A practical approach to compensate for diodic effects of PS converted waves

In inhomogeneous media, PS converted waves often suffer from severe diodic effects. The traveltime and amplitude of PS converted waves may be different in the forward and reverse shooting directions, giving rise to different stacking velocities of PS converted waves and velocity ratios. These effects, compounded with the asymmetric raypath of PS converted waves, will further increase the difficulties and costs in processing PS converted-wave data. One common method to solve this problem is to separate a data set into two volumes with different shooting directions (e.g., negative or positive offset directions). Different values of the PS converted-wave velocities are used to process the two data sets separately and the two results are combined in the final stage. The problem with this method is that sometimes it is difficult to correlate the data sets and the final combined result may be degraded. In this paper, we propose a method to overcome this problem and apply this method to a 2D data set for improving the PS converted-wave imaging

Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States

In this paper, we study a family of orthogonal polynomials $\{\phi_n(z)\}$ arising from nonlinear coherent states in quantum optics. Based on the three-term recurrence relation only, we obtain a uniform asymptotic expansion of $\phi_n(z)$ as the polynomial degree $n$ tends to infinity. Our asymptotic results suggest that the weight function associated with the polynomials has an unusual singularity, which has never appeared for orthogonal polynomials in the Askey scheme. Our main technique is the Wang and Wong's difference equation method. In addition, the limiting zero distribution of the polynomials $\phi_n(z)$ is provided

Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems

We study the Plancherel--Rotach asymptotics of four families of orthogonal polynomials, the Chen--Ismail polynomials, the Berg-Letessier-Valent polynomials, the Conrad--Flajolet polynomials I and II. All these polynomials arise in indeterminate moment problems and three of them are birth and death process polynomials with cubic or quartic rates. We employ a difference equation asymptotic technique due to Z. Wang and R. Wong. Our analysis leads to a conjecture about large degree behavior of polynomials orthogonal with respect to solutions of indeterminate moment problems.Comment: 34 pages, typos corrected and references update