One-way wave equation seismic prestack forward modeling with irregular surfaces

Mathematical geophone （MG） and equal-time stacking （ETS） principles are used to implement seismic prestack forward modeling with irregular surfaces using the oneway acoustic wave-equation. This method receives seismic primary reflections from the subsurface using a set of virtual MGs. The receivers can be located anywhere on an irregular observing surface. Moreover, the ETS method utilizes the one-way acoustic wave equation to easily and quickly image and extrapolate seismic reflection data. The method is illustrated using high single-noise ratio common shot gathers computed by numerical forward modeling of two simple models, one with a flat surface and one with an irregular surface, and a complex normal fault model. A prestack depth migration method for irregular surface topography was used to reoroduce the normal fault model with high accuracy.

Approximate Generalized Conditional Symmetries for the Perturbed Nonlinear Diffusion-Convection Equations

The concept of approximate generalized conditional symmetry （A GCS） as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the perturbed nonlinear diffusion-convection equations. Complete classification of those perturbed equations which admit cerrain types of AGCSs is derived. Some approximate solutions to the resulting equations can be obtained via the AGCS and the corresponding unperturbed equations.

3D wavefield extrapolation with optimal separable approximation

An accurate and wide-angle one-way propagator for wavefield extrapolation is an important topic for research on wave-equation prestack depth migration in the presence of large and rapid velocity variations. Based on the optimal separable approximation presented in this paper, the mixed domain algorithm with forward and inverse Fourier transforms is used to construct the 3D one-way wavefield extrapolation operator. This operator separates variables in the wavenumber and spatial domains. The phase shift operation is implemented in the wavenumber domain while the time delay for lateral velocity variation is corrected in the spatial domain. The impulse responses of the one-way wave operator show that the numeric computation is consistent with the theoretical value for each velocity, revealing that the operator constructed with the optimal separable approximation can be applied to lateral velocity variations for the case of small steps. Imaging results of the SEG/EAGE model and field data indicate that the new method can be used to image complex structure.

Topological defects on solutions of the non-relativistic equation for extended double ring-shaped potential

In this study, we focus into the non-relativistic wave equation described by the Schrodinger equation, specifically considering angular-dependent potentials within the context of a topological defect background generated by a cosmic string. Our primary goal is to explore quasi-exactly solvable problems by introducing an extended ring-shaped potential. We utilize the Bethe ansatz method to determine the angular solutions, while the radial solutions are obtained using special functions. Our findings demonstrate that the eigenvalue solutions of quantum particles are intricately influenced by the presence of the topological defect of the cosmic string,resulting in significant modifications compared to those in a flat space background. The existence of the topological defect induces alterations in the energy spectra, disrupting degeneracy.Afterwards, we extend our analysis to study the same problem in the presence of a ring-shaped potential against the background of another topological defect geometry known as a point-like global monopole. Following a similar procedure, we obtain the eigenvalue solutions and analyze the results. Remarkably, we observe that the presence of a global monopole leads to a decrease in the energy levels compared to the flat space results. In both cases, we conduct a thorough numerical analysis to validate our findings.

Full Wave Simulations of Lower Hybrid Waves in Toroidal Geometry with Non-Maxwellian Electrons

Analysis of the propagation of waves in the lower hybrid range of frequencies in the past has been done using ray tracing and the WKB approximation.Advances in algorithms and the availability of massively parallel computer architectures has permitted the solving of theMaxwell-Vlasov systemforwave propagation directly[Wright et al.,Phys.Plasmas(2004),11,2473-2479].These simulations have shown that the bridging of the spectral gap(the difference between the high injected phase velocities and the slower phase velocity at which damping on electrons occurs)can be explained by the diffraction effects captured in the full wave algorithm-an effect missing in WKB based approaches.However,these full wave calculations were done with a Maxwellian electron distribution and the presence of RF power induces quasilinear velocity space diffusion that causes distortions away from an Maxwellian.With sufficient power,a flattened region or plateau is formed between the point of most efficient damping on electrons at about 2-3 vthe and where collisional and quasilinear diffusion balance.To address this discrepancy and better model experiment,we have implemented[Valeo et al.,”Full-wave Simulations of LH wave propagation in toroidal plasma with non-Maxwellian electron distributions”,18th Topical Conference on Radio Frequency Power in Plasmas,AIP Conference Proceedings(2007)]a non-Maxwellian dielectric in our full wave solver.We will show how these effects modify the electron absorption relative to what is found for a Maxwellian distribution.