microtremor methods applied to groundwater studies

CSIRO PUBLISHING

www.publish.csiro.au/journals/eg Exploration Geophysics, 2007, 38, 125–131

Microtremor methods applied to groundwater studies∗

Camilla Sorensen1,2,3 Michael Asten1,3

1School of Geosciences, Monash University, Melbourne VIC 3800, Australia.2Current address: Geoscience Australia, Symonston ACT 2601, Australia.3Corresponding author. Emails: [email protected]; [email protected]

Abstract. The Campaspe Deep Lead, which underlies the modern-day Campaspe River Valley in north-eastern Victoria,is an important local source of ground water. The exact location of the lead near Goornong is disputed, and it is consequentlyof interest to see whether a geophysical method can add information to the existing hydrological and geological data.

Two microtremor methods have been applied in this area. The horizontal to vertical spectral ratio method (HVSR) wasused as a reconnaissance tool to gain information about the change in resonant frequency across the field area. Modellingof the HVSR data qualitatively estimated a basement depression below and east of the river. The passive seismic spatialautocorrelation (SPAC) method was applied at four locations in the vicinity of the aquifer to gain information aboutdepth to bedrock and layer intervals as well as shear wave velocities. Unconstrained inversion of SPAC data resulted insimilar basement topography, but overestimated by tens of metres. Constraining the basement depth to that found in nearbyboreholes gives a relatively unchanged data misfit, and an approximate location of the vertical boundaries of the deep lead.Use of these methods in groundwater exploration would primarily be for cost-effective mapping of regolith and basementstructure between boreholes, especially in saline overburden, land or urban environments.

Key words: Microtremors, HVSR, SPAC, groundwater studies.

Introduction

A range of geophysical techniques has traditionally been appliedto regolith studies, including electrical, electromagnetic, andseismic methods. Both resistivity and P-wave velocity imagingcan provide ambiguous results, and these methods performpoorly in noisy environments, such as near urban powerlinesor machinery generating vibrations. In a saline-saturatedsand-clay profile, electrical and electromagnetic techniqueshave poor signal penetration and a lithological interpretationcan be difficult. P-wave refraction and reflection signals mayrespond similarly to impermeable clay and permeable sands.Surface wave methods image shear wave velocities of the layers,irrespective of pore fluid salinity and saturation.

The Campaspe Deep Lead, which underlies the modern-dayCampaspe River valley in north-eastern Victoria, is an importantlocal source of groundwater. The exact location of the lead isdisputed and it is of interest to establish whether the microtremormethod can add information to the already existing hydrologicaland geological data.

The microtremor method is based on the measurement ofseismic noise (weak, low amplitude vibrations recorded on thesurface of the earth), generated by either natural sources such aswind and wave action or by humans, e.g., by road traffic. Twomicrotremor techniques that have been extensively described inthe literature are the horizontal to vertical spectral ratio method(HVSR) (Nakamura, 1989) and the Spatial AutocorrelationMethod (Aki, 1957).

The objectives of this study are, first, to test the microtremormethod for viability in regolith studies and second, and morespecifically, to locate the boundaries of the Campaspe Deep Leadnear Goornong.

∗Presented at the Australian Earth Sciences Convention, June 2006, Melbourne.

An overview of the microtremor methods used in thisstudy is provided; the spatial autocorrelation (SPAC) and thehorizontal to vertical spectral ratio (HVSR) methods. Thesemethods are applied to the groundwater study site and the resultsare compared with boreholes and the existing geoscientificknowledge.

Study area

In north-central Victoria the Campaspe River aquifer systemsconsist of two major units. The Campaspe Deep Lead (Tertiary)forms the major aquifer of the region. It is overlain bythe Shepparton Formation (Plio-Pleistocene), which forms acomplex shallow aquitard–aquifer system. In areas beyond thelead the Shepparton Formation directly overlies bedrock, andconsists predominantly of clay with minor shoestring sandaquifers (Arad and Evans, 1987).

These units have been studied by several authors includingArad and Evans (1987), Brown and Stephenson (1991), Chiewand McMahon (1991), and the location and the nature of thedeep lead seem to be well understood (Arad and Evans, 1987).Near Goornong it appears to diverge from the main deep leadsystem and along the Bendigo–Murchison Road the exact widthof this feature is poorly understood.

In the Campaspe valley the Tertiary deep lead incorporatesthe lithologically similar Renmark Group and the CalivilFormation. The deep lead starts at Axedale, becomes deeper andwider towards the north and consists mainly of gravel and sand,with minor parts of clayey sand or clay and varies from confinedto semi-confined. Shepparton Formation sediments on top ofthe lead form the main surface exposure. This formation variesfrom unconfined to semi-confined and consists predominantly

© ASEG 2007 10.1071/EG07016 0812-3985/07/020125

126 Exploration Geophysics C. Sorensen and M. Asten

of clay with minor sand aquifers. Palaeozoic bedrock underliesthe deep lead, and forms a fractured aquifer, which is capable oftransmitting water, but is considered to play a minor part in theoverall system (Arad and Evans, 1987).

The Tertiary–Quaternary sequences range in thickness from70–100 m in the south to 120–150 m in the north. In a typicalsequence the Shepparton Formation is at ∼0–50 m depth, theCalivil at ∼50–75 m and the Renmark Group at ∼75–100 mwith the Ordovician sedimentary bedrock intersected at ∼100 mdepth (Mark Reid, personal communication, 2006). Figure 1shows the location of the field area.

MethodsThe microtremor methods used in this investigation includedthe spatial autocorrelation method (SPAC) (Aki, 1957) and thehorizontal to vertical spectral ratio method (HVSR) (Nakamura,1989). These methods are based on the measurement of seismicnoise (weak, low amplitude vibrations recorded on the surface ofthe earth) generated either by natural sources, for example windand wave action, or man made noise such as road traffic andindustrial machinery. Because surface waves are dispersive andhave a phase velocity that varies with wavelength or frequency,inversion of dispersion data can result in an estimation ofthe shear wave profile for any given site (Tokimatsu, 1997;Okada, 2003).

The SPAC method applied uses an array of geophones,which simultaneously measure the vertical component of thewave-field. By calculating the coherency of waves betweensingle geophones in the array and azimuthally averaging thesefor geophones with the same separation distance, a coherencycurve can be obtained. This in turn can be described by aBessel function of zero order, the shape of which depends onthe station separation and the dispersion characteristics of theground, as represented by equation (1):

c(f ) = J0

(2πf r

V (f )

), (1)

where c(f ) is the azimuthally averaged coherency, f is thefrequency, J0 is the zero-order Bessel function, V( f ) is thevelocity dispersion relationship, and r is the station separation.

The model parameters (thicknesses, density and velocities)can be estimated by using a manual iterative process to comparethe measured coherency curve to a theoretical computedcoherency curve.

Fig. 1. Study location.

The HVSR method was first presented by Nogoshi andIgarashi (Nogoshi and Igarashi, 1971), it was popularised byNakamura (1989) and has since been studied by several others(Asten and Dhu, 2004; Tokimatsu, 1997; Bodin et al. 2001).In this method, three components of the wave field are measuredat single stations and the horizontal to vertical particle motionratio is calculated. It is generally accepted that the measurementand the calculation of the HVSR gives a peak frequency whichis characteristic of the shear-wave resonance of the sedimentsbetween the surface and the harder bedrock. The shear wavesediment resonances obtained are consequently very valuablefor mapping site amplification effects which makes the HVSRa useful method in earthquake risk assessment, (Konno andOhmachi, 1998; Asten and Dhu, 2004; Asten et al., 2004;Gallipoli et al., 2004).

For each HVSR measurement, the vector sum of thehorizontal components is calculated and the Fourier spectrumis produced for the horizontal as well as the vertical component.The horizontal to vertical spectral ratio can then be calculatedand the HVSR curve produced.

A change in peak frequency from one location to anotheris indicative of either a change in sediment thickness or achange in shear wave velocity. Lower level peaks indicateadditional layer boundaries with a significant velocity contrastbetween layers.

More detailed accounts on these methods can be found inTokimatsu (1997), Nakamura (1989, 2000) and Okada (2000).

Data acquisition

The HVSR survey was carried out along the Bendigo–Murchison Road, between the Elmore–Barnadown Road to thewest, and Houlden Road to the east. A stretch of ∼6.5 km wassurveyed with sample spacing of 400 m, and of 200 m towardsthe central part of the area. A three-component L4C-3D 1 Hzgeophone was used for the measurements. The ground vibrationswere measured for 200 s at a sampling rate of 200 samples persecond. Traffic along the road is the main source of vibration inthis area, and given that cars generate vibrations in the range of5–15 Hz, it may prove difficult to obtain enough energyoutside this interval to retrieve information from greater depths(e.g., depth to bedrock). The source as well as the materials aredetermining factors for depth penetration.

The SPAC survey consisted of four measurements locatedin the same area as the HVSR measurements, and two

Microtremor methods and groundwater Exploration Geophysics 127

IS ROAD

IGO-MURCHISON ROAD

DC

B

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G8005631/01Bedrock at 63 m

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BICKLEY ROAD

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SK

ER

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Fig. 2. Location of SPAC measurements (A–D) and boreholes, which reach bedrock.

measurements located each side of the Campaspe River. Themain reason for conducting this survey was to determine shearwave velocities and layer boundaries.

The SPAC locations were primarily chosen based onaccessibility, location of a borehole and the indicative trendsfrom the HVSR survey (Figure 2). The survey was conductedwith a hexagonal array of geophones with radii of 20 and 50 m.Mark L-28B 6 Hz geophones were used for the survey, a digitizerand a Kelunji recorder were used to record the measurements,with time windows of 3 min and a sampling rate of 200 samplesper second.

Results

Horizontal to vertical spectral ratio

A HVSR curve was produced for each location and the peakfrequency determined. Figure 3 shows the peak frequenciesacross the survey area.

The peak frequencies vary considerably over the study area.In the western part the values are high compared with the areadirectly to the east, with frequencies in the range 0.4–0.6 Hz.An increase in the peak frequency can be interpreted as eithera thinning or stiffening of the softer material overlying harderbedrock, or a combination of both.

A theoretical ellipticity curve was modelled and comparedto the measured HVSR curves. The modelled ellipticity curveis most sensitive to changes in velocity and thickness at higherfrequencies, while at low frequencies a larger change is neededin order to change the curve. The higher frequency range seemsto be better determined than the lower range, and it appears to beeasier to reproduce the shape of the HVSR curve in the higher(3–10 Hz) than in the lower range (Figure 4).

The velocity profiles were obtained by fixing the shear wavevelocities for a set number of layers. The knowledge that thesediment cover consists primarily of clays and sands overlyingbedrock made it possible to make reasonable guesses of thevelocities (VP and VS). This modelling led to interpreted apparentdepths that can be stitched together to form a 2D profile alongthe Bendigo–Murchison Road. The ellipticity modelled fromthe measured HVSR has a large margin of error attached toit, therefore the 2D section will only give a semiquantitativeestimate of velocities and thicknesses (Figure 5). The valuesat greater depth will in particular possess a certain degree ofambiguity, and the boundary between the sediment and thebedrock may be gradational due to a zone of weathered bedrock.

Nakamura (2000) showed that from the following genericequation (2) either the depth to bedrock or the shear wavevelocity of the sediments can be estimated assuming one of thosetwo parameters is known:

VS = 4H/T (2)

where VS is the shear wave velocity, H is the thickness ofthe sediment and T is the resonant period of the sediments,as indicated by the peak period on the HVSR.

A peak frequency of 0.6 Hz and an estimated average shearwave velocity of 300 m/s results in 125 m of sediment overlying

3.0

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1.0

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uenc

y (H

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Fig. 3. The measured peak frequencies [Hz].

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Ellipticity curve for model file: MBR1_F11

H/V Ratio: BMR_F11 : 07/24/05 02:51Freq (Hz)

Points 1 to 59000

Fig. 4. Measured HVSR curve (solid line) compared to the modelledHVSR curve (dashed line). HVSR modelled for the first-higher Rayleighmode is also shown (dotted line).


Dep

th (

m)

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284000 285000 286000 287000 288000

HVSR model section

Easting (m)Shear wave velocity

Fig. 5. Approximate depths derived by using fixed approximate shear wave velocities whenmatching the observed peak H/V frequency with the one obtained from the theoretical ellipticitycurves.

bedrock using equation (2). Boreholes from the area suggesta shallower depth to bedrock of between 60 and 85 m. Thesame calculation, with a shear wave velocity of 0.6 Hz anda thickness of sediment of 60 m (obtained from a nearbyborehole), results in an average shear wave velocity of 144 m/s.This fairly low average velocity suggests that the geology isdominated by very soft materials such as clay and very finegrained sand.

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AZIM AVE COHERENCY: BENC50F4: 29 MAR 2006



Frequency (Hz)Radius = 50 r1. Std Dev = 0.096



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m a

ve c

oher

ency

Azi

m a

ve c

oher

ency

Azi

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oher

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(a) (b)

Fig. 6. (a) Time series for the seven geophones at site C. A 50-s segment of data sampled at 200 samples per second. A typicalfile processed for coherencies has a length of 200 s. (b) Measured coherency curves for a station separation of 50 m (black line),plotted against the theoretically derived coherency curve for the fundamental mode (dashed line) for r1–r3.

Interpretation of SPAC dataFigure 6a shows a selected section (50 s out of a total of 200 s)of a measured time series at location C. This series showsthe energy generated from passing cars, and shows that thegeophones located closest to the road are the ones that receivethe energy first. In rural areas cars are the main energy source,and it may occasionally be necessary to drive the field vehicle toassist in producing measurable energy.


The measured coherency curves were compared totheoretically computed curves and a best-fit model was derived.The corresponding velocity profiles were produced for both the20 and the 50 m arrays. An example of the theoretically modelledcurve (dashed line) fitted to the measured coherency curve (solidline) is shown in Figure 6b. A close fit between the theoreticaland the modelled coherency curve is achieved for the frequencyband 3–20 Hz, which indicates that the model derived in theprocess is a credible model. In this type of SPAC modelling thedispersion curve (example curve shown in Figure 7) is bypassedand the SPAC spectra fitted directly.

To determine the sensitivity of the layers in the estimatedmodels a sensitivity study was undertaken. Changing the layerthicknesses and velocities one at a time made it possibleto establish the degree to which the parameters could bedetermined. This test showed that in some cases a change invelocity of as little as 10% was enough to give a significantlyless accurate fit between the measured and the modelled curves.This is seen by the increase of 5–25% in standard deviation of fitbetween measured and modelled coherency curves. A change of50% (especially for thicknesses) was in other cases required toinfluence the curve fit by the smallest amount. At greater depths,the thickness in particular required greater changes to make animpact on the curve fitting. In the upper layers, small parameterchanges resulted in a significantly worse fit between the dataand the model curves. Figure 8 shows the velocity profile (solidline) and the result of the sensitivity test (dotted lines) for twodifferent sites.

The coherency between geophones and the averagecoherency of geophones sharing the same separation distancecan be calculated. Deriving several coherency curves fordifferent separation distances and simultaneously fitting atheoretically modelled coherency curve to them increasesthe credibility of the estimated model. Figure 9 shows thedifferent radii usually used for the coherency calculations fora hexagonal array.

The SPAC data was first processed unconstrained and abest-fit model was derived for each of the SPAC locations.A good fit was not consistently obtained for all the locations,and a non-horizontal layered earth beneath the array might bethe cause. Choosing the station separation differently might showif a non-horizontal layered earth is present. An alternative tothe station separations shown in Figure 9 is a hexagonal setof triangles. This allows for a comparison of the coherencycurves for the different triangles in the hexagon. Similar looking

1000

1001 10

Velocity dispersion curves for model file: BENC5DF4_inv

Freq (Hz)

Vel

ocity

(m

/sec

)

Fig. 7. Phase velocities computed from field coherencies in Figure 6b (r1),plotted on modelled dispersion curves of the first two Rayleigh modes.

coherency curves indicate a horizontally layered earth, whereasdissimilarity indicates a change in geological features betweenthe triangle locations.

For the two sites where the fit between the theoretical andthe modelled coherency curves was distinctively worse (sites Aand B) this alternative processing approach resulted in dissimilarlooking coherency curves for the triangles. A non-horizontalfeature is therefore expected at these two sites.

The velocity profiles obtained from the manual iterativecomparison of measured and modelled coherency curves areshown in Figure 10. The 20 m arrays (dotted lines) arenot sensitive to changes of velocity or thickness at depthsgreater than 50 m, and consequently these values are practicallyunresolved. The 50 m array measurements (solid lines) aresensitive to greater depths, and at depths of 50 m or morethe values estimated from these measurements have superiorresolution to the ones from the 20 m arrays.

The profiles modelled from the 50 m arrays show a depthto bedrock ranging from 85–115 m (west to east, solid lineson Figure 10). Three boreholes located close to the SPACmeasurements show quite different values, but the trend ofincreasing depth to bedrock from west to east is observed forboth the SPAC models and the boreholes.

Site A 20 m array Site C 50 m array

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m)

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th (

m)

Fig. 8. Velocity profiles (solid lines) for site A and C (see Figure 2 forlocation). Dotted lines show the outer limits of the sensitivity test.

r1

r4

r2

r3

Fig. 9. Hexagonal array used for the SPAC measurements; r1–r4 showsthe different station separations for which the coherencies are calculated inthe array.


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Dep

th (

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Site C Site B Site ASilt

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Sand

Bedrock

Sand +Gravel

Fig. 10. Velocity profiles for SPAC sites (from west to east) D, C, B, and A. Dotted line denotes 20 m arrays, solidline 50 m arrays, and the dashed line shows the constrained SPAC models.

Table 1. Standard deviations derived from the fit between measured and modelled coherencycurves for models with (constrained) and without (unconstrained) borehole information.

BENA BENB BENC BENDUncon Con Uncon Con Uncon Con Uncon Con

r1 0.157 0.176 0.113 0.118 0.107 0.118 0.236 0.257r2 0.112 0.131 0.140 0.144 0.111 0.124 0.220 0.231r3 0.114 0.124 0.152 0.151 0.125 0.117 0.213 0.223r4 0.129 0.145 0.150 0.147 0.130 0.133 0.197 0.205r5 0.141 0.151 0.126 0.129 0.141 0.155 0.260 0.271r6 0.178 0.195 0.176 0.180 0.132 0.144 0.275 0.280

The boreholes G8005631/01, G8010638/01 andG8010331/01 with depth to bedrock of 60, 75 and 83 mmake it evident that the depth estimates from the SPAC arein disagreement with the geology. The information from theboreholes can be used to obtain a constrained best-fit modelthat is consistent with both geological and SPAC observations.Figure 10 (dashed line) shows the constrained models derivedfrom the SPAC measurements. Table 1 shows the standarddeviations for the fit achieved for the unconstrained (solid lineFigure 10) and the constrained models (dashed line Figure 10),for the different station separation distances (r1–r6).

Discussion

The unconstrained SPAC results lack resolution for establishingthe absolute depth to bedrock, although the correct trend fromwest to east is determined. The standard deviation of theunconstrained and the constrained models are similar whichmakes it difficult to determine which model has a superior fit. Themain difference between the two models exists at +50 m depth,and changes in the model parameters at these depths, influencethe frequency range of 0–5 Hz. Data quality in this interval isinferior to the range above 5 Hz, mainly due to lack of energysources. This makes it difficult to establish the best fit below5 Hz.

At great depths (+60 m) the uncertainty range seems to be solarge that it is only possible to establish depth to bedrock to within± 50%. Velocities and thicknesses in the upper layers (especially0–20 m but up to 50 m) appear to be well determined. The prior

knowledge of the deep lead thickness of 50 m in this area (directlyoverlying bedrock) can help determine an approximate deeplead thickness at the four SPAC stations. Figure 11 shows theinterpreted position of the lead, based primarily on the velocityprofiles obtained from the SPAC measurements. The boreholeinformation at site B has helped establish the upper limit of thelead as the SPAC profile most likely overestimates this boundary.

The SPAC model from site D indicates a layer with highshear wave velocity near the surface. This could be interpretedas Coliban Basalt, which was found at shallow depth (20–30 m)in a borehole ∼2 km west of this site.

The HVSR peak frequencies indicate significant changesacross the field area. The higher values to the west correspondwell with the shallower depth to bedrock estimated from the

140120100806040200

282563 283000 283500

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D

Topo

grap

hy (

m)

C Campaspe River

Interpreted deep lead section

B A

284000 284500 284906

Fig. 11. The velocity profiles from Figure 10 shown with the topography.Dotted lines denote the interpreted deep lead section, based on the SPACdata as well as prior information of deep lead thickness of approximately50 m.


SPAC measurements. The decrease in values towards the eastsuggests a greater depth to bedrock, provided the shear wavevelocities of the sediments remain constant.

Conclusion

The results obtained from the microtremor measurements havelittle impact on their own. It is difficult to establish the depthto bedrock with a reasonable degree of accuracy as well as thethickness of the deep lead. When existing knowledge such asborehole information is utilised the models derived from both theSPAC and the HVSR measurements become more trustworthy.The SPAC gives a useful estimate of the vertical boundaries ofthe deep lead.

With no significant lateral change in the shear wave velocity itwas not possible to delineate the eastern and western boundariesof the deep lead with this set of SPAC sites. An obvious thinningof the overlying sediment is mapped by the method and indicatesthat the western boundary might be located west of and closeto SPAC site D. For more constraints on the eastern boundary,more SPAC measurements are needed, but with no boreholesintersecting bedrock it will potentially be difficult to reach aconclusive result.

These methods are particularly useful for interpolatingbasement topography between known measurement locations.Furthermore they are cost effective for drilling program planningor follow up, particular in saline land or urban environments.

Acknowledgments

C.S. is supported by a Monash Graduate Scholarship and a MonashInternational Postgraduate Research Scholarship. The authors would liketo thank Mark Reid (Department Primary Industries Victoria) for providinginsight into the field area, CRCLEME for field work support and JamesRoberts for field work assistance.

References

Aki, K., 1957, Space and time spectra of stationary stochastic waves, withspecial reference to microtremors. Bulletin of the Earthquake ResearchInstitute 35, 415.

Arad, A., and Evans, R., 1987, The hydrogeology, hydrochemistryand environmental isotopes of the Campaspe River Aquifer system,north-central Victoria, Australia. Journal of Hydrology 95, 63.doi: 10.1016/0022-1694(87)90116-8

Asten, M. W., and Dhu, T., 2004, Site response in the Botany area, Sydney,using microtremor array methods and equivalent linear site responsemodelling: Australian Earthquake Engineering in the New Millennium,Proceedings of a conference of the Australian Earthquake EngineeringSoc., Mt Gambier South Australia, Paper 33.

Asten, M. W., Dhu, T., and Lam, N., 2004, Optimised array design formicrotremor array studies applied to site classification; observations,results and future use: Conference Proceedings of the 13th WorldConference of Earthquake Engineering, Paper 2903.

Bodin, P., Smith, K., Horton, S., and Hwang, H., 2001, Microtremorobservations of deep sediment resonance in metropolitan Memphis,Tennessee. Engineering Geology 62, 159. doi: 10.1016/S0013-7952(01)00058-8

Brown, C. M., and Stephenson, A. E., 1987, Geology of the MurrayBasin, Southeastern Australia: Bureau of Mineral Resources, Australia,Bulletin 235.

Chiew, F. H. S., and McMahon, T. A., 1991, Groundwater Recharge fromRainfall and Irrigation in the Campaspe River Basin. Australian Journalof Soil Research 29, 651. doi: 10.1071/SR9910651

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Konno, K., and Ohmachi, T., 1998, Ground-Motion CharacteristicsEstimated from Spectral Ratio between Horizontal and Verticalcomponents of Microtremor. Bulletin of the Seismological Society ofAmerica 88, 228.

Nakamura, Y., 1989, A method for dynamic characteristics estimation ofsubsurface using microtremors on the ground surface. Quarterly reportsof the Railway Technical Research Institute Tokyo 30, 25.

Nakamura, Y., 2000, Clear identification of fundamental idea ofNakamura’s technique and its applications: XII World Conference,Earthquake Engineering, New Zealand.

Nogoshi, M., and Igarashi, T., 1971, On the amplitude characteristics ofmicrotremor (part 2). Journal of the Seismological Society of Japan24, 26.

Okada, H., 2003, The Microseismic Survey Method: Society of ExplorationGeophysicists of Japan. Geophysical Monograph Series No. 12, Societyof Exploration Geophysicists.

Tokimatsu, K., 1997, Geotechnical site characterization using surface waves:in Ishihara (Ed.), Earthquake Geotechnical Engineering: Balkema.

Manuscript received 31 July 2006; accepted 4 May 2007.

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