in exploration seismology quality factor is widely used as a seismic attribute to identify anomalies related to attenuation, especially those caused by hydrocarbon. previous studies have indicated that seismic energy loss known as attenuation is greater for high frequency components of seismic data compared to the low frequency components. here the continuous wavelet transform is used to study ...

In this paper, the Cauchy problem for the Helmholtz equation is investigated. By Green's formulation, the problem can be transformed into a moment problem. Then we propose a modified Tikhonov regularization algorithm for obtaining an approximate solution to the Neumann data on the unspecified boundary. Error estimation and convergence analysis have been given. Finally, we present numerical resu...

Based on the integral representations of the solution derived via Fokas’ transform method, the high-frequency asymptotics for the solution of the modified Helmholtz equation, in a half-plane and subject to the Dirichlet condition, is discussed. For the case of piecewise constant boundary data, full asymptotic expansions of the solution are obtained by using Watson’s lemma and the method of stee...

This paper discusses the problem of determining an unknown source which depends only on one variable for the modified Helmholtz equation. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the quasireversibility regularization method. Convergence estimate is presented between the exact solu...

The finite element method has been widely used to discretize the Helmholtz equation with various types of boundary conditions. The strong indefiniteness of the Helmholtz equation makes it difficult to establish stability estimates for the numerical solution. In particular, discontinuous Galerkin methods for Helmholtz equation with a high wave number result in very large matrices since they typi...

The general solution of the modified Helmholtz equation, qxx(x, y)+qyy(x, y)− 4βq(x, y) = 0, in the wedge 0 ≤ x ≤ y ≤ ∞, is presented. This solution is used to find the explicit steady-state of diffusion-limited coalescence, A+A ⇀↽ A, on the half-line, with a trap-source at the origin. 02.60.L, 02.70, 61.43.H, 82.20.M 1 e-mail: [email protected] 2 Permanent address: Department of Mathematics, I...

An efficient finite volume approach has been used to develop a three dimensional Helmholtz acoustic solver for complex geometries. This acoustic solver was utilized to obtain characteristic mode shapes and frequencies of a baffled combustion chamber. An experimental setup, including stationary and moving sensors, has also been used to measure these quantities for the same model combustion chamb...

In this paper we describe and analyze some modified boundary element methods to solve exterior boundary value problems for the Helmholtz equation with either Dirichlet or Neumann boundary conditions. The proposed approach avoids spurious modes even in the case of Lipschitz boundaries. Moreover, the regularisation is done based on boundary integral operators which are already available in standa...