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Broadband electromagnetic frequency or time domain sensor techniques present high potential for quantitative water content monitoring in porous media. Prior to in situ application, the impact of the relationship between the broadband electromagnetic properties of the porous material (clay-rock) and the water content on the frequency or time domain sensor response is required. For this purpose, dielectric properties of intact clay rock samples experimental determined in the frequency range from 1 MHz to 10 GHz were used as input data in 3-D numerical frequency domain finite element field calculations to model the one port broadband frequency or time domain transfer function for a three rods based sensor embedded in the clay-rock. The sensor response in terms of the reflection factor was analyzed in time domain with classical travel time analysis in combination with an empirical model according to Topp equation, as well as the theoretical Lichtenecker and Rother model (LRM) to estimate the volumetric water content. The mixture equation considering the appropriate porosity of the investigated material provide a practical and efficient approach for water content estimation based on classical travel time analysis with the onset-method. The inflection method is not recommended for water content estimation in electrical dispersive and absorptive material. Moreover, the results clearly indicate that effects due to coupling of the sensor to the material cannot be neglected. Coupling problems caused by an air gap lead to dramatic effects on water content estimation, even for submillimeter gaps. Thus, the quantitative determination of the in situ water content requires careful sensor installation in order to reach a perfect probe clay rock coupling.

Modeling ultrasonic fields in front of a transducer in the presence and absence of a scatterer is a fundamental problem that has been attempted by different techniques: analytical, semi-analytical, and numerical. However, a comprehensive comparison study among these techniques is currently missing in the literature. The objective of this paper is to make this comparison for different ultrasonic field modeling problems with various degrees of difficulty. Four fundamental problems are considered: a flat circular transducer, a flat square transducer, a circular concave transducer, and a point focused transducer (concave lens) in the presence of a cavity. The ultrasonic field in front of a finite-sized transducer can be obtained by Huygens-Fresnel superposition principle that integrates the contributions of several point sources distributed on the transducer face. This integral which is also known as the Rayleigh integral or Rayleigh-Sommerfeld integral (RSI) can be evaluated analytically for obtaining the pressure field variation along the central axis of the transducer for simple geometries, such as a flat circular transducer. The semi-analytical solution is a newly developed mesh-free technique called the distributed point source method (DPSM). The numerical solution is obtained from finite element analysis. Note that the first three problems study the effect of the transducer size and shape, whereas the fourth problem computes the field in presence of a scatterer.

Interaction between a cavity or void in a liquid and a converging ultrasonic beam generated by a point-focused acoustic lens is investigated. A semi-analytical technique called the distributed point source method (DPSM) is adopted because no analytical solution is available for this problem involving cavities of different size and the finite element method is not very efficient for modeling high-frequency ultrasonic problems. The solution shows that if the cavity is placed very close to the focal point of the lens then it can be detected by the acoustic lens. The detectability of the cavity at the off-focus position depends on the distance of the cavity from the focal point. The variation of this distance as the cavity moves in horizontal and vertical directions from the focal point is also investigated.

Numerical modelling of the ultrasonic wave propagation is important for Structural Heath Monitoring and System Prognosis problems. In order to develop intelligent and adaptive structures with embedded damage detector and classifier mechanisms, detailed understanding of scattered wave fields due to anomaly in the structure is inevitably required. A detailed understanding of the problem demands a good modelling of the wave propagation in the problem geometry in virtual form. Therefore, efficient analytical, semi-analytical or numerical modelling techniques are required. In recent years a semi-analytical mesh-free technique called Distributed Point Source Method (DPSM) is being used for modelling various ultrasonic, electrostatic and electromagnetic wave field problems. In the conventional DPSM approach point sources are placed along the transducer faces, problem boundaries and interfaces to model incident and scattered fields. Every point source emits energy in all directions uniformly. Source strengths of these 360 degrees radiation sources are obtained by satisfying interface and boundary conditions of the problem. In conventional DPSM modelling approach it is assumed that the shadow zone does not require any special consideration. 360 degrees Radiation point sources should be capable of properly modelling shadow zones because all boundary and interface conditions are satisfied. In this paper it is investigated how good this assumption is by introducing the 'shadow zone' concept at the point source level and comparing the results generated by the conventional DPSM and by this modified approach where the conventional 360 degrees radiation point sources are replaced by the Controlled Space Radiation (CSR) sources.

Several investigators have modeled ultrasonic fields in front of transducers by Huygens-Fresnel superposition principle that integrates the contributions of a number of point sources distributed on the transducer face. This integral solution, also known as the Rayleigh integral or Rayleigh-Sommerfeld Integral solution, assumes the strengths of the point sources distributed over the transducer face. A newly developed technique called distributed point source method (DPSM) offers an alternative approach for modeling ultrasonic fields. DPSM is capable of modeling the field for prescribed source strength distribution as well as for prescribed interface conditions with unknown source strengths. It is investigated how the ultrasonic field in front of the transducer varies in different situations: (1) when the point source strengths are known, (2) when the point source strengths are unknown but obtained from the interface condition that only the normal component of the transducer velocity is continuous across the fluid-solid interface, (3) when all three components of velocity are assumed to be continuous across the interface for the no-slip condition, and (4) when the pressure instead of the velocity is prescribed on the transducer face. Results for these different interface conditions are compared with the analytical solutions along the central axis.

Phased array transducers are multi-element transducers, where different elements are activated with different time delays. The advantage of these transducers is that no mechanical movement of the transducer is needed to scan an object. Focusing and beam steering is obtained simply by adjusting the time delay. In this paper the DPSM (distributed point source method) is used to model the ultrasonic field generated by a phased array transducer and to study the interaction effect when two phased array transducers are placed in a homogeneous fluid. Earlier investigations modeled the acoustic field for conventional transducers where all transducer points are excited simultaneously. In this research, combining the concepts of delayed firing and the DPSM, the phased array transducers are modeled semi-analytically. In addition to the single transducer modeling the ultrasonic fields from two phased array transducers placed face to face in a fluid medium is also modeled to study the interaction effect. The importance of considering the interaction effect in multiple transducer modeling is discussed, pointing out that neighboring transducers not only act as ultrasonic wave generators but also as scatterers.