## 1 Introduction  
According to the US Geological Survey in 2014, the average cost of karst collapses in the United States over the past 15 years is more than $300 million per year. The subsidence from sinkhole collapse is especially highest in Florida, Texas, Alabama, Missouri, Kentucky, Tennessee, and Pennsylvania. It is impossible to know when a catastrophic sinkhole collapse occurs. However, it is possible to predict the occurrence of such likely events. Sinkholes in karst terrain occur naturally and from anthropogenic activity, e.g., groundwater development, oil and gas drilling, surface loading, and urban expansion into previously undeveloped sinkhole-prone areas and drought or precipitation extremes [1, 2]. Most states with substantial damage attributed to karst sinkholes have public resources documenting sinkholes and sinkhole density locations, except for Texas [3].  
Hence, the appropriate geophysical methods to provide subsurface information are crucial for the migration of catastrophic disasters due to subsidence or sinkholes. Non-instructive tests or non-destructive (NDT) such as ground-penetrating radar (GPR) [4, 5], spectral analysis of surface waves (SASW) [6, 7], multi-channel analysis of surface waves (MASW) [8, 9], and micro-tremor array measurement (MAM) [10, 11] are useful methodologies to detect underground voids. They can provide 2D or 3D subsurface stiffness profiles from the measurements at the ground surface. Each method has advantages and limitations. For example, GPR can identify layering sites, but it cannot resolve material properties. However, seismic methods SASW and MASW can resolve layer thickness and stiffness of materials. These methods can be inserted into boreholes and can be used to measure subsurface characteristics from the inside of a borehole. Accurate voids detection can be appreciable. However, the softening process that occurs before the air voids formation was not usually involved in the checklist for inspection. The density and mechanical propertiesundergo a clear decrease when the soil became soft. Unfortunately, those methods are limited to provide more in-depth engineering information, such as soil type, strength, stability, and so on [12].  
Furthermore, these techniques do not resolve subsurface layering in the presence of certain anomalies. Impedance contrasts, moisture, and cavities can affect different tests in different ways. Ultrasonic techniques have been recently used to study the underwater distribution in soil [13] and soil properties. Recently pulsed velocity ultrasound has been used to detect hard objects in farmland [14]. However, most of these techniques require close contact of the transducer with the soil.  
Therefore, it is necessary to find an appropriate non-contact method for mapping subsurface voids and monitoring the soil's healthy in terms of mechanical properties and density while providing material properties through the evaluation of geophysical methods. Electromagnetic and seismic monitoring systems are the most commonly used techniques to detect voids on land. To overcome the limitations in these methods, such as compactness, low penetrate depth, and leakage of the transverse sound wave propagating in underground fluid, we introduce a recently developed elastographic mapping technique. The effective bulk modulus and effective density detection (EBME) [15] have been applied to underground soil health monitoring and void detection in a compact monostatic setup.