An optimal wavelet for the detection of surface waves in Marine Sediments

We study seismic surface wave propagation in stratified shallow marine sediments media. Our goal is to predict dynamic (shear velocity, attenuation) and physical properties (stiffness, density) of sediments from seismoacoustic records of surface waves propagating along the water-seabed interface. To estimate and invert propagational parameters of surface waves (group and phase velocity) into shear velocity as a function of distance and depth we are using a multiscale wavelet cross-correlation technique. Standard wavelet transform series has indeed proven very useful for imaging different surface waves modes. However, to achieve a better resolution of each mode imaging we need to develop a new wavelet transform that includes optimality and adaptivity, based on the seismic data itself. Our main tool to develop such an optimal wavelet is the Karhunen-Loeve decomposition of the data series. This requires two steps: first, we calculate set of covariance matrices from the pairs of time series. Second, we estimate the corresponding eigenvalues and eigenfunctions. The calculated eigenfunctions have to be further regularized to obtain a new wavelet series. This new eigenfunctions basis has an optimal convergence in the sense of the least squares. It is sufficient to take a small number of the above set of eigenfunctions. They are naturally adapted to surface waves modes propagation in terms of scales values: time and periods (frequencies). Our approach makes it possible to decompose highly correlated reference data series into eigenvectors and then to use it to decompose field data records in the frequency and time domains with significant improvement of the image quality. We have processed different seismic records with surface waves. The results were compared with the wavelet analysis using standard wavelet kernel ('Morlet', 'Gaussian', 'Mexican hat'). We show that our new developed adaptive wavelet discriminates better between different surface wave modes propagating along seabed interface and also along interfaces separating sediment layers. This raises a new potential in using wavelet analysis to study seismic wave propagation and other kinds of problems such as elecromagnetic induction.