Stability estimation of the generalized solution to the direct problem for the acoustic equation

The initial-boundary value problem for the acoustic equation with data on a timelike surface is considered in this paper. Such a problem arises, for example, if it is required to determine the acoustic pressure inside the region from a fixed response to part of the boundary from the source involved at the same boundary. It is assumed that the medium is at rest up to a certain instant of time and the parameters of the medium, for example, acoustic density, are known. The problem is considered in a triangular domain. The advisability of this was shown in the second half of the last century in the works of Romanov V.G. (for example, [1]), where it was proved that the solution to the direct problem of acoustic is representable as the sum of a singular and a continuous terms. The author has written out the form of the singular part, investigated the problem in an integral statement, and also proved conditional well-posedness theorems for three cases: for a small parameter of the domain, for small data, and for the source representability of the sought solution. It is known that the initial-boundary value problem for the acoustic equation with data on a timelike surface is ill-posed. In this paper, the original ill-posed problem is reduced to an inverse problem with respect to some direct (well-posed) problem. The theorem is proved and a stability estimate of the generalized solution to the direct problem is obtained.

Least-Squares Reverse Time Migration Using the Gradient Preconditioning Based on Transmitted Wave Energy

A gradient preconditioning approach based on transmitted wave energy for least-squares reverse time migration (LSRTM) is proposed in this study. The gradient is preconditioned by using the energy of “approximate transmission wavefield,” which is calculated based on the non-reflecting acoustic equation. The proposed method can effectively avoid a huge amount of calculation and storage required by the Hessian matrix or approximated Hessian matrix and can overcome the influence of reflected waves, multiples, and other wavefields on the gradient in gradient preconditioning based on seismic wave energy (GPSWE). The numerical experiments, compared with that using GPSWE, show that LSRTM using the gradient preconditioning based on transmitted wave energy (GPTWE) can significantly improve the imaging accuracy of deep target and accelerate the convergence rate without trivial increased calculation.

THE RESEARCH FOR AN IDENTIFICATION OF CRACK – LIKE CORROSION – MECHANICAL DEFECT BY ACOUSTIC IN-LINE INSPECTION TOOLS

Problem of an identification of cracks in dents or corrosion damage, which is considered as a crack – like corrosion – mechanical defect type, is considered for acoustic in – line inspection tools during an in – line inspection of oil pipelines. For this purpose, a theoretical model has been provided and considered as a vertical notch with a convex base. For modeling an interaction of acoustic waves with the defect model there has been used a corresponded formula of an acoustic equation at a ray – acoustic approximation. Considering used simplifying assumptions there have obtained certain boundary conditions for acoustic equation of the crack – like corrosion mechanical defect. Based on this theoretical model here an experimental research were provided at specially manufactured test specimen which contained vertical notches with base of different curvature. At the specimen there are has been obtained a difference of echo signals amplitude from convex and flat surface based notches. Obtained results showed a sufficient agreement with provided by theoretical modeling and approve an adequacy of the proposed model for a theoretical description of considered interaction shear waves with the defect imitation. According to obtained trend of an echo – signal amplitude variation a method for identification of cracks in dents or corrosion damage during an oil pipeline inspection by inline inspection tools has been provided.

Numerical acoustic simulation of flow around circular cylinders based on Lattice Boltzmann method and Ffowcs Williams-Hawkings acoustic equation

Based on the GPU acceleration technique, Lattice Boltzmann method (LBM) and Ffowcs Williams-Hawkings (FW-H) acoustic equation are adopted to simulate the noise generated by flow around fixed and rotating circular cylinders when Reynolds number (Re) is 200. The results show that the sound pressure level has a peak in the vertical direction and it is higher than that in the streamwise direction. The maximum sound pressure level is significantly reduced when the cylinder rotates due to the suppression of vortex shedding compared to the case of a fixed cylinder. For tandem cylinders, the maximum sound pressure level in the vertical direction increases as the spacing ratio increases, and for parallel cylinders, it decreases as the spacing ratio increases. In addition, when using graphic processing unit (GPU), the computational efficiency is improved greatly and the speed-up reaches nearly 100.