Characterization of Acoustic Ground Impedance at Blossom 

Point Research Facility

by W. C. Kirkpatrick Alberts, II, Mark A. Coleman, and John M. Noble

ARL-TR-5352 September 2010

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ARL-TR-5352 September 2010

Characterization of Acoustic Ground Impedance at Blossom 

Point Research Facility

W. C. Kirkpatrick Alberts, II, Mark A. Coleman, and John M. Noble

Computational and Information Sciences Directorate, ARL

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Characterization of Acoustic Ground Impedance at Blossom Point Research 

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W. C. Kirkpatrick Alberts, II, Mark A. Coleman, and John M. Noble

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14. ABSTRACT

The propagation of sound in the atmosphere is greatly influenced by the acoustic impedance of the ground surface. As part of

a recent urban acoustics study (Alberts, et al. J. Acoust. Soc. Am. 2008, 124 (2)), and as part of the revision of American 

National Standards Institute (ANSI) standard S1:18-1999: Template Method for Ground Impedance, the ground impedance 

was measured at three sites at the U.S. Army Research Laboratory’s (ARL) Blossom Point Research Facility: a grass field, an 

asphalt road, and a gravel road. This report describes the measurements and results at each of the three sites.

15. SUBJECT TERMS

Acoustic ground impedance

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W. C. Kirkpatrick Alberts, II

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iii

Contents

List of Figures iv

List of Tables iv

1. Introduction 1

2. Experimental Configuration 1

3. Results and Analysis 3

4. Conclusions 15

5. References 16

Appendix A. Tables of Cumulative Errors 17

Distribution List 18
iv

List of Figures

Figure 1. Drawing of experimental configuration. .........................................................................2

Figure 2. Grassland data (blue) superimposed over 1-parameter model templates (black)............4

Figure 3. Grassland data superimposed over 2-parameter model templates (colors as in 

figure 2)......................................................................................................................................5

Figure 4. Asphalt road data superimposed over 1-parameter model templates (colors as in 

figure 2)......................................................................................................................................7

Figure 5. Asphalt road data superimposed over 2-parameter model templates (colors as in 

figure 2)......................................................................................................................................8

Figure 6. Gravel road data superimposed over 1-parameter model templates (colors as in 

figure 2)....................................................................................................................................10

Figure 7. Gravel road data superimposed over 2-parameter model templates (colors as in 

figure 2)....................................................................................................................................10

Figure 8. Non-linear least squares fit to level differences measured over grassland (blue) 

using one- (green) and two-parameter (red) ground impedance models. Geometry A is 

(a), geometry B is (b), and geometry C is (c). Fit parameters and cumulative errors are 

shown in the same colors as their respective models...............................................................13

Figure 9. Non-linear least squares fit to level differences measured over asphalt using oneand two-parameter ground impedance models. Color and geometry representations are 

the same as in figure 8. ............................................................................................................14

Figure 10. Non-linear least squares fit to level differences measured over gravel using oneand two-parameter ground impedance models. Geometry A is (a) and geometry B is (b). 

Color representations are the same as in figure 8. ...................................................................14

List of Tables

Table 1. Geometries specified in the Template Method (2). ..........................................................2
1

1. Introduction

Sound propagating in the atmosphere is affected by many processes (wind, turbulence, terrain 

shape, etc.) that change the magnitude and phase of a source’s signal as it travels to a receiver. 

Amongst these processes, the impedance of the ground is often important (1). The ground varies

from acoustically hard surfaces, such as asphalt and hard packed soil, to acoustically soft 

surfaces, such as snow (2, 3). These extremes in impedance have vastly different effects on the 

amplitude and phase of a ground-reflected wave. Thus, knowledge of the acoustic impedance of 

the ground is important in obtaining an overall picture of the environment through which sound 

is propagating.

As part of an ongoing urban acoustics study (4), the ground impedance at the Blossom Point 

Research Facility (BPRF) has been characterized using the method prescribed in American 

National Standards Institute (ANSI) S1.18-1999: Template Method for Ground Impedance (5), 

which will be henceforth referred to here as the Template Method. Several methods exist for the 

measurement/deduction of the specific acoustic ground impedance (6–8), the ratio of the surface 

pressure to the average particle velocity of the fluid directed at the ground surface, but the 

Template Method was chosen for its ease of use (5, 9).

The following section describes the experimental configurations used over three surfaces at 

BPRF. Section 3 presents level difference spectra for each of the surfaces superimposed on 

calculated level difference spectra. In addition, the third section offers qualitative comparisons 

between the measurements and calculations. Concluding remarks appear in the fourth section.

2. Experimental Configuration

In the Template Method, a point source is positioned a short distance from two microphones 

separated in height perpendicularly above the ground. This allows the difference in sound level 

between the microphones to be measured. Using this level difference spectrum, the acoustic 

impedance of the ground can be deduced by comparing the measurement with calculated level 

differences. The Template Method describes three different geometries (A, B, and C), listed in 

table 1, that are used to measure level difference spectra above ground surfaces. Figure 1 shows 

a drawing of the experimental configuration. Each geometry has been designated in the 

Template Method for its potential performance on a given soil type: geometry A tends to cover 

the largest frequency range; geometry B may produce best results over hard grounds at 

frequencies greater than 1 kHz; and geometry C is, perhaps, best used over soft grounds for 

frequencies below 1 kHz. All geometries were used during experiments over grass and asphalt. 

Only geometries A and B were used over gravel. The lack of geometry C in the gravel 
2

measurement is due to the revised standard in which geometry C has been removed in favor of 

the more general geometries A and B. ARL provided a worked example of the revised Template 

Method over gravel to the ANSI ground impedance measurement working group. 

Table 1. Geometries specified in the Template Method (2).

Geometry Source Height: hs

(cm)

Top Microphone 

Height: ht (cm)

Bottom Microphone 

Height: hb (cm)

Source/Microphone 

Horizontal Separation (m)

A 32.5 46 23 1.75

B 20 20 5 1

C 40 40 5 1

Figure 1. Drawing of experimental configuration.

The source used for this work was a pressure driver coupled to a pipe of 0.5 m length and

3.175 cm diameter. This pipe-driver combination can be approximated as a point source to a 

frequency of nearly 2.7 kHz. However, because the pipe is 50 cm in length, there is potential for 

reflections from the face of the driver at the highest operating frequencies. These reflections 

tend to degrade the point-source performance of the pipe-driver system and, thus, alter the 

experimental results when they are compared to level differences calculated assuming spherical 

waves. Microphones used were half-inch pressure field microphones. The source waveform 

used in all instances was white noise that was band-limited from 150 Hz to 2.7 kHz. 

Microphone data were collected using a data acquisition computer sampling at 10 kilo-samples 

per second. Recorded microphone data were also filtered from 150 Hz to 2.7 kHz. During 

grassland and asphalt experiments, 60 s of data were collected for each of five sub-sites on each 

surface. During gravel experiments 30 s of data were collected for each of four sub-sites. In 

post-processing, recorded data were separated into one-second blocks with one third overlap 

between blocks. Each block was Hanning windowed, Fourier transformed, and all blocks were 

magnitude averaged for each ground type. During each experiment wind speeds and air 

temperatures were monitored; wind speeds remained less than the 2.5 m/s called for in the 

Template Method and measured temperatures were used in calculations during the analysis of 

the results. Temperatures during the measurements over grass and asphalt were roughly 16 °C 

and over gravel were 17 °C. Throughout the asphalt measurements, the surface of the asphalt 

Air

L Ground

microphones pipe-driver 

source

hs

hb

ht
3

was dry. The soil below the grass was damp but not saturated. The gravel was saturated; pools 

of standing water were in the vicinity of the measurement area. Reference 2 contains further 

information regarding the experimental configuration.

3. Results and Analysis

Template spectra that appear in the following analysis are obtained by calculating the spherical 

wave reflection coefficient with either a one-parameter or a two-parameter model inserted to 

describe the impedance of the ground. The one-parameter model, attributed to Delany and 

Bazley (10), is an empirically derived model for the impedance of hard-backed thin layers of 

absorbing materials. When normalized by the density of air and the speed of sound in air (ρ0 and 

c0 at 20 °C and 1 atm, respectively), the one-parameter model appears in the Template Method, 

separated into its real and imaginary parts, as

0.7 3

0 0

0.7 5

0 0

Im( / ) 11.9(1000 / )

Re( / ) 1 9.08(1000 / )







 

s eff

s eff

Z c f

Z c f

 

 

, (1)

where f is the frequency in Hz, and σeff represents the effective flow resistivity of the ground in 

Pa∙s/m2(5, 10). A second model, using two adjustable parameters to describe the impedance of 

the ground is attributed to Attenborough (11). The specific acoustic impedance ratio described 

by the two-parameter model appears in the Template Method, again after separation into real and 

imaginary parts, as

f

c

f

Zs c

f

Zs c

e e

e



 











8

1

Im( / )

1

Re( / )

0

0

0 0

0

0 0

 



, (2)

where, γ is the ratio of specific heats in air, σe represents the effective flow resistivity of the 

ground in Pa∙s/m2, and αe represents the rate of change of porosity with depth in units of m–1(5,

11).

The following six figures present measured and calculated level differences based on the 

templates provided in the Template Method. Numbers beside the black curves in each template 

represent the value of the effective flow resistivity used in calculating the ground impedance. 

The effective flow resistivity is a parameter of the soil and, in all figures, has units of 103

Pa∙s/m2. Results over grassland appear in figures 2 and 3, where the measured level differences 

have been superimposed over the templates designated by ANSI S1.18-1999. Figures 4 and 5

show measured level differences over asphalt superimposed on the templates. Figures 6 and 7

depict level difference as measured on a gravel road superimposed on the templates. Even 
4

numbered figures show measured level differences superimposed on one-parameter model 

templates, and odd numbered figures show the same measured level differences superimposed on 

two-parameter model templates. In each of the six figures, error bars of ± one standard deviation 

have been placed at approximately third-octave center frequencies along the measured curves. 

Visual comparison between the templates and the measured level differences is used as a starting 

place for nonlinear least squares, fitting of the ground impedance models listed in the Template 

Method to the measured data. 

Figure 2. Grassland data (blue) superimposed over 1-parameter model templates (black).

(a) (b)

(c)
5

Figure 3. Grassland data superimposed over 2-parameter model templates (colors as in figure 2).

(a) (b)

(c) (d)

(e) (f)
6

Figure 3. Grassland data superimposed over 2-parameter model templates (colors as in figure 2) (continued).

(g) (h)

(i) (j)

(k) (l)
7

Figure 4. Asphalt road data superimposed over 1-parameter model templates (colors as in figure 2).

(a) (b)

(c)
8

Figure 5. Asphalt road data superimposed over 2-parameter model templates (colors as in figure 2).

(a) (b)

(c) (d)

(e) (f)
9

Figure 5. Asphalt road data superimposed over 2-parameter model templates (colors as in figure 2) (continued).

(g) (h)

(i) (j)

(k) (l)
10

Figure 6. Gravel road data superimposed over 1-parameter model templates (colors as in figure 2).

Figure 7. Gravel road data superimposed over 2-parameter model templates (colors as in figure 2).

(a) (b)

(a) (b)

(c) (d)
11

Figure 7. Gravel road data superimposed over 2-parameter model templates (colors as in figure 2)

(continued).

Inspection of figures 2 and 3 shows that, over grass, Templates 1C with σeff = 50x103Pa∙s/m2, 

and 2C with αe = 3 and σe = 32x103Pa∙s/m2, show the closest fit to the average level difference 

curve. The claim of closest fit is based predominantly on the frequency positions of the minima 

in the curve rather than on the overall fit between the measured and calculated curves. Recall 

that theses inspections serve as a starting place for more involved numerical fitting. Similar 

inspections of figures 4 and 5 show that Templates 1C with σeff = 320x103Pa∙s/m2, and 2C with 

σe = 100x103Pa∙s/m2and for all αe, fit well with the level difference obtained over asphalt. 

Repeating the procedure on the gravel level difference, as in figures 6 and 7, shows that none of 

the Templates exhibits a particularly good fit. These qualitative findings are reinforced if the 

procedures laid out in reference 5 are followed, where the cumulative errors between level 

differences calculated using equation 1 or 2 and measured level differences are found from the 

following expression:

 









   



f

Lc La E

2



(3)

In equation 3, ΔLc is the calculated level difference, ΔLa is an average measured level difference, 

and σ is the standard deviation of the averaged measurements. Note that to obtain the cumulative 

(e) (f)

(g) (h)
12

error, E, the difference between the calculated and measured level differences normalized by the 

standard deviation of the measurement must be summed over all frequencies. In appendix A, 

tables A-1 and A-2 show the results of using equation 3 to compute the cumulative error between 

each of the one-parameter model templates and the measured level differences. Table A-3 shows 

the cumulative errors computed between each of the two-parameter model templates and the 

measured level differences. All of the cumulative errors are on the order of 103or larger. This 

might be expected, even in cases where the calculated curves closely match the measurements, 

because the standard deviation of the measurements was often very small at many frequencies. 

In order to obtain values for σeff, σe, and αe, equations 1 and 2 were used in nonlinear least 

squares fitting of the measured level difference spectra (12). Results of the fit routines appear in 

figures 8 through 10, where the fit was performed over the portion of the data from 250 to 

2500 Hz in an attempt to minimize potential errors at the highest frequencies due to the length of 

the pipe. In each of the figures, measurements are in blue with error bars at approximate thirdoctave center frequencies, level difference fits based on equation 1 are in green, and level 

difference fits based upon equation 2 are in red. Fit values of σeff in equation 1, and σe and αe in 

equation 2, are shown in green and red, respectively. Cumulative errors, calculated by equation

3, due to each fit are shown in the same colors. It should be noted that the 1-parameter level 

difference fit to level difference curves, using all geometries, over gravel and asphalt are 

particularly poor (figures 9 and 10). Further, the large negative values of αe—on the order of 103

1/m—tend to make the two-parameter fit suspect even though the curves appear to agree well 

with the measurements. This difficulty in fitting calculated level differences to measured level 

differences over such acoustically hard surfaces as asphalt and gravel is not unexpected. The 

application of the Template Method to these surfaces is not valid, as their impedances approach

the upper limit of either impedance model. Thus, asphalt and gravel, in the case of BPRF, 

should be considered rigid. The one- and two-parameter fits to the level differences over grass, 

however, are much more reasonable (figures 8a through 8c). While the cumulative errors are 

large in the comparison to templates, values for σeff and σe are reasonable when compared to 

ranges listed in appendix B of the Template Method, where σeff can range from 40–300 ×103

Pa∙s/m2, and σe can range from 30–400 ×103Pa∙s/m2for various grass covered surfaces with 

varying moisture content (5). The negative values of αe are unexpected, but are reasonable 

considering that BPRF is part of the floodplain of the Potomac River and the Nanjemoy Creek. 

Thus, the soil may have a large concentration of river silt. That silt content, coupled with the 

regular mowing of the grassland where the measurement occurred and the aerated top layer (due 

to root growth), could lead to a more porous layer above a lower less porous layer.
13

Figure 8. Non-linear least squares fit to level differences measured over grassland (blue) using one- (green) and 

two-parameter (red) ground impedance models. Geometry A is (a), geometry B is (b), and geometry C 

is (c). Fit parameters and cumulative errors are shown in the same colors as their respective models.

σeff = 1.61 x105Pa∙s/m2

E = 1.75 x104

σe = 9.93 x104Pa∙s/m2

αe = -239.27 1/m

E = 5.15 x103

σeff = 1.29 x104Pa∙s/m2

E = 2.65 x104

σe = 6.56 x104Pa∙s/m2

αe = -222.21 1/m

E = 1.07 x103

σeff = 6.51 x104Pa∙s/m2

E = 7.01 x103

σe = 2.60 x104Pa∙s/m2

αe = -87.37 1/m

E = 2.48 x103

(a) (b)

(c)
14

Figure 9. Non-linear least squares fit to level differences measured over asphalt using one- and two-parameter

ground impedance models. Color and geometry representations are the same as in figure 8.

Figure 10. Non-linear least squares fit to level differences measured over gravel using one- and two-parameter

ground impedance models. Geometry A is (a) and geometry B is (b). Color representations are the 

same as in figure 8.

σeff = 8.80 x106Pa∙s/m2

E = 1.16 x105

σe = 4.22 x10

5

Pa∙s/m2

αe = -1.06 x1031/m

E = 2.85 x104

σeff = 6.85 x105Pa∙s/m2

E = 1.26 x104

σe = 6.69 x105Pa∙s/m2

αe = -1.77 x1031/m

E = 282.83

σeff = 1.85 x105Pa∙s/m2

E = 4.27 x104

σe = 5.86 x104Pa∙s/m2

αe = -281.86 1/m

E = 1.48 x104

(a) (b)

(c)

(a) (b) σeff = 5.61 x106

Pa∙s/m2

E = 3.72 x104

σe = 4.93 x105Pa∙s/m2

αe = -1.33 x1031/m

E = 3.05 x103

σeff = 6.04 x106Pa∙s/m2

E = 5.29 x104

σe = 4.90 x105Pa∙s/m2

αe = -1.60 x1031/m

E = 659.00
15

4. Conclusions

As part of a study of sound propagation in the vicinity of an isolated building, the acoustic 

ground impedances of several surfaces—grass, asphalt, and gravel road—at BPRF have been 

deduced from measurements of level difference spectra. These spectra were measured using the 

procedures put forth in ANSI S1.18-1999: Template Method for Ground Impedance. The flow 

resistivity values obtained for the grass surface agree with published results, while rate of change 

of porosity with depth, αe, tends to be much lower than that reported in the Template Method. 

The negative values of αe are likely explained by the soil composition at BPRF. Future acoustic 

research at BPRF should treat the parameters reported herein as a guide only. Ground 

impedance can vary significantly from site to site, and can vary significantly according to the 

meteorological and soil conditions present at the time of the measurement.
16

5. References

1. Attenborough, K.; Taherzadeh, S.; Bass, H. E.; Di, X.; Raspet, R.; Becker, G. R.; Gudesen, 

A.; Chrestman, A.; Daigle, G. A.; L’Esperance, A.; Gabillet, Y.; Gilbert, K. E.; Li, Y. L.;

White, M. J.; Naz, P.; Noble, J. M.; van Hoof, H.A.J.M. Benchmark Cases for Outdoor 

Sound Propagation Models. J. Acoust. Soc. Am. 1995, 97 (1), 173–191.

2. Albert, D. G. Acoustic Waveform Inversion with Application to Seasonal Snow Covers. J.

Acoust. Soc. Am. 2001, 109 (1), 91–101.

3. Sabatier, J. M.; Hess, H.; Arnott, W. P.; Attenborough, K.; Romkens, M.J.M.; Grissinger, E. 

H. In Situ Measurements of Soil Physical Properties by Acoustical Techniques. Soil Sci. 

Soc. Am. J. 1990, 54, 658–672.

4. Alberts, W.C.K. II; Noble, J. M.; Coleman, M. A. Sound Propagation in the Vicinity of an 

Isolated Building: An Experimental Investigation. J. Acoust. Soc. Am. 2008, 124 (2), 733–

742 ().

5. S1.18-1999: Template Method for Ground Impedance; American National Standards 

Institute, 1999.

6. Don, C. G.; Cramond, A. J. Soil Impedance Measurements by an Acoustic Pulse Technique. 

J. Acoust. Soc. Am. 1985, 77 (4), 1601–1609.

7. Sabatier, J. M.; Raspet, R.; Frederickson, C. An Improved Procedure for the Determination 

of Ground Parameters Using Level Difference Measurements. J. Acoust. Soc. Am 1993, 94

(1), 396–399.

8. Zuckerwar, A. J. Acoustic Ground Impedance Meter. J. Acoust. Soc. Am. 1983, 73 (6), 

2180–2186.

9. Williams, J. An Acoustic Ground Impedance Measurement; ARL-TN-221; U.S. Army 

Research Laboratory: White Sands Missile Range, NM, July 2004.

10. Delany, M. E.; Bazley, E. N. Acoustical Properties of Fibrous Absorbent Materials. Appl. 

Acoust. 1970, 3, 105–116.

11. Attenborough, K. Ground Parameter Information for Propagation Modeling. J. Acoust. Soc. 

Am. 1992, 92 (1), 418–427.

12. Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes in C: 

The Art of Scientific Computing; Cambridge University Press: New York, 1988.
17

Appendix A. Tables of Cumulative Errors

Tables in this appendix list the cumulative errors obtained from using equation 3 when 

comparing measurements to the templates.
18

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