<div>The atomic force microscope (AFM), traditionally known as a nanoscale instrument for surface topography imaging and compositional contrast, has a unique ability to investigate buried, subsurface objects in non-destructive ways with very low energy. The underlying principle is the detection of interactions between the AFM probe and the sample subsurface in the presence of an external wave or eld. The AFM is a newcomer to the field of subsurface imaging, in comparison to other available highresolution techniques like transmission or scanning electron microscopy. Nevertheless,</div><div>AFM offers signicant advantages for subsurface imaging, such as the operation over a wide range of environments, a broad material compatibility, and the ability to investigate</div><div>local material properties. These make the AFM an essential subsurface characterization tool for materials/devices that cannot be studied otherwise. </div><div><br></div><div><div>This thesis develops a comprehensive qualitative and quantitative framework underpinning the subsurface imaging capability of the AFM. We focus on the detection of either electrostatic force interactions or local mechanical properties, using 2nd-harmonic Kelvin probe force microscopy (KPFM) and contact-resonance AFM (CRAFM),</div><div>respectively. In 2nd-harmonic KPFM we exploit resonance-enhanced detection to boost the subsurface contrast with higher force sensitivity. In CR-AFM we use the dual AC resonance tracking (DART) technique, in which the excitation frequencies are near one of the contact resonance frequencies. Both techniques take advantage of the maximized response of the cantilever at resonance which improves the signal to noise ratio. These enable high-resolution subsurface mapping on a variety of polymer</div><div>composites.</div></div><div><br></div><div><div>A relevant challenge is the ability to reconstruct the properties of the subsurface objects from the experimental observables. We propose a method based on surrogate</div><div>modelling that relies on computer experiments using nite element models. The latter are valuable due to the lack of analytical solutions that satisfy the complexity of the geometry of the probe-sample system and sample heterogeneity. We believe this work is of notable interest because offers one of few approaches for the non-destructive characterization of buried features with sub-micron dimensions.</div></div>

For most electromagnetic (EM) geophysical systems, the contamination of primary fields on secondary fields ultimately limits the capability of the controlled-source EM methods. Null coupling techniques were proposed to solve this problem. However, the small orientation errors in the null coupling systems greatly restrict the applications of these systems. Another problem encountered by most EM systems is the surface interference and geologic noise, which sometimes make the geophysical survey impossible to carry out. In order to solve these problems, the alternating target antenna coupling (ATAC) method was introduced, which greatly removed the influence of the primary field and reduced the surface interference. But this system has limitations on the maximum transmitter moment that can be used. The differential target antenna coupling (DTAC) method was proposed to allow much larger transmitter moments and at the same time maintain the advantages of the ATAC method. In this dissertation, first, the theoretical DTAC calculations were derived mathematically using Born and Wolf's complex magnetic vector. 1D layered and 2D blocked earth models were used to demonstrate that the DTAC method has no responses for 1D and 2D structures. Analytical studies of the plate model influenced by conductive and resistive backgrounds were presented to explain the physical phenomenology behind the DTAC method, which is the magnetic fields of the subsurface targets are required to be frequency dependent. Then, the advantages of the DTAC method, e.g., high-resolution, reducing the geologic noise and insensitive to surface interference, were analyzed using surface and subsurface numerical examples in the EMGIMA software. Next, the theoretical advantages, such as high resolution and insensitive to surface interference, were verified by designing and developing a low-power (moment of 50 Am²) vertical-array DTAC system and testing it on controlled targets and scaled target coils. At last, a high-power (moment of about 6800 Am²) vertical-array DTAC system was designed, developed and tested on controlled buried targets and surface interference to illustrate that the DTAC system was insensitive to surface interference even with a high-power transmitter and having higher resolution by using the large-moment transmitter. From the theoretical and practical analysis and tests, several characteristics of the DTAC method were found: (1) The DTAC method can null out the effect of 1D layered and 2D structures, because magnetic fields are orientation independent which lead to no difference among the null vector directions. This characteristic allows for the measurements of smaller subsurface targets; (2) The DTAC method is insensitive to the orientation errors. It is a robust EM null coupling method. Even large orientation errors do not affect the measured target responses, when a reference frequency and one or more data frequencies are used; (3) The vertical-array DTAC method is effective in reducing the geologic noise and insensitive to the surface interference, e.g., fences, vehicles, power line and buildings; (4) The DTAC method is a high-resolution EM sounding method. It can distinguish the depth and orientation of subsurface targets; (5) The vertical-array DTAC method can be adapted to a variety of rapidly moving survey applications. The transmitter moment can be scaled for effective study of near-surface targets (civil engineering, water resource, and environmental restoration) as well as deep targets (mining and other natural-resource exploration).

This dissertation focuses on quantitative subsurface and mechanical properties imaging potential of AFM probes. Extensive modeling of AFM probes are presented for thorough understanding of capabilities and limitations of current techniques, these models are verified by various experiments, and different methods are developed by utilizing force-sensing integrated read-out active tip (FIRAT), which is an active AFM probe with broad bandwidth. For quantitative subsurface imaging, a 3-D FEA model of AFM tip-sample contact is developed and this model can simulate AFM tip scan on nanoscale-sized buried structures. FIRAT probe, which is active and broadband, is utilized for interaction forces imaging during intermittent contact mode and mechanical characterization capability of this probe is investigated. It is shown that probe dynamics, stiffness, stiffness ambiguity, assumed contact mechanics, and noise are important parameters for the accuracy of mechanical properties imaging. An active tip control mechanism is introduced to limit contact forces during intermittent contact mode. In addition to these, a combined ultrasonic AFM and interaction forces imaging method is developed and modeled to solve the reduced elasticity measurement sensitivity on composite materials. This method is capable of imaging a broader range of elasticity on combination samples such as metal nanoparticles in polymers at nanoscale.

The problem of sensing a medium by several sensors and retrieving interesting features is a very general one. The basic framework of the problem is generally the same for applications from MRI, tomography, Radar SAR imaging to subsurface imaging, even though the data acquisition processes, sensing geometries and sensed properties are different. In this thesis we introduced a new perspective to the problem of remote sensing and information retrieval by studying the problem of subsurface imaging using GPR and seismic sensors. We have shown that if the sensed medium is sparse in some domain then it can be imaged using many fewer measurements than required by the standard methods. This leads to much lower data acquisition times and better images representing the medium. We have used the ideas from Compressive Sensing, which show that a small number of random measurements about a signal is sufficient to completely characterize it, if the signal is sparse or compressible in some domain. Although we have applied our ideas to the subsurface imaging problem, our results are general and can be extended to other remote sensing applications. A second objective in remote sensing is information retrieval which involves searching for important features in the computed image of the medium. In this thesis we focus on detecting buried structures like pipes, and tunnels in computed GPR or seismic images. The problem of finding these structures in high clutter and noise conditions, and finding them faster than the standard shape detecting methods like the Hough transform is analyzed. One of the most important contributions of this thesis is, where the sensing and the information retrieval stages are unified in a single framework using compressive sensing. Instead of taking lots of standard measurements to compute the image of the medium and search the necessary information in the computed image, a much smaller number of measurements as random projections are taken. The data acquisition and information retrieval stages are unified by using a data model dictionary that connects the information to the sensor data.

The problem of subsurface imaging with Ground Penetrating Radar (GPR) is a challenging one. Due to the low-pass nature of soil sensors must utilise wave-lengths that are of the same order of magnitude as the object being imaged. This makes imaging difficult as straight ray approximations commonly used in higher frequency applications cannot be used. The problem becomes even more challenging when the target is shallowly buried as in this case the ground surface reflection and the near-field parameters of the radar need to be considered. This thesis has investigated the problem of imaging shallowly buried targets with GPR. Two distinct problems exist in this field radar design and the design of inverse scattering techniques. This thesis focuses on the design of inverse scattering techniques capable of taking the electric field measurements from the receiver and providing accurate images of the scatterer in real time. The thesis commences with a brief introduction to GPR theory. It then provides an extensive review of linear inverse scattering techniques applied to raw GPR data. As a result of this review the thesis draws the conclusion that, due to its strong foundations in Maxwell's equations, diffraction tomography is the most appropriate approach for imaging shallowly buried targets with GPR. A three-dimensional diffraction tomographic technique is then developed. This algorithm forms the primary contribution of the thesis. The novel diffraction tomography technique improves on its predecessors by catering for shallowly buried targets, significant antenna heights and evanescent waves. This is also the first diffraction tomography technique to be derived for a range of antenna structures. The advantages of the novel technique are demonstrated first mathematically then on synthetic and finally practical data. The algorithm is shown to be of high practical value by producing accurate images of buried targets in real time.

We are concerned with the high-fidelity subsurface imaging of the soil, which commonly arises in geotechnical site characterization and geophysical explorations. Specifically, we attempt to image the spatial distribution of the Lame parameters in semi-infinite, three-dimensional, arbitrarily heterogeneous formations, using surficial measurements of the soil's response to probing elastic waves. We use the complete waveforms of the medium's response to drive the inverse problem. Specifically, we use a partial-differential-equation (PDE)-constrained optimization approach, directly in the time-domain, to minimize the misfit between the observed response of the medium at select measurement locations, and a computed response corresponding to a trial distribution of the Lame parameters. We discuss strategies that lend algorithmic robustness to the proposed inversion schemes. To limit the computational domain to the size of interest, we employ perfectly-matched-layers (PMLs). The PML is a buffer zone that surrounds the domain of interest, and enforces the decay of outgoing waves. In order to resolve the forward problem, we present a hybrid finite element approach, where a displacement-stress formulation for the PML is coupled to a standard displacement-only formulation for the interior domain, thus leading to a computationally cost-efficient scheme. We discuss several time-integration schemes, including an explicit Runge-Kutta scheme, which is well-suited for large-scale problems on parallel computers. We report numerical results demonstrating stability and efficacy of the forward wave solver, and also provide examples attesting to the successful reconstruction of the two Lame parameters for both smooth and sharp profiles, using synthetic records. We also report the details of two field experiments, whose records we subsequently used to drive the developed inversion algorithms in order to characterize the sites where the field experiments took place. We contrast the full-waveform-based inverted site profile against a profile obtained using the Spectral-Analysis-of-Surface-Waves (SASW) method, in an attempt to compare our methodology against a widely used concurrent inversion approach. We also compare the inverted profiles, at select locations, with the results of independently performed, invasive, Cone Penetrometer Tests (CPTs). Overall, whether exercised by synthetic or by physical data, the full-waveform inversion method we discuss herein appears quite promising for the robust subsurface imaging of near-surface deposits in support of geotechnical site characterization investigations.

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