Multiscale Rayleigh Wave Full Waveform Inversion In F-K Domain

Rayleigh wave is characterized by low frequency,strong energy and dispersion.And it is sensitive to shear wave(S-wave)velocity in the shallow medium.Rayleigh wave prospecting is generally applied to measure the S-wave velocity in the shallow geological structure.The shear velocities and other elastic parameters can be obtained by inversion of the dispersion curve which is extracted in Frequency-Wavenumber(F-K)spectrum or Frequency-velocity spectrum.Due to horizontal-layered hypothesis,the one-dimensional(1D)velocity structures of different points are provided and interpolated to construct a pseudo two-dimensional(2D)velocity structure.Which is low horizontal resolution and insufficient to huge detect velocity variation.In this thesis,based on Full waveform inversion(FWI)theory,the Rayleigh surface inversion is studied to obtain S-wave velocity structure,which uses waveform characteristic including phase and amplitude to help to achieve high resolution.Rayleigh wave FWI is a nonlinear problem.To reduce cycle skipping,the inverse objective function is constructed in the F-K domain,which has a wider global minimum range.The first order velocity stress wave equation is approximated by staggered mesh finite difference method.And boundary conditions are implemented by using perfectly matched layers(PML)and mirror image method.Seismic wave are simulated and surface wave data are shown.Full waveform data are transformed to F-K domain by 2D fast Fourier transform(FFT),and it's amplitude spectrum is used to build the objective function.The objective function is optimized and iterative solutions are adopted to obtain optimization velocity structures.The initial model is the key parameter for full waveform inversion.The initial reference for velocity range is from the dispersion curve,and smooth in lateral direction and gradient variation in depth are processed to set the initial model to alleviate the cycle skipping.In order to avoid the inversion converges towards a local minimum,the multi-scale inversion strategies are used by selecting different frequency range data step by step.I only inverse S-wave velocity because surface wave is more sensitive to it than P-wave velocity and density.Based on the known geological background information,two frequency range selecting schemes are used in the inversion process,which is beneficial to a stable inversion operation.And the high resolution velocity structure is reconstructed step by step.Some tests for several typical geological models are made to verify the feasibility of the proposed method.Results demonstrate that the F-K domain Rayleigh wave waveform inversion method can effectively reconstruct the high-resolution shallow shear velocity structure.A relatively accurate velocity is derived and a layered structure is shown in depth and huge velocity variation is achieved to detect anomaly in lateral direction.Some tests are conducted to show the proposed method converges well from the simple initial velocity and derives a reliable velocity structure for noise data.