## 3 Results and Discussion
Before 2 ms, the sound wave has experienced the same media, and the first two echo were reflected at the interface between air and soil layers due to acoustic impedance mismatch. Between 2 ms and 4 ms, the temporal signal's zoomed-in view shows the reflections from the soft soil, softer soil, and air void in case Figure 3B-D compared to the normal soil (\"No cavity\"). The larger echo amplitude in case Figure 3C was due to the larger difference between the density and speed of sound properties in softer soil and healthy soil. The difference between the density and speed of sound in soft soil in case (Figure 3B) and healthy soil is smaller comparing with case Figure 3C (softer soil), which led to a smaller amplitude reflected echoes. The red dotted trace showed the two small symmetric reflection envelopes from the air void, as shown in Figure 3D. The air void's axial size could be estimated from the temporal distance between the highest peak of the two small symmetric reflection envelopes. Figure 3D shows the signal between 4.125 ms and 5 ms, which indicated the reflected wave from the interface between the soil and rock layers. As the sound wave in the four cases experiences different soil conditions during the two roundtrip propagation, the reflection from the interface between the soil and rock layers shows a clear time difference between the cases. Comparing Figure 3A, which is for healthy soil, and Figure 3D with one small air void, the reflected wave does not have any time delay for the arrival pulse. The attenuated amplitude of the signal in case Figure 3D was affected by the scattering due to the small air void. Due to slightly lower density and speed of sound in the soil's temperate region, the reflected wave in the case, Figure 3B, had a small amount of time delay compared to the healthy soil. When the decreased density and sound velocity values occurred more in the soft soil zone, the time delay between the soil with and without the soft region was larger, as illustrated in Figure 3C. From the temporal waveform in terms of pressure, as shown in Figure 3, the calculated relative density and effective bulk modulus values in healthy soil were normalized to 1. In the case of Figure 3B, the effective bulk modulus decreased to 0.923, and the effective density value of the soil layer reduced to 0.984. In the case of C, the effective bulk modulus decreased to 0.907, and the effective density value of the soil layer was lowered to 0.962. In the case of D, the effective bulk modulus decreased to 0.985, and the effective density value of the soil went down to 0.985. As the listed equations indicated, the amount of reflection time delay back from the rock layer provides a larger effect on the estimated effective bulk modulus and density values than the echo amplitude difference since sound speed is a square term in the equation. However, in Figure 3D, since the rock layer interface echo does not have a clear time delay in the measurement, the effective bulk modulus and effective density value decreased linearly by a small amount based on a decrease of the echo amplitude due to the scattering effect. In the numerical simulation, the defined media was not dispersive. In reality, the dispersion [20; 21] may be introduced by the nonuniform soil status. In a highly dispersive medium, the frequency components in a broadband acoustic pulse have different speed of sound (phase velocity). This dispersion would elongate the pulse width and modify the velocity of the acoustic pulses. For an accurate estimation of the effective bulk modulus and effective density values, the single frequency component phase velocity should be considered and used in place of the speed of sound value from the pulse envelope. Unlike the existing seismic methods of soil void detecting techniques, EBME uses a monostatic low-frequency sound wave to estimate the effective bulk modulus and effective density over the entire soil layer's depth in the effective area as large as the sound probe beyond the long-wavelength limit.