Surface Wave Analysis and its Application to the Calculation of Converted Wave Static Corrections
Using surface waves, we can estimate an S-wave velocity model to address the S-wave receiver statics of converted waves. Shear wave velocity is estimated from the inversion of either phase or group velocity. I address three major problems within the realm of S-wave receiver statics and these are the problem of inversion accuracy, misinterpretation of multi-modes, and the optimization of spatial analysis windows. To improve inversion accuracy, I develop a method to simultaneously estimate the phase and group velocities of surface waves based on the generalized S transform. The method is robust and it returns accurate results. To cope with noise and dispersion in the data, I introduce two cost functions. Though my method is robust where the surface wave is highly dispersed, I find that parameterization becomes ambiguous when the surface wave is multi-modal, and so it is possible for misinterpretation of different modes of the surface wave. To address multi-modality for the estimation of the group velocity, I develop a slant stack method that is based again on the generalized S transform. To control spectral localization, I use a scaling factor in the generalized S transform. I find that a small scaling factor should be chosen for low frequency surface-waves, whereas for higher frequencies a larger scaling factor should be chosen. Finally, I determine an accurate S-wave velocity model of the near surface for use in Swave statics estimation by optimizing the analysis spatial-window. To do this, I enlarge upon the idea of CMP Cross-Correlation of Surface Waves (CCSW). I obtain a precise estimation of a dispersion curve by limiting analysis to seismic traces that lie within a limited spatial window. I find that the optimum window length (aperture) should be close (one to one and half) to the maximum wavelength in a CMP gather. I find that, through experiment, when the aperture is optimum, a high resolution image of each mode within the dispersion curve is observable, and this avoids interpretation of modal interferences. A secondary benefit of my CCSW approach is its faster computational process than the conventional implementation.