Witrynaa fixed wave number and at most two incident directions are given. The main new points of this paper are: a combination of the enclosure method and the Herglotz wave function; explicit construction of the density in the Herglotz wave function by using the idea of the Vekua transform. By virtue of the construction, one can avoid any re- Witrynacomponent as a form of plane wave expansion (or Herglotz wave function) [13,14]: h R(r s) = T (˜h R;r s):= Z S 2×S eik(ˆr·r+ˆs·s)˜h R(ˆr,ˆs)dˆrdˆs, (6) where S2 is the unit sphere in R3, ˆs ∈ S2 and ˆr ∈ S2 represent plane wave component directions relating to source and receiver, re-spectively, and ˜h R is the plane-wave ...

Acousto-optic back-projection: Physical-model-based sound field ...

Witrynaof the classical description of the Herglotz wave functions given by P. Hartman and C. Wilcox. For α > 0 this characterization involves a mul-tivariable square function evaluated in a vector of entire solutions of the Helmholtz equation, while for α < 0 it is written in terms of an spherical Witrynaization of Herglotz Wave Functions in the plane. Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L2-Far-Field-Pattern. The behavior of this projection is reminiscent of the Disc Multiplier Operator on both Lp and mixed Lp-normed spaces. In particu-lar a Kakeya type set plays a central role in our analysis. shoemaker\u0027s group of companies

Mapping Properties of a Projection Related to the Helmholtz …

Witrynaparticular case of Herglotz wave functions. Definition 1.1. Let α∈ R. We say that the function u: Rd → C is a α-Herglotz wave function if u= Ef for some f ∈ Hα(Sd−1), … WitrynaIn the 1990s, Dassios and Rigou [14] extended the Herglotz wave function concept to the context of elasticity. They defined the three-dimensional elastic Herglotz wave functions as entire solutions u of the spectral Navier equation satisfying the so called Herglotz condition given by kuk2 A:= limsup R→∞ 1 R Z x WitrynaThis paper presents a direct gravity inverse method of multilayered variable density models, and gives gravity forward formulae under various conditions of den shoemaker\\u0027s bench hamburg ny