2,630 research outputs found
Asymptotic wave-splitting in anisotropic linear acoustics
Linear acoustic wave-splitting is an often used tool in describing sound-wave
propagation through earth's subsurface. Earth's subsurface is in general
anisotropic due to the presence of water-filled porous rocks. Due to the
complexity and the implicitness of the wave-splitting solutions in anisotropic
media, wave-splitting in seismic experiments is often modeled as isotropic.
With the present paper, we have derived a simple wave-splitting procedure for
an instantaneously reacting anisotropic media that includes spatial variation
in depth, yielding both a traditional (approximate) and a `true amplitude'
wave-field decomposition. One of the main advantages of the method presented
here is that it gives an explicit asymptotic representation of the linear
acoustic-admittance operator to all orders of smoothness for the smooth,
positive definite anisotropic material parameters considered here. Once the
admittance operator is known we obtain an explicit asymptotic wave-splitting
solution.Comment: 20 page
On the Construction of Virtual Interior Point Source Travel Time Distances from the Hyperbolic Neumann-to-Dirichlet Map
We introduce a new algorithm to construct travel time distances between a
point in the interior of a Riemannian manifold and points on the boundary of
the manifold, and describe a numerical implementation of the algorithm. It is
known that the travel time distances for all interior points determine the
Riemannian manifold in a stable manner. We do not assume that there are sources
or receivers in the interior, and use the hyperbolic Neumann-to-Dirichlet map,
or its restriction, as our data. Our algorithm is a variant of the Boundary
Control method, and to our knowledge, this is the first numerical
implementation of the method in a geometric setting
Recovery of a Smooth Metric via Wave Field and Coordinate Transformation Reconstruction
In this paper, we study the inverse boundary value problem for the wave
equation with a view towards an explicit reconstruction procedure. We consider
both the anisotropic problem where the unknown is a general Riemannian metric
smoothly varying in a domain, and the isotropic problem where the metric is
conformal to the Euclidean metric. Our objective in both cases is to construct
the metric, using either the Neumann-to-Dirichlet (N-to-D) map or
Dirichlet-to-Neumann (D-to-N) map as the data. In the anisotropic case we
construct the metric in the boundary normal (or semi-geodesic) coordinates via
reconstruction of the wave field in the interior of the domain. In the
isotropic case we can go further and construct the wave speed in the Euclidean
coordinates via reconstruction of the coordinate transformation from the
boundary normal coordinates to the Euclidean coordinates. Both cases utilize a
variant of the Boundary Control method, and work by probing the interior using
special boundary sources. We provide a computational experiment to demonstrate
our procedure in the isotropic case with N-to-D data.Comment: 24 pages, 6 figure
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