Topological sensitivity based far-field detection of elastic inclusions

Tasawar Abbas; Shujaat Khan; Muhammad Sajid; Abdul Wahab; Jong Chul Ye

doi:10.1016/j.rinp.2017.12.041

Topological sensitivity based far-field detection of elastic inclusions

Tasawar Abbas, Shujaat Khan, Muhammad Sajid, Abdul Wahab, Jong Chul Ye

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

The aim of this article is to present and rigorously analyze topological sensitivity based algorithms for detection of diametrically small inclusions in an isotropic homogeneous elastic formation using single and multiple measurements of the far-field scattering amplitudes. A L²-cost functional is considered and a location indicator is constructed from its topological derivative. The performance of the indicator is analyzed in terms of the topological sensitivity for location detection and stability with respect to measurement and medium noises. It is established that the location indicator does not guarantee inclusion detection and achieves only a low resolution when there is mode-conversion in an elastic formation. Accordingly, a weighted location indicator is designed to tackle the mode-conversion phenomenon. It is substantiated that the weighted function renders the location of an inclusion stably with resolution as per Rayleigh criterion.

Original language	English
Pages (from-to)	442-460
Number of pages	19
Journal	Results in Physics
Volume	8
DOIs	https://doi.org/10.1016/j.rinp.2017.12.041
Publication status	Published - Mar 2018

Keywords

Elasticity imaging
Inverse elastic scattering
Resolution analysis
Stability analysis
Topological derivative

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/j.rinp.2017.12.041

Cite this

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title = "Topological sensitivity based far-field detection of elastic inclusions",

abstract = "The aim of this article is to present and rigorously analyze topological sensitivity based algorithms for detection of diametrically small inclusions in an isotropic homogeneous elastic formation using single and multiple measurements of the far-field scattering amplitudes. A L2-cost functional is considered and a location indicator is constructed from its topological derivative. The performance of the indicator is analyzed in terms of the topological sensitivity for location detection and stability with respect to measurement and medium noises. It is established that the location indicator does not guarantee inclusion detection and achieves only a low resolution when there is mode-conversion in an elastic formation. Accordingly, a weighted location indicator is designed to tackle the mode-conversion phenomenon. It is substantiated that the weighted function renders the location of an inclusion stably with resolution as per Rayleigh criterion.",

keywords = "Elasticity imaging, Inverse elastic scattering, Resolution analysis, Stability analysis, Topological derivative",

author = "Tasawar Abbas and Shujaat Khan and Muhammad Sajid and Abdul Wahab and Ye, {Jong Chul}",

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doi = "10.1016/j.rinp.2017.12.041",

language = "English",

volume = "8",

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journal = "Results in Physics",

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TY - JOUR

T1 - Topological sensitivity based far-field detection of elastic inclusions

AU - Abbas, Tasawar

AU - Khan, Shujaat

AU - Sajid, Muhammad

AU - Wahab, Abdul

AU - Ye, Jong Chul

PY - 2018/3

Y1 - 2018/3

N2 - The aim of this article is to present and rigorously analyze topological sensitivity based algorithms for detection of diametrically small inclusions in an isotropic homogeneous elastic formation using single and multiple measurements of the far-field scattering amplitudes. A L2-cost functional is considered and a location indicator is constructed from its topological derivative. The performance of the indicator is analyzed in terms of the topological sensitivity for location detection and stability with respect to measurement and medium noises. It is established that the location indicator does not guarantee inclusion detection and achieves only a low resolution when there is mode-conversion in an elastic formation. Accordingly, a weighted location indicator is designed to tackle the mode-conversion phenomenon. It is substantiated that the weighted function renders the location of an inclusion stably with resolution as per Rayleigh criterion.

AB - The aim of this article is to present and rigorously analyze topological sensitivity based algorithms for detection of diametrically small inclusions in an isotropic homogeneous elastic formation using single and multiple measurements of the far-field scattering amplitudes. A L2-cost functional is considered and a location indicator is constructed from its topological derivative. The performance of the indicator is analyzed in terms of the topological sensitivity for location detection and stability with respect to measurement and medium noises. It is established that the location indicator does not guarantee inclusion detection and achieves only a low resolution when there is mode-conversion in an elastic formation. Accordingly, a weighted location indicator is designed to tackle the mode-conversion phenomenon. It is substantiated that the weighted function renders the location of an inclusion stably with resolution as per Rayleigh criterion.

KW - Elasticity imaging

KW - Inverse elastic scattering

KW - Resolution analysis

KW - Stability analysis

KW - Topological derivative

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VL - 8

SP - 442

EP - 460

JO - Results in Physics

JF - Results in Physics

ER -

Topological sensitivity based far-field detection of elastic inclusions

Abstract

Keywords

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