Regularization of the boundary control method for numerical solutions of the inverse problem for an acoustic wave equation

2020 ◽  
pp. 1-20
Author(s):  
A. Timonov
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Acoustic Wave ◽  
Boundary Control ◽  
Numerical Solutions ◽  
Control Method ◽  
Acoustic Wave Equation ◽  
Boundary Control Method

COMPARISON OF TWO AND THREE SPATIAL DIMENSIONAL SOLUTIONS OF A PARABOLIC APPROXIMATION OF THE WAVE EQUATION AT OCEAN-BASIN SCALES IN THE PRESENCE OF INTERNAL WAVES: 100–150Hz

2010 ◽  
Vol 18 (02) ◽  
pp. 117-129 ◽  
Author(s):  
JOHN L. SPIESBERGER
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Internal Waves ◽  
Gravity Waves ◽  
Numerical Solutions ◽  
Internal Gravity Waves ◽  
Ocean Basin ◽  
Acoustic Wave Equation ◽  
Parabolic Approximation ◽  
Spatial Dimensions

Numerical solutions are given for a parabolic approximation to the acoustic wave equation at 100 and 150 Hz in two and three spatial dimensions to determine if azimuthal coupling in the horizontal coordinate significantly affects horizontal correlation in the presence of internal gravity waves in the sea. Coupling is a small effect at 4000 km. This implies that accurate solutions are possible using computations from uncoupled vertical slices. Shape of horizontal correlation is inconsistent with shapes given by two theories. Estimates of horizontal correlation at 4000 km and 100 and 150 Hz are about 1 km and 0.5 km respectively.

COMPARISON OF TWO AND THREE SPATIAL DIMENSIONAL SOLUTIONS OF THE WAVE EQUATION AT OCEAN-BASIN SCALES IN THE PRESENCE OF INTERNAL WAVES

2007 ◽  
Vol 15 (03) ◽  
pp. 319-332 ◽  
Author(s):  
JOHN L. SPIESBERGER
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Internal Waves ◽  
Gravity Waves ◽  
Numerical Solutions ◽  
Internal Gravity Waves ◽  
Ocean Basin ◽  
Acoustic Wave Equation ◽  
Parabolic Approximation ◽  
Spatial Dimensions

Numerical solutions are given for a parabolic approximation to the acoustic wave equation at 75 Hz in two and three spatial dimensions to determine if azimuthal coupling of the field significantly affects horizontal coherence. Coupling is a small effect at 4000 km in the presence of internal gravity waves. This implies that accurate solutions are possible using computations from uncoupled vertical slices through the field. The shape of horizontal coherence is inconsistent with shapes given by two theories. Estimates of horizontal coherence at 4000 km and 25, 50, and 75 Hz are 10, 2, and 1 km respectively.

scholarly journals On an application of the Boundary control method to classical moment problems.

2021 ◽  
Vol 2092 (1) ◽  
pp. 012002
Author(s):  
A S Mikhaylov ◽  
V S Mikhaylov
Keyword(s):  
Dynamical System ◽  
Inverse Problem ◽  
Boundary Control ◽  
Control Method ◽  
Jacobi Matrices ◽  
Moment Problems ◽  
Control Approach ◽  
Boundary Control Method ◽  
Dynamic Inverse ◽  
Dynamic Inverse Problem

Abstract We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of moments with the Boundary control approach to a dynamic inverse problem for a dynamical system with discrete time associated with Jacobi matrices. We show that the solution of corresponding truncated moment problems is equivalent to solving some generalized spectral problems.

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