Introduction

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.

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.

Method

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

(c)

(b)

(a)

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).

Conclusions

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.

Acknowledgements

The writers be thankful to Center for Energy

Studies, Universitas Gadjah Mada as the place to do this research

References

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