Estimation of Low-Velocity Landfill Thickness with Multi-Method Seismic Surveys

Abstract

Conventional geophysical methods are suitable for estimating the thicknesses of subsoil layers. By combining several geophysical methods, the uncertainties can be assessed. Hence, the reliability of the results increases with a more accurate engineering solution. To estimate the base of an abandoned landfill, we collected data using classical approaches: high-resolution seismic reflection and refraction, with more modern methods including passive surface wave analysis and horizontal-to-vertical spectral ratio (HVSR) measurements. To evaluate the thickness of the landfill, three different datasets were acquired along each of the two seismic lines, and five different processing methods were applied for each of the two arrays. The results of all the classical methods indicate very consistent correlations and mostly converge to clear outcomes. However, since the shear wave velocity of the landfill is relatively low (<150 (m/s)), the uncertainty of the HVSR results is significant. All these methods are engineering-oriented, environmentally friendly, and relatively low-cost. They may be jointly interpreted to better assess uncertainties and therefore enable an efficient solution for environmental or engineering purposes.

1. Introduction

Abandoned landfills can pose a significant environmental hazard, especially in cases where there is no information about the materials deposited or the geometry of the landfill. To estimate the area extent of the landfill, we can use historical and recent satellite photos. However, estimating the thickness of the landfill presents a much more challenging task.

The methods generally used to solve these challenges are geological surveys, mechanical drilling, and, in some cases, geophysical surveys. The classic seismic methods, seismic refraction and seismic reflection, are recognized as effective in finding boundaries between different layers in the subsurface [1,2,3,4,5]. These methods can certainly succeed in a landfill where the velocity of the waves is probably less than that of the adjacent soil or the host rock [6,7,8,9,10].

Surface wave processing techniques, such as extended spatial autocorrelation (ESAC) [11,12], multi-analysis of surface waves (MASW) [13], and refraction microtremor (ReMi) [14] are also methods to map the subsurface, and have been found to successfully image the subsurface [15,16,17,18,19,20,21].

Over the last decades, methods using a single station to record environmental noise have provided promising results in estimating the horizontal-to-vertical spectral ratio (HVSR) [22,23,24,25,26,27,28,29]. Several studies indicated the thickness of sediments and showed a good correlation with boreholes [30,31].

As part of a plan to expand a road south of Afula in northern Israel (Figure 1), an estimation of the depth of the base of a landfill was critical to the engineering and environmental aspects. To efficiently assess the depth without any environmental damage, we acquired data over two seismic lines. Each line was processed by five different techniques: seismic reflection, seismic refraction, refraction microtremor (ReMi), extended spatial autocorrelation (ESAC), and horizontal-to-vertical spectral ratio (HVSR).

2. Background and Geological Setting

The area’s geology consists of Eocene deposits, mainly characterized by limestone and Miocene basalts (Figure 2 and Figure 3). A normal fault lies on the west side of the estimated landfill border (Figure 2) and is expressed in the surface’s topography (Figure 3). No boreholes or other geological information are available in the area or environs. Unfortunately, no information is available regarding the thickness and features of the landfill in its various parts. Finally, no information is available regarding the type and characteristics of the materials buried within the landfill. According to aerial photos, we estimate the landfill’s area to be ~18,000 m² (Figure 3).

3. Methods

In this study, we used five different geophysical methods to evaluate landfill thickness. We used classical seismic reflection and seismic refraction, together with passive surface wave analyses: ReMi, ESAC, and HVSR measurements.

3.1. Seismic Reflection

The general principle of the method involves probing the subsurface with artificially generated acoustic waves. Seismic reflections occur at boundaries where a contrast in the acoustic impedance (density times acoustic velocity) is encountered. The raw data consist of measured travel times of the reflected waves from a source down to a buried interface, and its reflection back to the surface, where it is detected by a geophone.

The RadExPro software processing sequence of the seismic reflection data consists of the following steps: defining the array geometry (source and receiver locations), trace editing, FK filter—noise removal, Butterworth filter, spherical divergence correction, deconvolution, amplitude correction, normal moveout, and stacking.

3.2. Seismic Refraction

The wide-angle seismic refraction method estimates the travel times of the first arrivals at the linear array of geophones on the surface (direct wave or critically refracted waves), in order to define the geometry of any subsurface layers under the acquisition array.

The collected seismic dataset was processed for automatic inverse problem solving under the delay-time method using the RadExPro software. The seismic refraction data processing sequence consists of assigning the array geometry (source and receiver locations), filtering and enhancing the data, picking first arrivals, and building refraction boundaries.

3.3. Surface Waves (SW)

Most SW methods are based on three main steps: (1) acquisition of experimental data, (2) signal processing to obtain the experimental dispersion curve (velocity versus frequency), and (3) one-dimensional (1D) inversion to estimate vs. [32,33,34]. These SW methods are commonly divided into two main groups: active methods, where the source of the seismic waves can be a sledgehammer or a ‘dropped’ accelerated weight, versus passive methods, in which the waves result from spatially random sources (also known as random noise). In this research, we acquired passive data for the ReMi method described by Louie (2001) and for the ESAC method [11]. The ESAC approach allows the determination of phase velocities by evaluating the Bessel functions for each frequency considered [11].

The SW data were processed using the WinMASW software (ELIOSOFT Geophysical Software and Services) using the following sequence: assigning array geometry, transforming from the space–time domain to the frequency–velocity domain of each window, and finding the most informative dispersion image.

3.4. Horizontal-to-Vertical Spectral Ratio—HVSR

The horizontal-to-vertical spectral ratio (HVSR) technique, also known as the Nakamura method, was first introduced by Nogoshi and Igarashi (1971) [35] and spread widely by Nakamura (1989) [36]. This method uses a single station comprising a three-component seismometer that records ambient vibrations. By comparing the spectrum of the average horizontal components to their vertical component, the fundamental frequency of the site can be defined. An interference wave going through the surface will cause resonance when the wave’s length equals four times the thickness of the soft layer (Equation (1)) [37].

f₀ = Vs/4H

(1)

The HVSR data were processed based on the HVSRpy and Geopsy software [38]. The sequence consisted of removing the instrument response, filtering out transient noise, selecting time windows, calculating Fast Fourier Transform (FFT), averaging the two horizontal components for each time window, calculating the horizontal-to-vertical spectral ratio for each window, automated frequency-domain window-rejection algorithm, and using lognormal statistics, averaging all horizontal-to-vertical spectral ratios and calculating the standard deviation.

4. Equipment and Acquisition

Datasets for P-wave seismic reflection and refraction from two mutually perpendicular arrays were acquired (Figure 4). These lines were acquired with 48 vertical R.T.Clark Co (Oklahoma City, OK, USA). 28 Hz geophones and recorded on a Geometrics’ 24-bit Geode seismograph. The total lengths of the arrays were 47 m and 94 m, with 1 m and 2 m intervals (line 1 and line 2, respectively) (

Table 1. Acquisition parameters.

Method	Line Number	Source	Stacking	Sampling Interval (ms)	Record Length	Number of Sensors	Geophone Intervals (m)	Length of the Line (m)
Seismic reflection and refraction	1	8 kg sledgehammer	3	0.125	1	48	1	47
	2						2	94
ReMi and ESAC	3	---	---	4	20–45 (min)	12	4.5	49
	4						7.5	81
HVSR	---	---	---	1	15–60 (min)	24	---	---

). An 8 Kg sledgehammer was struck at an aluminum plate every 1 m or 2 m, including several meters offset along the lines (Table 1). For the ReMi, ESAC, and HVSR measurements (shown in white dots as Lines 3 and Line 4 in Figure 4), we used SmartSolo IGU-BD3C 0.2 Hz (Table 1).

5. Results

5.1. Seismic Reflection

The seismic reflection stack images show a strong reflector likely indicating the base of the landfill to be at a depth of 10 ± 2 m from the surface (Figure 5 and Figure 6).

5.2. Seismic Refraction

The data of Line 2 show seismic refraction events, and the base of the landfill is modeled to an approximate depth varying from 11 to 12 ± 1 m (Figure 7). Unfortunately, from the data of Line 1, it is impossible to estimate the landfill base because no refractions were found.

5.3. SW

According to the two seismic lines acquired, the passive SW results indicate a landfill’s thickness to be about 10 m (Figure 8, Figure 9, Figure 10 and Figure 11).

5.4. HVSR

The resonance frequency was estimated using the spectral ratio of the average horizontal components to the vertical component (HVSR). Twenty-four measurements were analyzed and interpreted (Figure 12). The peak frequencies varied between ~3.2 and ~10 Hz. Several measurements did not indicate any peak frequency.

6. Discussion

6.1. Thickness from HVSR Measurements

Due to the nature of the waste deposits, the landfill may exhibit lateral variations. However, we used Equation (1) to evaluate thickness from the HVSR measurements. According to the seismic reflection, seismic refraction, and SW results, the landfill thickness is roughly 10 m. Therefore, we calculated the average shear wave velocity (Vs) of the topmost ~10 m (Figure 13) and evaluated the landfill thickness for each HVSR sample. According to the peak frequency picked, and velocity of ~130 m/s, the thickness varies between ~4.8 and 11.2 m (Figure 14).

6.2. Uncertainties of the Different Methods

The vs. profiles from all methods vary by as much as ~30% (Figure 13), yielding Vs10 values that are within 25%. Some studies had comparable uncertain results [34,40,41], and others had lower values [42].

Each HVSR result has its own standard deviation (STD) for the fundamental frequency (f₀). This STD can reach 1 Hz but is usually less than 0.5 Hz. According to Equation (1), this STD can be expressed as an approximately 25% difference in landfill thickness. These findings are similar to previous studies [43].

More than 90% of the HVSR results of Line 3 are very comparable. Unfortunately, this cannot be said about the results in Line 4, which indicates significant variance. The reason for such variance may be the limestone rocks at the north-west side, which are probably less deep and with steeper slopes than other parts of the landfill. This can also explain the higher values of f_0, which indicates a lower boundary.

The seismic reflection ±2 m uncertainty yield from the resolution of the results. Both show a clear boundary around the same depth at the overlapping area.

6.3. Comparing All Results

Putting all the data together indicates that all methods converge to similar results (Figure 14). The seismic reflection result of the shorter seismic array (line 1) is very comparable to the SW results (line 3) (Figure 14). The HVSR results of this section are within the standard deviation of both the seismic reflection and SW results.

For the second segment, Lines 2 and 4 (Figure 14, lower panel), the seismic refraction result is similar to the SW results. The seismic refraction results fall within the lower STD boundary of the seismic reflection. The HVSR results of this section show a thinner thickness of the landfill layer.

It is important to note that due to the significant low Vs, the uncertainty of the HVSR results is considerably higher as compared to all other methods.

7. Conclusions

• This study demonstrates the advantages of integrating information from five seismic approaches to estimate landfill thickness and constrain its content via its average shear velocity.
• The results of all methods correlate comparably well with each other. Although the uncertainty of the HVSR results is more significant, the results are still within the uncertainty of the other methods.
• By combining several geophysical methods, which are non-destructive, environmentally friendly, and relatively low-cost, the reliability of the results may increase and yield a more accurate solution.
• All these methods can be jointly interpreted to assess uncertainties better and allow an efficient solution for environmental or engineering purposes.