Comptes Rendus de l Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy
Résumé/Abstract The location and generally complex shape of an impenetrable body submitted to a s... more Résumé/Abstract The location and generally complex shape of an impenetrable body submitted to a sonic wave are determined from measurements of the diffracted field and known solutions of a canonical problem involving a body of simple shape.
... When x' E fit c flo, we have Hr20 (x') = 1, and find that the field in fit ... more ... When x' E fit c flo, we have Hr20 (x') = 1, and find that the field in fit can be represented (conveniently) by: 00 u(x') = ui(x') + L an exp [ik(snx' + cny')] N L Emnan = bm; n=-N m = -N, ... ,1,0,1, ... , N, (27) an 2d1 r (P + 1)-1/2( - jSn + cn) Cn ira . exp [ - ik(snx + cn!)] d,(x), (24) ...
We show how to cope with the acoustic identification of poroelastic materials when the specimen i... more We show how to cope with the acoustic identification of poroelastic materials when the specimen is in the form of a cylinder. We apply our formulation, based on the Biot model, approximated by the equivalent elastic solid model, to a long bone-like or borehole sample specimen probed by low frequency sound.
In recent years, due to the rapid development of computation hard- and software, time domain full... more In recent years, due to the rapid development of computation hard- and software, time domain full-wave inversion, which makes use of all the information in the seismograms without appealing to linearization, has become a plausible candidate for the retrieval of the physical parameters of the earth's substratum. Retrieving a large number of parameters (the usual case in a layered substratum comprising various materials, some of which are porous) at one time is a formidable task, so full-wave inversion often seeks to retrieve only a subset of these unknowns, with the remaining parameters, the priors, considered to be known and constant, or sequentially updated, during the inversion. A known prior means that its value has been obtained by other means (e.g., in situ or laboratory measurement) or simply guessed (hopefully, with a reasonable degree of confidence). The uncertainty of the value of the priors, like that of data noise, and the inadequacy of the theoretical/numerical model...
Acoustics, Mechanics, and the Related Topics of Mathematical Analysis - Proceedings of the International Conference to Celebrate Robert P. Gilbert's 70th Birthday, 2002
This work deals with the inverse problem of the determination of the shape of a generally non-sph... more This work deals with the inverse problem of the determination of the shape of a generally non-spherical penetrable 3D body from the way it scatters incident sonic plane waves. The measurements of the diffracted field are matched to a partial wave representation involving unknown coefficients. Rather than solve for these coefficients (i.e., forward problem) by invoking the transmission conditions, it is supposed that they are locally those of the penetrable sphere of the same composition (as that of the given body) which intersects the given body at its boundary (this is the so-called ICBA, i.e., Intersecting Canonical Body Approximation). These coefficients are known explicitly to within a single parameter which is none other than the length of the position vector joining the origin of the laboratory system to the given point on the boundary of the body. By varying the locations of the measurement point and corresponding boundary point, one generates a discrete form of the parametri...
The inverse problem of the identification of an anomalous object (e.g., cyst or tumor) in a femal... more The inverse problem of the identification of an anomalous object (e.g., cyst or tumor) in a female breast immersed in water is solved by the matching of theoretical fields (for trial objects), employing an approximate field ansatz, to the scattered ultrasonic wave field measured on a surface fully enclosing the object.
This work deals with the determination of the shape of a generally-non-circular impenetrable cyli... more This work deals with the determination of the shape of a generally-non-circular impenetrable cylinder from the way it scatters incident sound. A complete family (of generally non-orthogonal functions) representation of the scattered field is employed to match the total ...
Comptes Rendus de l Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy
Résumé/Abstract The location and generally complex shape of an impenetrable body submitted to a s... more Résumé/Abstract The location and generally complex shape of an impenetrable body submitted to a sonic wave are determined from measurements of the diffracted field and known solutions of a canonical problem involving a body of simple shape.
... When x' E fit c flo, we have Hr20 (x') = 1, and find that the field in fit ... more ... When x' E fit c flo, we have Hr20 (x') = 1, and find that the field in fit can be represented (conveniently) by: 00 u(x') = ui(x') + L an exp [ik(snx' + cny')] N L Emnan = bm; n=-N m = -N, ... ,1,0,1, ... , N, (27) an 2d1 r (P + 1)-1/2( - jSn + cn) Cn ira . exp [ - ik(snx + cn!)] d,(x), (24) ...
We show how to cope with the acoustic identification of poroelastic materials when the specimen i... more We show how to cope with the acoustic identification of poroelastic materials when the specimen is in the form of a cylinder. We apply our formulation, based on the Biot model, approximated by the equivalent elastic solid model, to a long bone-like or borehole sample specimen probed by low frequency sound.
In recent years, due to the rapid development of computation hard- and software, time domain full... more In recent years, due to the rapid development of computation hard- and software, time domain full-wave inversion, which makes use of all the information in the seismograms without appealing to linearization, has become a plausible candidate for the retrieval of the physical parameters of the earth's substratum. Retrieving a large number of parameters (the usual case in a layered substratum comprising various materials, some of which are porous) at one time is a formidable task, so full-wave inversion often seeks to retrieve only a subset of these unknowns, with the remaining parameters, the priors, considered to be known and constant, or sequentially updated, during the inversion. A known prior means that its value has been obtained by other means (e.g., in situ or laboratory measurement) or simply guessed (hopefully, with a reasonable degree of confidence). The uncertainty of the value of the priors, like that of data noise, and the inadequacy of the theoretical/numerical model...
Acoustics, Mechanics, and the Related Topics of Mathematical Analysis - Proceedings of the International Conference to Celebrate Robert P. Gilbert's 70th Birthday, 2002
This work deals with the inverse problem of the determination of the shape of a generally non-sph... more This work deals with the inverse problem of the determination of the shape of a generally non-spherical penetrable 3D body from the way it scatters incident sonic plane waves. The measurements of the diffracted field are matched to a partial wave representation involving unknown coefficients. Rather than solve for these coefficients (i.e., forward problem) by invoking the transmission conditions, it is supposed that they are locally those of the penetrable sphere of the same composition (as that of the given body) which intersects the given body at its boundary (this is the so-called ICBA, i.e., Intersecting Canonical Body Approximation). These coefficients are known explicitly to within a single parameter which is none other than the length of the position vector joining the origin of the laboratory system to the given point on the boundary of the body. By varying the locations of the measurement point and corresponding boundary point, one generates a discrete form of the parametri...
The inverse problem of the identification of an anomalous object (e.g., cyst or tumor) in a femal... more The inverse problem of the identification of an anomalous object (e.g., cyst or tumor) in a female breast immersed in water is solved by the matching of theoretical fields (for trial objects), employing an approximate field ansatz, to the scattered ultrasonic wave field measured on a surface fully enclosing the object.
This work deals with the determination of the shape of a generally-non-circular impenetrable cyli... more This work deals with the determination of the shape of a generally-non-circular impenetrable cylinder from the way it scatters incident sound. A complete family (of generally non-orthogonal functions) representation of the scattered field is employed to match the total ...
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