Time-reversal imaging

Abstract

We consider the problem of locating buried objects by generating an acoustic wavefield in the medium and using data from the detected waves. Making images that displays such targets can be done with little interfering of the medium under investigation. If there are reflecting features present, acoustic sources can be excited and measured outside the medium and the detecions are used to make an image of the interior. In this thesis we study two techniques named MUSIC and backpropagation. The reader should be aware of that although MUSIC appears frequently in areas of signal processing, it is not the traditional version which recognizes a signal through its frequencies when there is additional noise present. The technique discussed herein is referred to as MUSIC in other litterateur and it is not made an exception here. Both algorithms are built upon the same theory of time-reversing acoustic waves. In Chapter 1 some of the underlying theory on this subject is presented together with additional proposals of applications. This chapter also introduces central concepts for the following work. It is discussed in a somewhat simpler form but with support of mathematics and physics describing wave propagation in a convenient way. Chapter 2 contains a complete theoretical description with focus on deriving the two algorithms. The treatment of this is general but with an underlying thought of cases that are studied here. The model for emitting and detecting waves follows the geometry of a borehole-acquisition. Sources are then placed on the surface of a medium and the measurements are done in a well within it. MUSIC and backpropagation are tested on data extracted from simulating propagating waves. It is desired to obtain data that behaves like in physical experiments, but at the same time have good control over the generated data. The purpose is to investigate the results from employing these techniques to pointlike targets present in a homogeneous background medium. It is done in a 2D environment by numerically simulating waves according to the physical laws of propagation. Discussion about how this is done is given in Chapter 3. Similar work has been published and the article given in [1] has inspired some of the questioning for this thesis, both in underlying theory and when testing the imaging algorithms. It is tried to make a more complete description herein, this gains awareness about the validity of theoretics versus restrictions in experiments. Results from simulated experiments are shown and discussed in Chapter 4. They are compared with images and results from ideally generated data. It is focused mainly on monochromatic waves (signals with a single frequency), but under the treatment of ideal data the question of exploiting signal bandwidth is briefly studied. This question naturally comes to mind when considering the way data is generated. Under the same treatment we will see how extending the arrays can improve the accuracy of images. We will be using limited apertures in a certain bore-hole geometry. From this it follows that the performance of the algorithms are tried with restricted access to data. In previous work there are strong indications of MUSIC being the better technique, but we do not exclude the other because it is expected that backpropagation also can be a well performing technique. MUSIC will be tested on several target geometries, also on cases that obviously violates assumptions from the theory. A usual problem when gathering data from measurements in real or experimental data-acquisitions is the presence of noise on output recordings. This defines the final test, where MUSIC is employed to simulated data that contains noise of different levels.