The velocity-construction algorithm using the Laplace-Fourier-domain inversion for a land dataset

Abstract

Currently, brilliant advances in the acquisition offer the possibility of solving the problem of the absence of low-frequency components that hinders the full-waveform inversion, yet, most real datasets do not contain these components. Thus, the long-wavelength velocity model that can be obtained using the Laplace- or Laplace-Fourier-domain inversion should be conducive to delineating the subsurface structure via migration or Fourier-domain inversion starting from this algorithm. In this thesis, the 2D elastic Laplace-Fourier inversion algorithm was developed for the application to a land dataset could recover the long-wavelength velocity models. This velocity-estimation algorithm adopts the finite element method on an unstructured grid with expectation of mitigating the high nonlinearity observed in datasets that originate from topography via accurate depiction of an irregular surface. For the inversion methodology, the novel pseudo-Hessian matrix is suggested in this thesis. This modified pseudo-Hessian matrix allows for a deeper penetration depth of the inverted result and promises a more convergent result regardless of damping factor that generally required for pseudo-Hessian matrix. Also, the normalized stopping criterion was introduced using multi-objective assumption based on the property of the logarithmic objective function, the natural separation of the phase and amplitude error, to ensure that the phase and amplitude information contribute to the inversion result with parity. This method could help to prevent the result of an acquiring of an over- or under-inverted result caused by over-fitting or an unsuitable determination of the number of inversion iterations. The developed inverse algorithm was tested using a time domain synthetic dataset generated with a realistic foothill model. The results of the test demonstrate that this algorithm can recover an adequate velocity model without requiring low-frequency information and with the dataset containing an expected noise.