Quantitative 2D VLF data interpretation - Directory UMMdirectory.umm.ac.id/Data Elmu/jurnal/J-a/Journal Of... · 2010-03-29 · 36 D. BeamishrJournal of Applied Geophysics 45 2000

Ž .Journal of Applied Geophysics 45 2000 33–47www.elsevier.nlrlocaterjappgeo

Quantitative 2D VLF data interpretation

David Beamish)

British Geological SurÕey, Kingsley Dunham Centre, Keyworth, Nottingham, NG12 5GG, UK

Received 10 August 1999; accepted 28 April 2000

Abstract

Ž .The ability of the VLF-R Resistivity method to provide quantitative subsurface resistivity information is examined. TheŽ .frequencies used in conventional VLF 15 to 30 kHz provide the deepest penetrations of the multi-frequency, extended

method of RadioMT. Both methods are considered. VLF data, being effectively single frequency, are insufficient to resolveŽ . Ž .one-dimensional 1D vertical structure in any detail. At the site investigation scale, however, it is the departures from the

Ž .background vertically uniform structure that are of interest. Improved methodologies for the quantitative assessment ofVLF data derive from advances in regularised inversion techniques. Hydrogeological and waste-site examples of VLF-R

Ž .survey data, aided by wide-band VLFrRadioMT synthetic modelling and inversion studies, are used to illustrate theirŽ .shallow 0 to 20 m resolution capabilities in conductive environments. q 2000 Elsevier Science B.V. All rights reserved.

Ž .Keywords: Electromagnetic; Very low frequency VLF ; Radiomagnetotelluric; 2D modelling; Inversion

1. Introduction

The plane-wave, VLF technique convention-ally operates in the frequency range from 15 to

Ž .30 kHz. Keller and Frischknecht 1966 discussradio wave geophysical methods prior to theintroduction of the first commercial VLF instru-ment in 1964. The VLF method was first devel-oped as an inductive profiling technique mea-

Ž .suring the amplitude and subsequently phaseŽ .relationship between the vertical secondary

magnetic field Z relative to the horizontal pri-mary field H. This method, referred to here as

) Tel.: q44-115-936-3432; fax: q44-115-936-3261.Ž .E-mail address: [email protected] D. Beamish .

Ž .VLF-Z elsewhere as VLF-EM , relies on wave-Ž .field interaction with two-dimensional 2D and

Ž .three-dimensional 3D resistivity structure. Thetechnique has since been extended to include ameasure of the induced horizontal electric fieldcomponent E. This VLF-R measurement pro-

Ž .vides a surface impedance value e.g. ErH ,usually expressed as apparent resistivity and

Ž .phase, using short e.g. 5 m electric dipoles.The methods, conventionally used for min-

eral and hydrogeological investigations, havebeen applied to a number of environmental

Žproblems McNew and Arav, 1995; Benson et.al., 1997 . Typically, only limited quantitative

use is made of the data since it is perceived thatthe modelling of single frequency VLF-R is notwarranted. The purpose of the present paper is

0926-9851r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0926-9851 00 00017-3

( )D. BeamishrJournal of Applied Geophysics 45 2000 33–4734

to demonstrate the degree to which quantitativeresistivity information can be obtained fromVLF-R data in the context of detailed site as-sessment.

The source fields used are line spectra pro-vided by military communication installations.

Ž .McNeill and Labson 1991 give global scalesignal strength contour maps for a number ofimportant transmitters. The VLF bandwidth inthe UK is usually dominated by the megawatt

Žtransmissions from Rugby GBRs16 kHz,. Ž .GBZs19.6 kHz and Anthorn GQDs19 Hz .

Other common VLF peaks include 16.8, 18.3,21.4, 23.4 and 24 kHz.

In moderately resistive environments, theconventional VLF bandwidth provides penetra-tion depths of the order of tens of metres. Inprinciple, the VLF bandwidth can be extended

Ž .to higher frequencies i.e. towards 1 MHz us-ing a variety of civil and commercial radiosources which again have directional propaga-tion characteristics and which exist as line spec-tra. The higher frequencies are intended to pro-vide a much shallower sounding capability, sincepenetration depths can be reduced towards 1 m.One early system, operating at 60 kHz, is de-

Ž .scribed by LaFleche and Jensen 1982 . Morerecently the extension of VLF-R to higher fre-quencies has been denoted radiomagnetotel-

Žlurics RadioMT, Turberg et al., 1994; Zacher et.al., 1996 . The highest frequencies used in Ra-

dioMT are reported to be 240 kHz and work isin progress to extend the bandwidth towards 1MHz.

Subsurface penetration in plane-wave electro-magnetic investigations is determined by theelectrical skin-depth, which is a function offrequency. The requirement for multi-frequency

Ž .observations is a one-dimensional 1D ‘verti-cal-sounding’ concept dating back to the origi-nal founding work on magnetotelluricsŽ .Cagniard, 1953 . For a 1D resistivity assess-ment, there is a clear requirement to obtain asufficient density of measurements per decadeof bandwidth in the sounding curve in order toadequately resolve subsurface layering. When

the resistivity structure is 2D and 3D, subsur-face resolution issues are more complicated butclearly depend both on the spectral density con-

Žtent of the observations including both high.and low frequency limits and the lateral scale

and density of the measurements.The VLF method differs from the more com-

mon DC resistivity site investigation techniqueŽ .in being a roving mobile sensor survey ope-

ration. Commercial VLF systems offer bothŽ . Žgalvanic contacting and capacitive non-con-

.tacting electrode sensors. The non-contactingmeasurement of the electric field allows opera-tion over made-ground. In contrast to many

Ž .methods, the techniques use vector directionalfields to probe 2D and 3D resistivity configura-tions.

Increasingly detailed investigations of thenear-surface are a requirement of applied geo-physical investigations particularly in the envi-ronmental and hydrogeological sectors. In orderto avoid misleading interpretations, the resolu-tion attributes of single frequency data whencombined with recent plane-wave regularisedinversion schemes are investigated here. Whensingle frequency VLF data are collected at a

Ž .high lateral density 1 to 5 m , the measure-ments can be used to infer the main elements ofthe subsurface resistivity distribution.

VLF-R survey data from both hydrogeologi-cal and waste-site assessments, aided by wide-

Ž .band VLFrRadioMT synthetic modelling andinversion studies, are used to illustrate their

Ž .shallow 0 to 20 m resolution capabilities inpredominantly conductive environments.

2. 1D assessments

The limited frequency range of VLF andRadioMT data provides a problem for the as-sessment of the 1D vertical resistivity structure.Fig. 1 shows the plane-wave response, across 4decades of frequency, of both a two-layer and athree-layer model. Both models contain a firstinterface depth at 10 m. The two-layer model

( )D. BeamishrJournal of Applied Geophysics 45 2000 33–47 35

Fig. 1. Plane-wave response of two 1D resistivity models. Two-layer model comprsises a 20 V m, 10-m-thick layer above aŽ .half-space of 5 V m. solid line . The three-layer model has an additional layer of 1 V m between depths of 10 and 11 m

Ž .line with symbols .

has a resistivity of 20 V m above a half-spaceof 5 V m. The three-layer model is similar buthas an additional thin layer of 1 V m between10 and 11 m. The thin layer is detectable since

Ž .its conductance 1 S exceeds that of the over-Ž .burden 0.5 S .

The diffusive nature of the plane-wave re-sponse of a 1D environment is illustrated in theresponse of both models. In order to fully detect

Ž . Ž .both near surface 20 V m and deeper 5 V mfeatures of the models it is evident that mea-surements across a wide frequency range, of theorder of the 4 decades shown, are required. The

Ž .conventional VLF bandwidth 15 to 30 kHz ,for the models used, provides a response that is

intermediate between the shallow and deeperresponse characteristics. The extended higher

Ž .frequency RadioMT response is likely to im-prove the resolution of the upper layer but fulldefinition of the lower half-space is beyond itsbandwidth. The lack of deep resolution is due tothe moderate resistivity assigned to the upperlayer. Limited bandwidth provides only weakvertical resolution, but at the site-investigationscale, it is often the departures from uniformitythat are of interest.

In 2D and 3D situations, the detection of theresistivity distribution relies on the excess cur-

Žrents generated at resistivity contrasts Price,.1973 . The distribution of excess currents then


modifies the surface fields. In order to providethe excess currents, the fields must have suffi-cient penetration to interact with the resistivitydistribution at any particular depth and location.Fig. 2 shows the decay of the horizontal E-fieldamplitude in uniform materials having resistivi-ties from 1 to 500 V m at frequencies of 20

Ž . Ž .kHz Fig. 2a and 500 kHz Fig. 2b . Thehorizontal dashed line denotes one skin-depthacross the set of resistivities. Investigationdepths for a 1D structure can be considered tobe a factor of 1.5 times the skin-depths shownŽ .Spies, 1989 . For a moderate resistivity of 50V m, investigation depths range from about 40m at 20 kHz to about 7.5 m at 500 kHz. When

Ž .highly conductive materials e.g. 1 V m , suchas leachate plumes, are encountered, inÕestiga-tion depths are confined to the upper 6 m at 20kHz and the upper 1.2 m at 500 kHz.

Fig. 2. Attenuation of electric field at frequencies of 20and 500 kHz within uniform materials having resistivitiesfrom 1 to 500 V m. The horizontal dash line indicates 1skin-depth.

3. 2D assessments

Ž .As discussed by Fischer et al. 1983 andŽ .Beamish 1994 , in order to ensure consistency

with a 2D approach, the directional VLF datamust conform to one of the two principal modesof 2D induction. The assumption of infinite

Ž .strike which defines the 2D case provides twodecoupled modes involving separate combina-tions of the field components. The E-polarisa-

Žtion mode or TE mode, electric field parallel to.strike involves the surface fields E , H andx y

ŽH . The H-polarisation mode or TM mode,z.magnetic field parallel to strike involves the

fields H , E and E with E being non-zerox y z z

only below the surface. Due to the directionalnature of VLF measurements, we require there-fore that the measurements be made in at leastone of the two principal directions. Whereanomaly strikes are not known, the survey op-tion of taking measurements from several az-imuthally distinct transmitters is suggested.

The E-polarisation mode provides VLF-R andVLF-Z data and anomaly wavelengths are gen-erally larger than their H-polarisation modecounterparts. In the H-polarisation mode, noVLF-Z field is generated and thus combinedmeasurements of VLF-R and VLF-Z can beused as a means of mode identification. Thestarting point in the modelling of VLF data arethe developments in non-linear inversion whichhave arisen in the context of the multi-frequency

Ž .magnetotelluric MT technique. The new ap-proaches involve regularising an otherwise ‘ill-posed’ problem by introducing a smooth orminimum-structure constraint. In 2D inversion,the problem of equivalence becomes particu-larly acute because of the larger number ofdegrees of freedom within the model space. Theessential point is that the minimum-structureinversion concept acknowledges this fact and

Žallows the construction of credible non-ex-.treme resistivity models.

For 2D MT inversion, deGroot-Hedlin andŽ .Constable 1990 implemented a minimum-

structure inversion, which is referred to as OC-


CAM and is based on the finite-element forwardŽ .solution of Wannamaker et al. 1987 . A more

rapid 2D inversion code involving a non-linear,Ž .conjugate gradient NLCG algorithm has re-

cently been described by Rodi and MackieŽ .1999 . The algorithm implements first-deriva-tive smoothing and includes a regularisation

Ž .parameter t that controls the degree of modelŽsmoothnessrroughness often a trade-off with

.misfit . VLF studies using the former methodŽ .were described by Beamish 1994 . The latter

method is used in the present study since itreadily permits the use of a regular subsurfacefinite-difference grid comprising in excess of100=100 1 m cells. The use of such a high

Ždefinition subsurface grid in terms of electrical.scale lengths allows the true nature of smooth

Žresistivity models to be displayed i.e. resistivity.boundaries imaged as spatial gradients .

The measured data should possess errorbounds. An exact fit between measured andmodelled data is rarely warranted. The errorbound must comprise the variance associatedwith physical measurement but it can also en-compass the degree to which a particular level

Ž .of modelling e.g. 1D, 2D or 3D is thought tobe appropriate. Given a set of N observationsŽ . Ž .d , is1,N with standard errors s , the con-i i

cept is to only fit the observations to within aprescribed level of misfit. When the data anderrors conform to Gaussian behaviour the chi-

Ž 2.square x statistic is a natural measure ofmisfit :

N22 2x s d ym rsŽ .Ý i i i

iy1

where m refers to the ith model response. Ani

rms measure of misfit defined as x 2rN with anexpectation value of unity is used here.

4. A synthetic example

In the use of VLF for many types of investi-gation, the choice of transmitter appears to beeither a signalrnoise issue or is not discussed at

all. For resistivity mapping purposes the use oftwo azimuthally distinct transmitters is recom-

Ž .mended Guerin et al., 1994; Beamish, 1998 .The two joint data sets allow rotational invari-ants to be formed thus overcoming the depen-dence of anomaly response using single trans-

Ž .mitter data. The choice of survey transmitter sis also a critical issue when subsurface resistiv-

Ž .ity information in cross-section is required.Ž .The initial choice s will govern the direction of

the survey profile and the azimuth at which theorthogonal E and H field components will berecorded. For a given resistivity distribution thechoice of transmitters and their directions willgovern the form and resolution characteristics ofthe data set obtained. For the elongate, 2Danomalies principally discussed here, the mainissue is the combination of transmitter azimuthand anomaly strike direction that determine themode of the response that is measured.

A synthetic example is used to demonstratethe differences in data characteristics that areobserved in the two modes. The study alsoallows resolution issues of the field data exam-ples to be examined. The model study uses atypical site-investigation profile length of 100m. The central subsurface of the model com-

Ž . Ž .prises 100 horizontal =50 vertical , 1 m cellsbefore expansion to satisfy boundary conditionrequirements.

The study model, shown in Fig. 3, containsŽ .two concealed conductive 5 V m bodies lo-

cated at depths of 2 and 5 m in host materialwith a resistivity of 50 V m. The larger and

Fig. 3. 2D, three-body synthetic model. Resistivity valuesshown in V m.


deeper conductive feature is laterally extensiveand has a rotated ‘L’ shape. An at-surface resis-

Ž .tive feature 500 V m with a thickness of 2 mis also present. As will be demonstrated, thepresence of at-surface resistivity contrasts has aprofound influence on the characteristics of the

Ž .H-polarisation mode data Fig. 5 . The multi-body model provides anomaly wavelengths that

Ž .overlap in the E-polarisation mode Fig. 4making simple interpretation of the observa-tional data difficult.

In order to extend the context of single fre-quency VLF observations, the response of the

Žmodel at a range of higher frequencies Ra-.dioMT has been examined. Four frequencies of

Ž .20 VLF , 50, 200 and 500 kHz are used.Skin-depths range from 25 m at 20 kHz to 5 mat 500 kHz in the host background of 50 V m.

Fig. 4. Apparent resistivity and phase data calculated forthe E-polarisation mode using the synthetic model of Fig.3. The results for four frequencies are shown.

In Fig. 3 profile measurements are across thepage with body strike into the page. The E-polarisation mode uses E-field measurementsinto the page while in the H-polarisation modethe E-field would be measured across the page.Following a discussion of the data character-

Ž .istics inversions of the single VLF frequencyand multi-frequency data are performed.

When dealing with complex resistivity distri-butions at the site investigation scale, the be-haviour of the H-polarisation mode apparentresistivity for near-surface resistivity contrasts isan important feature. As noted in the review by

Ž .Jiracek 1990 , any resistivity contrast due tosmall-scale heterogeneities in the vicinity of theelectric field measurement can give rise to aparticular class of perturbation referred to asgalvanic distortion or static shift. Such effects

Žare observed irrespective of electrode type e.g..contacting or non-contacting .

The phenomenon is well-known from lowerfrequency magnetotelluric investigations but isalso evident at VLF and higher frequencieswhen near-surface features cause large fluctua-tions in apparent resistivity. If the phenomenonis not understood, the data may be dismissed as‘erratic’; however, such data may often be ofpotential interest at the site investigation scale.Static shift is generated by a body of small

Želectrical dimensions i.e. in terms of skin-. Ždepth in the proximity again in terms of skin-.depth of the measurement electrodes. The

measured electric field is perturbed from itsŽ‘regional’ value i.e. the value in the absence of

.the small-scale body by a frequency indepen-dent shift of apparent resistivity. The phasebetween the electric and magnetic fields is unaf-fected. The scale of the perturbation depends on

Žthe resistivity contrast encountered Beamish.and Travassos, 1993 .

If the problem considered is strictly 2D, thenstatic perturbation effects are confined to theH-polarisation mode measurements. In practice,when the small-scale body is 3D, the perturba-

Žtion will affect both modes i.e. any VLF-R data.that is collected, irrespective of orientation .


The response of the synthetic model has beencalculated every 1 m along the surface at a VLFfrequency of 20 kHz and additional RadioMTfrequencies of 50, 200 and 500 kHz. The VLF-Rresponse in the E- and H-polarisation modes isshown in Figs. 4 and 5, respectively. In the

Ž .E-polarisation mode Fig. 4 , the at-surface re-Ž .sistive body located between 40 and 50 m

produces a large amplitude perturbation in am-Ž .plitude apparent resistivity but is far less con-

spicuous in the phase response. The anomalywavelengths decrease with increasing frequencyallowing better lateral definition of the location

Ž .of the bodies. At the lowest VLF frequencythe observational baseline is insufficient for theresponse to return to its half-space values of 50

Ž . Ž .V m apparent resistivity and 458 phase . Theelectrical scale of the left-most conductive body

Fig. 5. Apparent resistivity and phase data calculated forthe H-polarisation mode using the synthetic model of Fig.3. The results for four frequencies are shown.

Ž .located between 20 and 30 m produces aŽ .phase inversion between low 20 and 50 kHz

Ž .and high 200 and 500 kHz frequencies.Ž .In the H-polarisation mode Fig. 5 , the am-

plitude response is dominated by the largelygalvanic response of the at-surface resistivebody. The asymmetric behaviour of the re-sponse is due to the combined effects of themultiple bodies. When the wavenumber be-

Ž .haviour i.e. the spatial scale of the E- andŽH-polarisation mode response data to all three

.bodies is compared it can be seen that theH-polarisation mode response consistently pro-

Žvides the highest lateral definition smallest.anomaly wavelengths .

4.1. Data inÕersion

The response characteristics of both modescontain diagnostic information on the subsur-face resistivity distribution. The degree of reli-able information is examined by inverting eachmode separately using first the VLF single fre-quency data and then the RadioMT multi fre-quency data. Joint inversions of the two modeswere also performed. As expected, the resultingmodels take on the ‘best-resolution’ character-istics of the individual modes. The inversions ofthe synthetic data use apparent resistivity andphase data sampled at 1 m intervals. Nominal2% errors have been assigned to the data and norandom errors have been introduced. The analy-sis undertaken therefore represents the best pos-sible resolution case. A half-space of 100 V mwas used to initiate the inversions. A smoothingparameter of ts1 was used to provide a highdegree of roughness. Using the assigned errorlimits, an rms misfit of unity is achieved byboth inversions. Since the data are ideal, all

Ž .features of the data Figs. 4 and 5 can beaccurately reproduced.

The E- and H-polarisation mode inversionresults are shown in Figs. 6 and 7, respectively.

Ž .The single frequency 20 kHz, VLF inversionresult is shown above the result obtained usingfour frequencies in each case. The results are


Ž .Fig. 6. Minimum structure resistivity models obtained by inverting the E-polarisation mode synthetic model data. aŽ . Ž . Ž .Single-frequency 20 kHz result. b Four-frequency 20, 50, 200 and 500 kHz result. The rms misfit of both models is

Ž .unity assuming 2% data errors . Original model shown by white lines. Logarithm of resistivity is contoured. Verticalexaggeration=2.

contoured using the logarithm of resistivity soŽthat the target values are 0.7 conductive bodies

. Ž .of 5 V m , 2.7 resistive body of 500 V m andŽ .1.7 host of 50 V m . The outline of the

original model is shown by the heavy whitelines. Inversion models with smooth constraintscannot recover discontinuous resistivity distribu-tions; they are imaged by gradients.

In the E-polarisation mode single frequencyŽ .result Fig. 6a the least well-resolved feature

Ž .both laterally and vertically is the at-surfaceŽ .resistive zone located between 40 and 50 m .

The larger and deeper conductive zone is thebetter resolved of the two concealed zones. Theminimum resistivity values returned by the in-version appear to be located towards the


Ž .Fig. 7. Minimum structure resistivity models obtained by inverting the H-polarisation mode synthetic model data. aŽ . Ž . Ž .Single-frequency 20 kHz result. b Four-frequency 20, 50, 200 and 500 kHz result. The rms misfit of both models is

Ž .unity assuming 2% data errors . Original model shown by white lines. Logarithm of resistivity is contoured. Verticalexaggeration=2.

‘centre-of-gravity’ of the L-shaped body. Themodel returned using 4 frequencies of the E-

Ž .polarisation mode Fig. 6b clearly possessesŽhigher resolution much tighter spatial gradi-

.ents than the single frequency case. All threefeatures are well resolved both laterally andvertically in the attitudes and gradients of theinversion result. The conductive zones are mod-

elled at the correct value in the central portionsof each feature.

In the H-polarisation mode single frequencyŽ .result Fig. 7a the least well-resolved feature is

probably the shape and depth of the deeperŽ .conductive zone located between 50 and 80 m .

The lateral extent of all three features is well-resolved. The single frequency H-polarisation


mode produces very well defined images of theupper-most conductive and the at-surface resis-tive features. The H-polarisation mode model

Ž .returned using four frequencies Fig. 7b pos-sesses the highest resolution characteristics ofall the inversions considered.

General resolution features of both modesinclude the fact that the upper surfaces of con-cealed zones are better resolved than their lower

Ž .surfaces see also Beamish, 1994 . Resolutionof detailed subsurface features such as that ex-emplified by the rotated L-shaped body is not

Ž .possible using regularised smooth model in-version schemes.

5. A hydrogeological field example

An example of VLF-R and VLF-Z data col-lected across a 200-m profile in the vicinity of a

Žhydrogeological test site monitoring boreholes.and additional shallow geophysics is used to

Ž .illustrate: i the accuracy of field measure-Ž .ments, ii the importance of mode identifica-Ž .tion and iii small amplitude static effects.

ŽThe geological strata superficial clays on.chalk at the site is considered to be highly

uniform. Standard Schlumberger resistivitysoundings along the location of the VLF tra-verse indicated cover sand of resistivity 200 V

Ž .m 0 to 1.3 m , clay till of resistivity 27 to 32 V

Ž .m 1.3 m to between 11 and 15 m overlyingchalk with a resistivity of 76 V m. The VLFmeasurements were made with a Scintrex IGS-2system employing 5-m dipoles and capacitiveelectrodes. Separations were 5 m, making theVLF-R measurements contiguous along the di-rection of the profile. The transmitter used was

Ž .the 16 kHz signal Rugby, GBR . Since the sitewas considered laterally homogeneous, no pre-defined idea of mode orientation could be estab-lished and the survey azimuth and E-field orien-tation was based on the signalrnoise of theVLF transmitter.

The real and imaginary components of theVLF-Z response are shown in Fig. 8 with values

Fig. 8. Hydrogeological field example: Real and imaginarycomponents of VLF-Z, 16 kHz measurements obtainedalong a 200-m profile. Measurement separation is 5 m.

being expressed as percentage. The uniformityof the response across the 200-m profile is suchthat a very detailed vertical scale of "4% hasbeen used. At this scale, the instrument noiselevel of 1% in both real and imaginary compo-nents can be observed. Although the real com-ponent shows a consistent negative offset of 1%to 2%, the majority of the imaginary componentlies very close to zero. Overall, the responsemeasured is as close to a VLF-Z zero responseas can be observed over profile baselines of thislength.

If only VLF-Z data had been obtained, theresults might be used to provide an interpreta-tion in terms of an entirely horizontally uniformsubsurface resistivity distribution. This is clearlynot the case when the coincident VLF-R mea-surements are taken into account. Fig. 9 shows

Žthe behaviour of the VLF-R response shown as.symbols along the profile. A frame box has

been used to highlight the behaviour observedacross the first 140 m of the profile; apparent


Fig. 9. Hydrogeological field example: VLF-R, 16 kHzŽ .measurements symbols obtained along a 200-m profile.

Measurement separation is 5 m. The field data are com-Žpared with the response of an inversion model continuous

.line . The rms misfit between data and model is 1.5%Ž .assuming 2% data errors .

resistivities are largely confined to 25 to 30 V

m and phase values to 408 to 458. The instru-

ment resolution level is 1 V m and 18. Withinthe frame box, apparent resistivities tend tooscillate at the measurement separation scale of5 m while the phase values are laterally farmore consistent. The behaviour is not instru-mental or measurement noise; it is an exampleof small-scale near-surface static effects that canbe observed on many VLF-R data sets whenthey are examined in detail.

Beyond 140 m, a clear longer wavelengthanomalous response is observed that is not‘complete’ by the end of the observational pro-file at 200 m. In view of the absence ofany VLF-Z response, the response must beinterpreted as a strictly H-polarisation moderesponse to a resistivity gradient. It is worthnoting that the VLF data contain virtually noinformation on the vertical resistivity profile atthe site, being influenced largely by the resistiv-

Ž .ities of the clay sequence 27 to 32 V m .


The VLF-R data have been inverted using theNLCG method. The subsurface model com-

Ž . Ž .prises a 5 m lateral by 1 m vertical gridacross the central region. The inversions were

Fig. 10. Hydrogeological field example: Minimum-structure resistivity model obtained by inverting the VLF-R, H-polarisa-Ž .tion mode data shown in Fig. 9. The rms misfit of the model is 1.5% assuming 2% data errors . Cross-section is contoured

using linear resistivity. Vertical exaggeration=3.


initiated using a half-space of 25 V m. As withthe synthetic data, arbitrary error bounds of 2%were assigned for the analysis of misfit. Withthese error assignments, an rms misfit of 1.5%was achieved by the inversion. The observed

Ž .data symbols are compared with the modelŽ .response continuous solid line to the data in

Fig. 9. It can be seen that all the high wavenum-ber components of the apparent resistivity dataare well modelled. The greatest level of misfitoccurs at the maximum phase excursion.

The resistivity model obtained is shown, us-ing a linear resistivity scale, in Fig. 10. It can beseen that the major uniform resistivity valuereturned in the model is in the range 25 to 35 V

m in keeping with the DC resistivity surveyvalues for the clay sequence of 27 to 32 V m.The longer wavelength anomaly appears to be

Žgenerated by a more resistive feature 55 to 60.V m within the clay sequence centred on 180

Ž .m. The clay sequence Lowestoft till can besubdivided into oxidised and unoxidised units

Žwith the latter showing a large 4 orders of.magnitude decrease in hydraulic conductivity.

It is likely that resistive feature represents anisolated zone of tighter, unoxidised clay.

6. A waste-site example

The next single-frequency field examplecomes from an assessment of a site, which hasbeen used for the disposal of industrial wastes.The data were obtained across a former sand-stone quarry that was used for the disposal of awide-variety of industrial wastes, with originaland by-products being lime slurries, brines,metal waste, DNAPLs and acidic leachates. Themeasurements were made with a Scintrex IGS-2system employing 5-m dipoles and used the

Ž .Rugby VLF transmitter GBR, 16 kHz .The profile comprises 83 observations made

in the H-polarisation mode with a station sam-pling of 1 m. The H-polarisation mode is de-fined with the E-field measurements made per-pendicular to the former quarry edge. The data

ŽFig. 11. Waste-site example: VLF-R measurements sym-.bols obtained between 17 and 100 m along profile. Mea-

surement separation is 1 m and frequency is 16 kHz. Thefield data are compared with the responses of two inver-

Ž .sion models: Model 1 solid line has an rms misfit of 5%Ž .and Model 2 dash line has an rms misfit of 3.6%

Ž .assuming 2% data errors .

obtained are shown by the symbols in Fig. 11.The 1-m data interval represents oversamplingsince the dipole length remains fixed at 5 m.The discontinuous nature of the H-polarisationmode response and the likely presence of debrisnoise suggests that oversampling may be appro-priate in the absence of an ability to use dipolelengths of 1 m. In this example, apparent resis-tivities reach a minimum instrument level of 1V m and phase values reach a value of 908.


The VLF-R data have been inverted using theNLCG method and assuming the data conformto the H-polarisation mode. The subsurface

Ž . Žmodel comprises a 1 m lateral by 1 m verti-.cal grid across the central region of 100 m. The

inversions were initiated using a half-space of10 V m. As with the synthetic data, arbitrary


error bounds of 2% were assigned for the analy-sis of misfit.

Fig. 12 shows the results of two inversions.In Fig. 12a, a smoothing parameter of ts30was used and the rms misfit achieved was 5%.The fit of the model to the data is shown in Fig.

11 by the continuous solid line. It can be seenthat the misfit largely stems from the observedphase excursions to high values. The resulting

Ž .inversion model Fig. 11a contains largelymoderate wavenumber components in the resis-tivity distribution.

Fig. 12. Waste-site field example: Two resistivity models obtained by inverting the VLF-R H-polarisation mode data shownŽ . Ž .in Fig. 11. The rms misfits are a 5% and b 3.6%. Cross-sections are contoured using the logarithm of resistivity. Vertical

exaggeration=2.


It is possible to reduce the misfit by decreas-ing the degree of smoothing in the inversionmodel. Fig. 12b shows the result of decreasing

Ž .the smoothing parameter ts1 which allowsthe rms misfit to decrease from 5% to 3.6%.The fit of this second model to the data isshown in Fig. 11 by the broken line. It isevident that only a marginal improvement in fitis achieved. The resulting model, however, whileretaining the moderate wavenumber features ofthe previous model, amplifies two highwavenumber components of the resistivity dis-tribution which are associated with the maxi-mum phase excursions. It is likely that only theresistivity distribution shown in Fig. 11a is war-ranted by the fit to the data. The high wavenum-ber components introduced into the most con-ductive zones are likely to be 3D effects, whichcannot be effectively modelled.

The result of Fig. 12a represents the mini-mum structural model that is consistent with theobservations. Discontinuous features, if they ex-ist, are represented by the changes in gradients.A large wavenumber trend of low resistivity

Ž .values -10 V m suggests a dip of conduct-ing infill from left to right across the westernmargin of the profile. Several metres of resistiveinfill occur between stations 50 and 100 m. Two

Ž .highly conducting -1 V m zones are de-tected between depths of 5 and 10 m, centred onprofile locations of 70 and 90 m. The zones arelaterally compact and may be less than 5 m inwidth. The base of conducting infill of the

Žquarry the original quarry floor is thought to be.at a depth of 25 m cannot be resolved due to

rapid attenuation in the conductive environment.

7. Conclusions

VLF data can be obtained rapidly, accuratelyand at low survey cost over both made andunmade ground at the site investigation scale.Often large quantities of such data are acquiredbut the information contained is not exploited ina quantitative manner. The study has demon-

strated that when single frequency VLF data areŽ .collected at a high lateral density 1 to 5 m , the

measurements can be used to infer the mainelements of the subsurface resistivity distribu-tion. The tools required are the regularised,smooth model inversion schemes that have beendeveloped for multi-frequency, magnetotelluric

Ždata sets. The use of extended frequency Ra-.dioMT data, when available, will invariably

add to the resolution capabilities of the methodas long as signalrnoise remains high. The addi-tional constraints essentially provide only sec-ond-order improvements in the detection of tar-get structure boundaries. It appears that the

Ž .spatial gradients generated at the lowest VLFfrequency contain a high degree of informationon the configuration of the subsurface resistivitydistribution. A critical issue in VLF surveyplanning and transmitter selection is the choiceof anticipated structural strike and thus the modeof the profile data obtained. As the hydrogeo-logical example shows, the joint acquisition ofVLF-Z and VLF-R data can be used as an aid tomode identification.

Acknowledgements

The report is published with the approval ofthe Director, British Geological Survey, a com-ponent body of the Natural Environment Re-search Council. Thank you to the two anony-mous referees.

References

Beamish, D., 1994. Two-dimensional, regularised inver-sion of VLF data. J. Appl. Geophys. 32, 357–374.

Beamish, D., 1998. Three-dimensional modelling of VLFdata. J. Appl. Geophys. 39, 63–76.

Beamish, D., Travassos, J.M., 1993. A study of magne-totelluric static distortion in the context of intrusivevolcanism. Geophys. Prospect. 41, 61–82.

Benson, A.K., Payne, K.L., Stubben, 1997. Mappinggroundwater contamination using dc resistivity and VLFgeophysical methods — a case study. Geophysics 62,80–86.


Cagniard, L., 1953. Basic theory of the magneto-telluricmethod of geophysical prospecting. Geophysics 18,605–635.

deGroot-Hedlin, C.M., Constable, S.C., 1990. Occam’sinversion to generate smooth, two-dimensional modelsfrom magnetotelluric data. Geophysics 55, 1613–1624.

Fischer, G., Le Quang, B.V., Muller, I., 1983. VLF groundsurveys, a powerful tool for the study of shallow two-dimensional structures. Geophys. Prospect. 31, 977–991.

Guerin, R., Tabbagh, A., Benderitter, Y., Andrieux, P.,1994. Invariants for correcting field polarisation effectsin MT-VLF resistivity mapping. J. Appl. Geophys. 32,375–383.

Jiracek, G.R., 1990. Near-surface and topographic distor-tions in electromagnetic induction. Surv. Geophys. 11,163–203.

Keller, G.V., Frischknecht, F.C., 1966. Electrical Methodsin Geophysical Prospecting. Pergamon.

LaFleche, P.T., Jensen, O.G., 1982. Wave impedance mea-surements at 60 kHz. In: Collett, L.S., Jenson, O.G.Ž .Eds. , Geophysical Applications of Surface WaveImpedance Measurements. Geological Survey ofCanada pp. 67–78, Paper 81-15.

McNeill, J.D., Labson, V.F., 1991. Geological mapping

Ž .using VLF radio fields. In: Nabighian, M. Ed. , Elec-tromagnetic Methods in Applied Geophysics: Part B.Application. SEG, Tulsa, pp. 521–640.

McNew, E.R., Arav, S., 1995. Surface geophysical surveysof the freshwater–saltwater interface in a coastal areaof Long Island, New York. Groundwater 33, 615–626.

Price, A.T., 1973. The theory of geomagnetic induction.Phys. Earth Planet. Int. 7, 227–233.

Rodi, W., Mackie, R.L., 1999. Nonlinear conjugate gradi-ents algorithm for 2-D magnetotelluric inversion. Geo-physics, submitted for publication.

Spies, B.R., 1989. Depth of investigation in electromag-netic sounding methods. Geophysics 54, 872–888.

Turberg, P., Muller, I., Flury, F., 1994. Hydrogeologicalinvestigations of porous environments by radiomagne-totelluric-resistivity. J. Appl. Geophys. 31, 133–143.

Wannamaker, P.E., Stodt, J.A., Rijo, L., 1987. A stablefinite element solution for two-dimensional magnetotel-luric modelling. Geophys. J. R. Astron. Soc. 88, 277–296.

Zacher, G., Tezkan, B., Neubauer, F.M., Hordt, A., Muller,I., 1996. Radiomagnetotellurics: a powerful tool forwaste-site exploration. Eur. J. Environ. Eng. Geophys.1, 139–159.

Documents

Quantitative 2D VLF data interpretation - Directory UMMdirectory.umm.ac.id/Data Elmu/jurnal/J-a/Journal Of... · 2010-03-29 · 36 D. BeamishrJournal of Applied Geophysics 45 2000