Acoustic Tomography for Scalar and Vector Fields: Theory and Application to Temperature and Wind Estimation

Abstract

Acoustic tomography is a type of inverse problem. The idea of estimating physical quantities that influence sound propagation by measuring the parameters of propagation has proven to be successful in many practical domains, including temperature and wind estimation in the atmosphere. However, in most of the previous work in this area, the algorithms used have not been proven mathematically to provide the correct solution to the inverse problem.This paper considers the problem of reconstructing 2D temperature and wind fields by using acoustic tomography setups. Primarily, it shows that the classical time-of-flight measurements are not sufficient to reconstruct wind fields. As a solution, an additional set of measurements related solely to the parameters of sound propagation-more precisely, to the angles of departure/arrival of sound waves-is suggested. To take the full benefit of this additional information, the bent-ray model of sound propagation is introduced. In this work, it is also shown that, when a temperature and a source-free 2D wind field are observed on bounded domains, the complete reconstruction is possible using only measurements of the time of flight. Conversely, the angles of departures/arrivals are sufficient to reconstruct a temperature and a curl-free 2D wind fields on bounded domains. Further, an iterative reconstruction algorithm is proposed and possible variations to the main scheme are discussed. Finally, the performed numerical simulations confirm the theoretical results, demonstrate fast convergence, and show the advantages of the adopted bent-ray model for sound propagation over the straight-ray model.

The feasibility of unmanned aerial vehicle-based acoustic atmospheric tomography

“…The propagation delays were determined by integrating over the RBFs that represent the temperature and wind profiles, i.e., combining Eqs. (13), (14), and (15). The inversion procedures described in Sec.…”

“…ACOUSTIC ATMOSPHERIC TOMOGRAPHY Acoustic atmospheric tomography has been used to observe horizontal 2D atmospheric temperature and wind velocity profiles and to examine their evolution in time and space. The first implementation was based on a series of 10 m towers that support microphones and loud speakers covering an area of 200 Â 240 m. 12 Other arrays have subsequently been built at the University of Leipzig [13][14][15] and the Boulder Atmospheric Observatory, which allows 3D tomography. 16,17 A number of different techniques have also been developed, [17][18][19][20][21][22] including some that passively observe atmospheric properties using impulsive noise sources such as birds or meteors 23 or commercial aircraft.…”

Calibration Using Matrix Completion With Application to Ultrasound Tomography

“…Lemma 2: In the model defined in the previous section, sensors are distributed independently and uniformly at random on a circular ring of width with central radius . Then, with probability larger than , there exists a constant such that (11) where and are defined as in (3). The proof of this lemma can be found in Appendix C Now, to show that (9) (12) (13) for some constant .…”

“…We denote the observed measurement matrix by (3) Notice that the matrix has the same shape as shown schematically in Fig. 5.…”

Solving inverse source problems for linear PDEs using sparse sensor measurements

“…The wave equation is pervasive in the modeling of signals prevalent in speech recognition [8], acoustic tomography [9], speech and sound enhancement [10], sound/wave source localization [10], [11], whilst the Poisson equation is of huge importance in biomedical engineering applications, such as the localization of sources of neuronal activity (also known as brain source imaging (BSI)) from electroencephalographic (EEG) signals [1], [12], [13].…”