves with relatively small number of traces. The extraction of dispersion
properties of surface waves can be used to find many useful applications in
geophysical (Park et al., 1996; 1998) and geotechnical (Stokoe et al., 1994)
engineering projects.


Therefore, Numerical simulation of surface wave
propagation has been made using finite difference staggered-grid method in
MATLAB. This program is used to create a wave propagation using three models:
three layers model, stepping-up model, and low velocity layer model to get the
snapshot result and synthetic seismic data.




We develop a wavefield transformation method that
provides images of dispersion curves directly from the recorded wavefields of a
single shot gather. With this method, different modes are separated with higher
resolution even if the shot gather consists of a relatively small number of
traces collected over a limited offset range. In this research, we create
create a wave propagation using three models: three layers model, stepping-up
model, and low velocity layer model to get the snapshot result and synthetic
seismic data.


To address the goal of developing dispersion curve
properties, this research is divided into 3 steps. First, we will obtain the
input parameter such as P-Wave model, S-Wave model, density model, source
position, receiver interval, and recording time. Second, we will define source
parameter. Ricker wavelet with dominant frequency 25 Hz is used as source in
this program. Third, Boundary condition is represented naturally by changes of
elastic parameter and density as they are in a heterogeneous formulation.


Examples –
Synthetic Data


We Generate three models are used in this
simulation: three layers model, stepping-up model, and low velocity layer model
(Figure 1). Before doing simulation, we verify the numerical of dispersion
curve with the theoretical curve that obtained by calculation of two layer
medium using Rix and Lai’s algorithm. This comparison shows the suitability
between fundamental-mode of Rayleigh wave.


Physical parameter such as P-Wave velocity has
maximum value 2941 m/s and minimum value 865 m/s, S-Wave velocity has maximum
value 1700 m/s and minimum value 500 m/s, and Density has maximum value 2000
kg/m3 and minimum value 1200 kg/m3. Meanwhile, 25
receiver with interval 2 m and 1000 iteration are used in this simulation.
Figure 2 shows snapshot of wave propagation at 0.09 s and 0.16 s.


In this simulation, each recorded time signal is
transformed into frequency domain using FFT algorithm. Considering each pair of
signals, an estimate of the relationship between wave velocity and

frequency over a certain range of frequency is
obtained. For stepping-up model we can analyse fundamental mode at range 10 Hz
– 60 Hz (Figure 3) and shows
the suitability with analytic equation of Rix and Lai (Rix and Lai, 2003)




Figure 1 Three different models are
used in this simulation (a) Normal model, (b) Stepping-up model, (c) Low
velocity layer model. Each model has a configuration with interval geophone 2 m
(triangle), near offset 2m. Meanwhile, stepping up model has 3 shots to study
fundamental mode variations with subsurface features.


Figure 2 The snapshot of wave
propagation (a) at 0.09 s and (b) at 0.16 s









Figure 3 Dispersion curve snapshot (a)
at shot 12 m (b) at shot 75 m (c) at shot 150m


Dispersion curve which can be
observed has a variation of fundamental mode. This variation is controlled by difference
of shot position to subsurface features. Therefore, subsurface features such as
layer thickness, geological structure beneath the surface, and heterogeneity
control the variation of fundamental mode. To study this effect, we must
isolate seismic energy from recorded signal at specified frequency band (Tran, 2008).




Resulting dispersion curves show match in the high
frequency range for three layers model with the theoretical of dispersion
curves. The stepping-up model is used to explore the interaction source
position with the near surface structure. When elastic waves interact with the
near surface structure, diffraction process occurs at the location of the near
surface structure. The near surface structure is suspected to be responsible
for the complexity of the recorded seismogram. Then, dispersion curve image is
extracted from the recorded seismogram which can enhance the structure’s
signature. And low velocity layer model illustrates high-low velocity
interface. The observed of dispersion curves allows the prediction of change in
the dispersion curves shape under the influence of velocity’s medium.



The writers be thankful to Center for Energy
Studies, Universitas Gadjah Mada as the place to do this research                         




Park, C. B., Miller, R. D., and Xia, J. 1996. Multi-channel analysis of surface waves
using Vibroseis, Presented at the
66th Ann. Mtg. of SEG, Denver, Expanded Abstracts, 68-71.


Park, C. B., Miller, R. D., and Xia, J. 1998. Ground roll as a tool to image near-surface
anomaly; Submitted for presentation at the 68th Ann. Mtg. of SEG, New Orleans.


Rix, G.J., and C.G. Lai. 2003. Surface wave
inversion using a continuous subsurface model. J Geotech Geoenviron Eng. In


Stokoe II, K. H., Wright, G. W., James, A. B., and
Jose, M. R. 1994. Characterization of
geotechnical sites by SASW method, in Geophysical characterization of sites,
ISSMFE Technical Committee #10, edited by R. D. Woods, Oxford Publishers, New


Tran, K. T. 2008. “An Appraisal of
Surface Wave Methods for Soil Characterization.” Thesis, University of Florida.


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