ABSTRACT Testing the Feasibility of Using PERM to Apply Scattering-Angle Filtering in the Image-Domain for FWI Applications Hani Ataiq Alzahrani Full Waveform Inversion (FWI) is a non-linear optimization problem aimed to estimating subsurface parameters by minimizing the mis t between modeled and recorded seismic data using gradient descent methods, which are the only practical choice because of the size of the problem. Due to the high non-linearity of the problem, gradient methods will converge to a local minimum if the starting model is not close to the true one. The accuracy of the long-wavelength components of the initial model controls the level of non-linearity of the inversion. In order for FWI to converge to the global minimum, we have to obtain the long wavelength components of the model before inverting for the short wavelengths. Ultra-low temporal frequencies are sensitive to the smooth (long wavelength) part of the model, and can be utilized by waveform inversion to resolve that part. Un- fortunately, frequencies in this range are normally missing in eld data due to data- acquisition limitations. The lack of low frequencies can be compensated for by uti- lizing wide-aperture data, as they include arrivals that are especially sensitive to the long wavelength components of the model. The higher the scattering angle of a 5 recorded event, the higher the model wavelength it can resolve. Based on this prop- erty, a scattering-angle ltering algorithm is proposed to start the inversion process with events corresponding to the highest scattering angle available in the data, and then include lower scattering angles progressively. The large scattering angles will resolve the smooth part of the model and reduce the non-linearity of the problem, then the lower ones will enhance the resolution of the model. Recorded data is rst migrated using Pre-stack Exploding Re ector Migration (PERM), then the resulting pre-stack image is transformed into angle gathers to which an angle ltering process is applied to remove events below a certain cut-o angle. The ltered pre-stack image cube is then demigrated (forward modeled) to produce ltered surface data that can be used in waveform inversion. Numerical tests con rm the feasibility of the proposed ltering algorithm. However, the accuracy of the ltered section is limited by PERM's singularity for horizontally-traveling waves, which in turn is dependent on the velocity model used for migration and demigration

Full waveform inversion (FWI) for reflection events is limited by its linearized update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate the resulting gradient can have an inaccurate update direction leading the inversion to converge into what we refer to as local minima of the objective function. In this thesis, I first look into the subject of full model wavenumber to analysis the root of local minima and suggest the possible ways to avoid this problem. And then I analysis the possibility of recovering the corresponding wavenumber components through the existing inversion and migration algorithms. Migration can be taken as a generalized inversion method which mainly retrieves the high wavenumber part of the model. Conventional impedance inversion method gives a mapping relationship between the migration image (high wavenumber) and model parameters (full wavenumber) and thus provides a possible cascade inversion strategy to retrieve the full wavenumber components from seismic data. In the proposed approach, consider a mild lateral variation in the model, I find an analytical Frechet derivation corresponding to the new objective function. In the proposed approach, the gradient is given by the oriented time-domain imaging method. This is independent of the background velocity. Specifically, I apply the oriented time-domain imaging (which depends on the reflection slope instead of a background velocity) on the data residual to obtain the geometrical features of the velocity perturbation. Assuming that density is constant, the conventional 1D impedance inversion method is also applicable for 2D or 3D velocity inversion within the process of FWI. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearized representations of the reflection response. To eliminate the cross-talk artifacts between different parameters, I utilize what I consider being an optimal parameterization. To do so, I extend the prestack time-domain migration image in incident angle dimension to incorporate angular dependence needed by the multiparameter inversion. For simple models, this approach provides an efficient and stable way to do full waveform inversion or modified seismic inversion and makes the anisotropic inversion more practical. Results based on synthetic data of isotropic and anisotropic case examples illustrate the benefits and limitations of this method.