Wavelet Correlation Analysis Applied to Study Marine Sediments

Transcription

1 Wavelet Correlation Analysis Applied to Study Marine Sediments Alexander Kritski D.A. Yuen A.P.Vincent Centre for Marine Science and Technology Curtin University. Australia Department of Geology and Geophysics and Supercomputing Institute,University of Minnesota, U.S.A. Département de Physique Université de Montreal, Canada

2 Outline Abstract Wavelet Transform and Wavelet Correlation Function Applications of Wavelet Cross-Correlation Correlation Analysis. Synthetic and Experimental data Images of the first and second shear modes and the Scholte wave Conclusions

3 Abstract The major motivation and objective of this work is to apply the wavelet correlation analysis to study near surface sediments and develop a new diagnostic technique for extracting physical properties from seismic data. Physical properties p of near surface sediments play a prominent role in the geosciences and underwater u acoustics. Near surface sediments affect acoustic wave fields in shallow water waveguides and govern conditions for operation of active sonar. Some progress has been made in understanding the propagation and attenuation characteristics c of interface waves in different geological environments. However,, the generating mechanisms are poorly understood. In particular, what is the acoustic ustic-seismic seismic energy conversion process? As seismic waves involve both time and d space parameters, we can relate directly the propagation characteristics tics of the ocean bottom interface waves to the physical properties of the sediments over the propagation area. To address these problems we have applied the wavelet correlation method to examine the variations of bottom characteristics and their role in coupling waterborne sound into the sea bottom. To confirm m the validity of the developed modeling technique, we have produced synthetic seismograms and applied wavelet correlation analysis for synthetic seismograms ms ad marine field data. We display images of the first and second shear modes and the Scholte wave (interface wave) component as a function of both arrival time t and frequency for both synthetic and field data.

4 Applications Marine Acoustics Exploration Geophysics. Potential fields

5 Introduction We study the propagation characteristics of the ocean bottom interface and shear waves to extract physical properties of marine sediments over the propagation area The wavelet analysis presents an unique capability for extracting g the most essential scales of structures that change both in time and space. Seismic waves involve both time and space parameters it should be b able to decompose properties of seismic waves over a two dimensional time and period (frequencies). We develop a new technique based on the wavelet correlation method to examine the variations of bottom characteristics and their role in coupling waterborne sound into the sea bottom.

6 Wavelet Transform Continuous wavelet transform of function f(t) at location b, relative to wavelet ϕ(t) at scale a: 1 t b Wf ( b, a) = f ( t) ψ ( ) dt a a [Holschneider, 1995]

7 Morlet Wavelet ψ (t ) = π 1 / 4 * exp( iω 0t ) * exp( t / 2) 2

8 H n Gaussian Wavelet 0 π 4α ( t) = ω0e Cos( ω0t) 2α ω 2 t 2 4

9 Wavelet Cross-Correlation Function for two different signals fx(t) and fy(t): WC xy T 1 = lim Wf T T / 2 / 2 x ( b, a) Wf y ( b +τ, a) db τ - time delay Wfx(b,a), Wfy(b,a) - wavelet coefficients [Li, 1998; Yuen et al., 2000]

10 Wavelet Cross-Correlation Correlation Analysis applications to: Synthetic Data from an environment that lead to dispersion characteristics in i agreement with the experimental results obtained from the shallow water trial in May, 2001 (Rottnest( Island). Experimental data shallow water trial, May / 2001 (Rottnest( Island).

11 Synthetic Data Acquisition scheme for generating synthetic seismograms source water column direct arrivals interface waves marine sediments

12 Synthetic Data 0 as[db/ls] Cs [m/s] Cw=1.7 km/s density=1870 kg/m3 αp = 0.1 db/λp 20 Depth, m 40 Physical Parameters of the Model Environment used for generating synthetic seismograms for inreface and shear waves. [Schmidt et al., 1984]

13 Synthetic Data Synthetic Source 0.7 source signal amplitude 0.1 Time signal time, sec 5 source signal, spectrum Spectrum amplitude frequency

14 Synthetic Data Synthetic Data m/s Synthetic seismograms 130 m/s Trace number m/s 5 Range, km range, km time, sec Time, sec

15 Synthetic Data Wavelet modulus for traces 5 (2.5 km) using Gaussian wavelet Wavelet transform. Signal 5 Surface wave 1st shear mode 2nd shear mode

16 Synthetic Data Wavelet modulus for traces 3 (1.5 km) using Gaussian wavelet Wavelet transform. Signal 5

17 Synthetic Data Wavelet modulus for trace 2 (1.0 km) using Gaussian wavelet

18 Synthetic Data Group Velocity Dispersion Gaussian Wavelet analysis. Synthetic data. Receiver at 2.5 km from the Source 300 2nd Share mode st Shear Mode Group 150Velocity, m/sec 100 Scholte Wave Frequency, hertz

19 Synthetic Data Wavelet Cross Correlation Coefficients Synthetic data Traces 5 and 3

20 Synthetic Data Wavelet Cross-Correlation for traces 5 (2.5 km) and 4 (2.0km) using Morlet Wavelet Cross-Correlation Trace 5 Trace Time delay, s Time, s Frequency, Hz 0.0

21 Experimental Data

22 03 and 04/ Map of the southern Rottnest Basin

23 03 and 04/ Map of the southern Rottnest Basin Trial Area

24 Experimental Setup

25 Experimental Data m/s bottom hydrophone Trace number m/s 137 m/s 127 m/s 77 m/s Range, km time, sec

26 Field Data Wavelet Transform of Field Signals

27 Field Data Coefficients and Phases of Wavelet Cross Correlation Phase of WCR Traces 5 and 3 WCR Moduli Traditional Cross-Correlation Phase of WCR Traces 5 and 2 WCR Moduli Traditional Cross-Correlation

28 Group Velocity Dispersion Experimental Data 300 1st Shear mode 2nd shear mode Group Velocity, m/s Scholte wave Frequency, Hz

29 Field Data The phase velocity dispersion can be studied directly from the phase field of WCR n 1 1 ΘWC xy ( ω, x, t) = [ ω j( τ + ( ) x1 (1 + x)] V1 V 2 j j j ω j - frequencies Phase of the wavelet cross-correlation correlation function - the field of phase velocities differences (V( 1, V 2 ) between two surface waves measurement at two points (X( 1, X 2 ) on the ocean-sediments interface for given frequencies.

30 Conclusions 1). The peaks of wavelet correlation coefficients perform the relative energy distribution in the first two shear modes and Scholte wave in the experimental seismic data showing dispersion. 2). Contributions of different periods (frequencies) to the correlation are kept reasonably separated. 3). The phase velocity dispersion can be studied directly from the phase field of the Wavelet Cross-Correlation Correlation Function.

31 Conclusions (II) 4). The wavelet cross-correlation correlation coefficients can be used for the detecting of group-velocity dispersion curve over as wide a frequency band. 5). From the phase field of the wavelet cross-correlation correlation function the inversion of phase- velocity dispersion can be evaluated over a narrow frequency range where the signal is strong and the phase differences are easily determined.

32 Future work: To perform a better resolution in the phase velocity inversion a cross-correlation correlation in spatial domain can be introduced as well. In case of a cross-correlation correlation in x direction (distance along the interface) in addition to the time domain cross-correlation correlation the spatial component of phase of the WCR will be: n n ω Θ = j WC xy ( ω jτ + ) V j Inversion for geacoustical models; density, porosity, attenuation profiles, shear moduli. k j

33 References: 1. Holschneider,, M. Wavelets and Analysis, Oxford Science Publication, Li, H. Identification of coherent structures in turbulent shear flow with wavelet correlation analysis,, Transactions of the ASME, Vol. 120, Yuen,, D. A., A. P. Vincent, S.Y. Bergeron, F. Dubuffet,, A.A. Ten, V.C. Steinbach, L. Strain, Crossing of scales and non-linearities in geophysical processes, Problems in Geophysics for the New Millenium,, Eds. Enzo Boschi, Göran Ekström and Andrea Morelli,, pp , 432, Godin,, O.A., D.M.F. Chapman, Dispersion of interface waves in sediments with power-law shear speed profiles. I. Exact and approximate analytical results sults. J.Acoust Acoust.. Soc. Am., 110(4), Schmidt, H., G. Tango, Efficient global Matrix Approach to The Computation of Synthetic Seismograms, Geophys.. J.R.Astron. Soc. pp , 359, 1984.

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