REfERENCE ONLY

FEASIBILITY OF RADIO SOUNDING TOTHE GROUNDWATER TABLE IN HAWAII

by

George R. Jiracek

Technical Report No. 10

August 1967

No. 2 of 5 Reports in Completion

of

GEOPHYSICAL EXPLORATION FOR HAWAIIAN GROUNDWATER, PHASE I

OWRR Project No. B-005-HI~Grant Agreement No. 14-01-0001-1061

Principal Investigators: Leonard A. Palmer, Doak C. Cox, William M. Adams

Project Period: July 1,1966 to June 30, 1967

The programs and activities described herein were supported in part by fundsprovided by the United States Department of t he Interior as authorized underthe Water Resources Act of 1964, Public Law 88- 379.

ABSTRACT

The reported high values of resistivity in the near surface zones

in semi-arid regions on the is land of Haioai i. motivated research into

the feasibility of using radio waves t o sound the depth to the ground

water table. Field tests using a 35 MHz ranging system (built in Eng­

land for ice depth sounding) were made i n areas of differing geology

and climate~ but in no instance was an echo i dentified as having ori­

ginated from the water table . Measurement s made of transmissions

from within an inclined tunnel and r eceived at the surface gave rise

to a signal which may have travelled through a water saturated rock

column at a velocity of 27 m/veec while attenuated by about 3 db/me

Equipment ringing~ due to antenna miss-matches~ contributed to the

lack of success in measuring water table echoes. However~ subsequent

laboratory dielectric measurements in the frequency range 102 to 6.2

x 107 Hz on representative Hawaiian rocks and soil indicate that even

smal l amounts of moisture result in prohibitive attenuation losses.

For example~ in a low density basalt~ the attenuation at 18 MHz is

0.26 db/m when dry ~ but increases to 1 .66 db/ m with less than 4% water

by volume. In a volcanic ash soil sample~ the loss increases at 18

MHz from 0.04 db/m to 1.3 db/m as the soil water content is increased

from zero to 19% by volume. Electromagnetic propagation velocities

decrease markedly with increasing moisture content~ an effect which i s

most striking at low frequencies . In situ moisture conditions above

the water table in the semi-arid regions in Hawaii are expected to

be approximately > 4% in rock and > 19% in soil. Considering al.l:

factors~ usable echoes at 35 MHz are consequently expected when sound­

ing water table depths of ~25 m, Haaeoer; frequencies as high as

0.1 MHz may prove useful in sounding depths to many hundred meters .

The use of VHF (30-300 MHz ) waves to probe the depths of drier en­

vironments such as possibly exist on the moon is considered f easi b le.

iii

TABLE OF CONTENTS

LIST OF TABLES v

LIST OF FIGURES vi

INTRODUCTION 1

THEORETICAL PROPAGATION OF ELECTROMAGNETIC WAVES 1

FI ELD MEASUREMENTS 9Equi pment 9Locations of Investigation 9Investigations 10

LABORATORY MEASUREMENTS 19Samples and Experimental Techniques 19Measured and Derived Results 20Di scuss i on 24

THEORETICAL HYDROGEOLOGIC MODEL STUDIES 26

CONCLUSIONS 32

ACKNOWLEDGEMENTS - 33

REFERENCES " 34

APPENDIX 37

LIST OF TABLESTable

Dielectric Properties of Hawaiian Red Desert Soil as a Func-tion of Frequency with Varying Moisture Content 2l

2 Dielectric Properties of Low Density Hawaiian Basalt as aFunction of Frequency with Varying Moisture Content. . . . . • . .. . 22

3 Dielectric Properties of High Density Hawaiian Basalt as aFunction of Frequency with Varying Moisture Content 23

4 Theoretical Losses for 35 MHz Radio Waves Reflected from aGround Water Table in Hawaii at 25 m Depth (Model 1) 30

v

Figure1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

LIST OF FIGURES

35 MHz Radio Sounding Transmitter 7

Vehicles Mounted with Folded Dipole Antennas 8

"Spot" Radio Sounding on Keonee1ee1e Flat, Island of Hawaii 11

Locations of 35 MHz Radio Soundi ng Experiments on the Islandof Hawai i 12

Oscilloscope Presentation of Signals Received on Keonee1ee1eFlat, Island of Hawaii 14

Schematic Representation of Transmitting and ReceivingPositions at Pahala Inclined Shaft 15

Oscilloscope Presentation of Signals Received through RG 58Transmission Line and by Receiving Antenna at PahalaInclined Shaft l6

Relative Dielectric Constant of Hawaiian Red Desert Soil 39

Dielectric Conductivity of Hawaiian Red Desert Soi1 40Attenuation in Hawaiian Red Desert SoiL 41

Relative Dielectric Constant of Low Density Hawaiian Basa1t 42

Dielectric Conductivity of Low Density Hawaiian Basa1t 43Attenuation in Low Density Hawaiian Basa1t 44

Relative Dielectric Constant of High Density Hawaiian Basa1t 45

Dielectric Conductivity of High Density Hawaiian Basa1t 46Attenuation in High Density Hawaiian Basalt 47

vi

"I-3

INTRODUCTION

Radio waves have recently been employed with great success to sound

the thickness of the polar ice caps, e.g. Jiracek and Bentley (1966), Evans

(1967). The method is basically that of radar ranging system utilizing a

pulsed transmitter and a receiving unit to detect and measure bottom echo

time delay. The technique has proven successful through ice primarily be­

cause ice has low dielectric absorption properties. Suspected radio pene­

tration into sub-glacial material and the reported high values of electrical

resistivity for rocks and soils, e.g. Jakosksy (1950), led to the expecta­

tion of useable radio penetration into frozen or dry soil or rock.

Using the terminology suggested by Davis and DeWiest (1966), the earth's

surface in many areas has a layered structure with a relatively dry vadose

zone underlain by a highly conductive phreatic zone with the water table

marking the transition. It is thought that in some areas the radio sound­

ing method might prove valuable in determining the depth to the water table

providing the overlying material permits sufficient penetration of energy.

Measured high electrical resistivity in the surface -layer in semi~arid re­

gions on the island of Hawaii (Zohdy, 1966) motivated research into the

feasibility of using radio wayes to sound ground water depths in these areas.

The feasibility study consisted of basically three studies: field tests,

laboratory dielectric measurements, and theoretical hydrogeologic model

studies.

THEORETICAL PROPAGATION OF ELECTROMAGNETIC WAVES

The radio sounding method .i n this application is basically limited by

energy losses within the soil and/or rock column, at reflecting interfaces,

e.g. the water table, and by equipment factors. A quantitative evaluation

of these losses may be made by considering the wave equation for the elec­

tric field intensity,

(1)

~

whereE is the electric field intensity, E* the complex dielectric constant,

2

and ~* the complex magnetic permeability. The dielectric constant is a com­

plex quantity owing to the finite dielectric conductivity of the materials

under consideration. Thus,

E* = E' - j c" (2)

where E' is the dielectric constant and E" is the dielectric loss factor.

The dielectric conductivity is frequency dependent and related to the loss

factor by

o = WE" (3)

W being equal to 2n times the frequency f. The electrical resistivity is

equal to 1/0. The dimensionless ratio

K*r e (4)

is the complex relative dielectric constant,

being the dielectric constant of free space.

the relative dielectric constant and relative

material.

The relationship

E" . K :"etan 0=-- =--E' ~.' e

EO (8.854 x 10- 12 F/m)

K'e and K"e are, respectively,

dielectric loss factor of the

(5)

defines the loss tangent which will prove useful in the determination of the

attenuation loss through rocks and soil.

Similar equations apply to magnetic permeability, but even in volcanic

rocks and soils in Hawaii, magnetic polarization is considered weak com­

pared to the electric case (see section on Laboratory Measurements). Hence,

for propagation proposes, ~* = ~ o resulting in K*m = 1.

The monochromatic, plane wave solution to equation 1 is

....... ~ jwt-yzE = Eoe (6)

3

representing a travelling wave i n the +zdirection with a complex propaga­

tion factor

y j w-V;;;; = a +jS . (7)

Here a is the attenuation factor and S is the phase factor of the wave.

Surfaces of constant phase propagate with a velocity

vwS

(8)

while the electric field strength decreases exponentially as

'"""'E -- .....E - czoe (9)

Upon separation of the real and imaginary parts of equation 7, it can be

shown that

v =c (10)

where c = 300 m/~sec, the velocity of electromagnetic radiation in free space.

In low-loss materials (tan 0« 1) , equation 10 reduces to

cv =---v;;-: (11)

Considering the real part of equation 7, the attenuation factor is

(12)

(13)

a =

In the low-loss case,

TIf "" r-;- ~a = c V K'e tan u

Having determined a, the attenuation of an electromagnetic wave passing

4

through a material may now be computed using equation 9 or more desirably

by defining the decibel loss as

20 log E (0) = 8 686E (z) . c z ,

i.e., the decibel loss per meter is

(14)

8.686 a (15)

The propagating electromagnetic field has been treated as a plane wave

and the so-called free space or inverse square law power loss due to spher­

ical spreading has not been considered. To account for this loss, the peak

radiated power flowing through a unit area at a distance r from the trans­

mitting antenna emitting pulses of total peak power PT is defined as

dP _ GPTdA - 4 21fr

(16)

where G is the power gain of the antenna.

If an antenna similar to that used for transmitting also receives the signal,

the received peak power PR is given by

Here, AO is the free space ·wave length. In terms of decibel loss, the fre e­

space signal decrease is expressed as

(18)

When the electromagnetic wave encounters a reflecting interface (e.g.air/soil, dry rock/water saturated rock), the relative strength of reflected

and refracted waves is computed by using a modified form of Fresnel's equa­

tions. Such a form accounts for the finite dielectric conductivity of the

materials. A complex reflection coefficient is postulated,

yie l ding ,

R

S

(19)

(2 0)

whi ch is the reflect ion coe ffic i ent def ined as the ma gnitude of the ratio

of the r eflected to t he incident electr i c fie l d i ntens i t ies . In the cas e

of waves polari zed normal to the plane of i ncidence (hor izont a l ly pol ari zed

waves ) , the relations for Rl and R2 have been shown by McPet r i e (1938 ) to be

Rlcos 2 8 - (c 2 + d2) (21)=cos 2 8 + (c2 + d2) + 2c cos 8

R2-2d cos 8 (22)=

cos 2 8 + (c 2 + d2) + 2c cos 8

whe r e 8 is the ang le of i ncidence and

I f the t wo materials are loss-less, the r efl ection coefficient can be'writ­

ten in reduced form:

I R Icos 8 - (K 'e - sin 2

cos 8 + (K'e - sin 2

!<8) 2

!<8) 2

(2 5 )

The r elative dielectric constant and loss f actor values i ndi cated in equ a­

tions 23, 24 , and 2S are those of the second medium relat ive to the f irst.

The los s in s ignal energy upon r efle ct i on from an interface i s de f i.ned as

110 logIRI 2

(26)

6

whereas, the signal is reduced by

110 loge )

1 - lRI 2

(27)

when penetrating a new material. One should be cautious when applying these

equations since Fresnel's equations assume a smooth specular interface . If

the interfac e is not sharply defined or is irregular, IRI is usually less

than the equations predict.

FIG. 135 MHz RADIO SOUNDING TRANSMITTER (LEFT) AND RECEIVER (RIGHT). (RULER ONRECEIVER INDICATES SCALE.)

"-J

t-L~1lit;~~'.iOO,~~.:.;i@.:··· · ·· " !~_.• ~-'.

FIG. 2 VEHICLES WITH FOLDED DIPOLE ANTENNAS MOUNTED FROM THE SIDES IN A PARALLEL INLINE CONFIGURATION AS USED WHEN "CONTINUOUSLY" RADIO SOUNDING.

00

9

FIELD MEASUREMENTS

Equipment

Radio sounding equipment (Figure 1) on loan from the University of

Wisconsin Geophysical and Polar Research Center consisted in part, of a

transmitter with a rated peak power of 500 watts into 50 ohms terminal

impedance. The unit operates on a carrier frequency of 35 MHz producing

pulses of 0.24 ~sec duration at a repetition interval of 150 ~sec. The

receiver has an RF gain of 90 db with a band pass of 28 to 42 MHz. The

entire system performance (i. e. the ratio of the transmitted peak power

to receiver sensitivity) is rated at 155 db. The combined weight of the

transmitter and receiver is less than 25 lbs. and each unit operates

from a l2-V battery power source. The equipment was designed by S. Evans

of Scott Polar Research Institute, Cambridge, England and was built by

Randall Electronics, Ltd. It was used in the present study prior to its

extensive use in ice sounding experiments in Antarctica.

Antennas used for transmitting and receiving were folded-dipoles

(F~gure 2). Impedance matching them to the transmitter and receiver

required quarter wave matching stubs at the antenna inputs. The power

gain of each antenna is equal to 1.64.

A Tektronic 453 oscilloscope and a Polaroid camera were used to

visually and photographically record received signals (Figure 3). The

entire radio sounding system is highly mobile and can easily be rendered

airborne since no physical contact with the earth is necessary.

The equipment was operated on the island of Hawaii with the approval

of the Federal Communications Commission as experimental mobile radio

station KA2XVI. ·

Locations of Investigation

Spot and continuous radio soundings were attempted in late October

1966, in four general areas on the island of Hawaii as shown in Figure 4.

Area A, Keoneeleele Flat is a region of almost bare pahoehoe lava

directly south of Pahala. Experiments were also performed in the in­

clined shaft at Pahala. Continuous soundings in area B were attempted

10

for six miles along a recently constructed road on the property of the

Hawaiian Ocean View Estates. Measurements in area C wer e made in the

Milolii section along the road from Hoopuloa to Papa from approximately

sea level to an elevation of 250 m. Extensive investigations were made

in the Kawaihae region (area D) near the northwestern boundaries of the

Parker Ranch and along the yet to be opened new section of highway north

of Kawaihae. Elevations in the areas ranged from sea level to nearly

1200 m; however, the majority of the wor k was done at <:150 m elevation.

The basal water table was, therefore, expected to be at approximately

sea level in most cases.

Aerial photographs together with detailed land classification and

annual rainfall information may be found for each area in the University

of Hawaii Land Study Bulletin No.6, 1965.

Investigations

Area A: Keoneeleele Flat. Initial radio soundings were attempted on

the bare lava flows of the Keoneeleele Flat at an elevation of 58 m

above sea level (Figure 3). The location coincides with a portion of

the area recently investigated by another research team from the Water

Resources Research Center using conventional resistivity techniques.

Figure 5 shows an oscilloscope presentation of the radio signal received

in this region and is typical of that obtained throughout much of the

study . In this case, the oscilloscope sweep speed was set at 0.5 ~sec/

div and the transmitted 35 MHz pulse is evident at the fat left as an

initial pulse burst of 0.24 ~s e c duration. Following it are a series

of repeated or ringing pulses. Recovery to zero amplitude is not accom­

plished until approximately 3 ~sec after the initial rise of the trans­

mitted pulse.

The ringing effect is related to impedance miss-matches ·probably

between transmitter/antenna and/or receiver/antenna. Attempts to decrease

the ringing by adjusting antenna matching stubs were largely unsuccessful.

S. Evans (personal communication) has suggested that adjustable matching

arrangements, particularly in the transmitter feed, would be advisable.

Some receiver miss-matches were also obvious s ince the oscilloscope

pattern varied with receiver attenuator setting . . Separating transmitter

11

FIG. 3 "SPOT" RADIO SOUNDING ON KEONEELEELE FLAT, ISLAND OF HAWAII.

oSCALE

5 10

cB

15 MILES

ISLANDof

HAWAII

N

1

AREAS

A Keoneeleele FlatB Hawaii Ocean View EstatesC MiloliiD Kawaihae

~

N

FIG. 4 LOCATIONS OF 35 MHz RADIO SOUNDING EXPERIMENTS ON THE ISLAND OF HAWAii.

13

and receiver horizontally to over 200 m resulted in a small decrease in the

ringing time duration; however, no water table echo was evident at the ex­

pected echo time. Subsequent laboratory results (detailed under Laboratory

Measurements) confirmed that the estimated velocity (100 m/~sec) of radio

waves through volcanic rocks of low moisture content was very nearly cor­

rect. This velocity value yields an estimated vertical echo time at this

location of just over 1 ~sec assuming a reflecting basal water table at

approximately sea level.

Careful analysis of Figure 5 fails to show any expression of a return­

ing pulse near 1 ~sec; rather, ringing and a condition of partial r eceiver

saturation is evident at that time. The unwanted multiple ringing echoes

have increased the receiver recovery time to beyond that expected for the

returning water table echo. More sophisticated equipment arrangements would

be necessary to record the desired short range echoes, if they are recover­

able.

Pahala Inclined Shaft. In contrast to the bare lava flows of Keoneeleele

Flat is the nearby village of Pahala where the average annual rainfall is

nearly 50 inches. A 30° inclined "Maui type" well was dug here in 1945 by

the Hawaiian Agriculture CompanY, beginning at an elevation of 246 m. The

shaft is nearly 325 m long and reaches a fresh water table 71 m above sea

level. In an attempt to determine in situ electromagnetic velocity and

attenuation losses, measurements were made of transmissions from within the

tunnel which were received at the surface.

Figure 6 diagrammatically shows the situation which gave rise to the

oscilloscope presentation shown in Figure 7. The transmitter was located

64 m down the shaft in a position approximately 39 m below the receiving unit

which was monitored in a large metal building in an attempt to isolate it

from stray radio radiation leaking out from the mouth of the tunnel. A 305 m

length of RG 58 transmission line physically connected the transmitter to the

receiving unit and provided an absolute time reference for the transmitted

pulses. Figure 7 shows the received signal patterns as viewed on dual trace

presentation with horizontal sweeps set at 0.5 ~sec/div. The top trace shows

first the transmitted pulse group which passed directly through the trans­

mission line. Recorded passage time through the cable of 1.525 ~sec was later

confirmed in the laboratory. The lower amplitude group on the top right is

14

LLoo

5Vl......

"~LL

UJ-lUJUJ-lUJUJZoUJ~

5oUJ>......UJUUJe:::lfl-l

~(J).....lfl

LLo

5......I-

~ZUJlflUJe:::0-

UJ0­oUlflo-l-l ............ «U3:

~:e

.(J)......LL

METAL BUILDING

TUNNEL

SCALE! iiiiiiiiiiiililo 5 10 15 METERS

1::::::1::::\:::::1ROCK 0 A IR

FIG. 6 SCHEMATIC REPRESENTATION OF TRANSMITTING AND RECEIVING POSITIONS AT PAHALAINCLINED SHAFT.

f-'(Jl

~,:~~~~~~~~~i:'~~~ ~-- _. "l'-'· "'-= ...!!!!!!- ....--_.

FIG. 7 OSCILLOSCOPE PRESENTATION OF SIGNALS RECEIVED THROUGH RG 58 TRANSMISSION LINE(TOP TRACE) AND BY RECEIVING ANTENNA (BOTTOM TRACE) AT PAHALA INCLINED SHAFT.

f-'(]\

17

a cable multiple reflection having travelled additionally back and forth

in the line. The lower trace shows the signals (inverted) intercepted by

the receiving antenna. The initial larger pulse has travelled 64 m in the

air up the tunnel and, in accordance with Huygens' Principle, has completed

the path to the receiver through an additional 58 m of air travel. Assum­

ing the velocity of propagation as 300 m/~sec, it is concluded that the

pulse arrived after a delay of 0.41 ~sec. The descrepancy between the cable

minus air pulse times (1.115 ~sec) and the measured difference (1.00 ~sec)

is considered to be due to oscilloscope trigger delay time and reading errors.

It is evident in the bottom trace that another pulse of lower ampli­

tude is recorded at an apparent time of 0.9 ~sec. This converted to abso­

lute delay time yields 1.425 ~sec. Assuming that this pulse has travelled

up through the rock column (r = 39 m), the propagation velocity was just

over 27 m/~sec yielding an apparent relative dielectric constant of approx­

imately 100.

Keller, et aZ (in press) found that the resistivity of the water

saturating the near surface rocks in Hawaii ranged from about 1 ohm-m to

about 10 ohm-m. The relative dielectric constant of water up to about

108 Hz may be considered constant and equal to 78 at room temperature in

this resistivity range (e.g. von Hippel, 1954a). Using equations pre­

sented in the section on Theoretical Propagation of Electromagnetic Waves,

the velocity of propagation at 35 MHz would, therefore, be<: 20 m/~sec

in the water saturating the rocks in Hawaii. The pulse recorded at 1.425

~sec may, consequently, represent a signal having passed through nearly

water saturated rock. A velocity as low as 27 m/~sec was not expected,

though, since even in porous basalt the water content can rarely be 50%

and certainly less moisture would be present in the rocks above the tun­

nel in Pahala. However, interfacial polarization in a dielectric mix­

ture, e .g . , water and rock, can result in electromagnetic propagation

velocities which are even less than that in either constituent (see

Laboratory Measurements). Normally this phenomenon is only observed at

low frequencies but even small amounts of moisture spread the effect

over several decades. Possible re-radiations from metal pipes and cables

leading out of the tunnel also may be responsible for this pulse. Al­

though these conductors were grounded prior to making the measurements

there is still some doubt that the pulse at 1.425 ~sec actually travelled

18

through the rock column. If this description is correct then amplitude

measurements indicate that the absorption loss in propagation through

the rock was about 3 db/m.

Time restrictions pr evented an exhaustive invest i gation at the Pahala

shaft, but present r esults woul d seem to justify further expe r i ment at i on

with electromagnetic techniques through this and similar tunnels.

Area B: Hawaii an Ocean Vi ew Estat es . Recently constructed roads on the

property of Hawaii an Ocean View Estates provided easy acce ss to an area where

perched water tables may exi s t . The area is wel l suited to el ectromagnet ic

sensing since it is still largely fr ee of overhead wires, wire fence~, et c .

which can interfere with measurements. The s ix-mile l ength of Tiki Drive,

mostly passing through lava (aa) clinkers, was selected for continuous meas­

urements.

The vehicle arrangement used in the soundings is shown is Figure 2 al­

though in practice the vehicles moved at a constant separ at i on of 30 m. This

helped to reduce ringing as did the parallel in-line positioning of antennas.

Even so, ringing persisted for a l mos t 3 ~sec. Received signals were moni­

tored continuously as the vehicles moved al ong Tiki Drive from an elevation

of 1185 m to 610 m above sea level. Changes in the oscilloscope patterns

were detectable and in many cases could be rel ated to rock surface irregu­

larities. Most recorded pulses were attributed to ringing because the pulses

changed in amplitude and position as receiver att enu ation was changed as on

Keoneeleele Flat.

Area C: Mi lo lii . The secondary road from Papa wind s its way through bare

aa clinkers reaching the sea near the t ail of the 1926 Hoopuloa lava flow.

Continuous radio sounding traverses were made along the road from an eleva­

tion of 250 m to nearly sea level and back. Results were similar to those

obtained in other areas. Ringing and receiver s aturation occurred beyond 3

~sec and completely screened any short range echoes that may have been pres­

ent. Echoes obviously originating from rough surface features were recorded,

but no reflections thought to be from the ground water table were observed.

Echoes from a basal water table~175 m in depth would be . expected to arrive

after the receiver had recovered (appr oxi mat e l y 3.5 ~sec) but 'none were de­

tected. The maximum sounding depth in this area i s , therefore, less than

19

175 m for the exi s ting equipment . Hydrogeologic model studies and l aboratory

measurements presented later i n this r eport conc l ude that this range is prob­

ably<25 m.

Area D: Kawaihae . The l eeward s ides of the Kohal a and Mauna Ke a Domes,

particularly near sea level, are strik ing examp l es of orographically produced

rain shadows. This region , including Kawai hae and lower Parker Ranch, is

one of the driest in the st ate of Haw ai i, repor t i ng less than 10 in. of

rainfall annually. Since r adio los ses were expe ct ed to vary with moisture

content, it was thought that this area was poten,tially one of the best in

Hawaii for radio sounding to the ground wat e r table. AlthouW1 most of the

area is covered with less than 1 mof volcanic ash soil, other areas inves­

tigated were largely bare lava.

· Thr ee days of extensive radio soundings were carried out in this re­

gion, but again no water table echoes were detected. Measurements were made

along approximately 8 miles of the new road north of Kawaihae and at various

locations .upto 140 m elevation in lower Parker ·Ranch generally east of

Puako Bay. On several occasions, when it appear ed that an echo was recorded,

changing the receiver attenuation resulted in shifts in the oscilloscope

pattern. . Thus , the "echoes" are interpreted as ringing ' characteris tics of

the transmitter and/or receiver feeds.

Experiments in the Kawaihae harbor area verified that echoes could be

easily measured from large metal buildings after the receiver had recovered

(~2.0 ~sec). Echoes expected to occur be f or e this time were not observed,

hence, the receiver appeared to be effectively blanked until about 2.0 ~s e c ;

LABORATORY MEASUREMENTS

Samples and Experimental Techniques

Laboratory me asurements of the appropriate dielectric properties of

two representative Hawaiian rocks and one s oi l sample were 'made at the

Massachusetts Institute of Technology Laboratory for Insulation Research.

Specimens selected were a low density (dry = 1.4001 g/cm 3) pahoehoe tholeiite

basalt from the 1881 Mauna Loa flow near Kaumana, a high density (dry =2.6671 g/cm 3) nephelite-melilite basalt from a construction site on the

20

University of Hawaii Manoa campus, and a loose ash sample of red desert

soil from the Kohala district on the island of Hawaii. The soil sample was

first passed through a 24-mesh screen to remove most organic material.

Measurements were made under various moisture conditions beginning

with presumably no free water (run 1), the specimens having been oven dried

at 105° C for three days. Other conditions wer e obtained by wetting or

saturating materials wi t h a KCl salt solution of r esistivity 10.55 ohm-m,

followed by vacuum pumping or applying various pressures of air or dry N2 .

The resistivity value was selected as being representative of natural ground

waters. Some additional measurements of the soil in "as received" condition

and after adding distilled water were made. Moist rock samples required

surface blotting prior to taking the actual measurements. Water content

was calculated on a dry weight basis, a wet weight basis, and by volume.

Volume measurements are not as precise as weight measurements and in the case

of the soils the packing of each sample often differed. Dielectric meas­

urements wer e all made at room temperature, approximately 25° C.

A wide-range modified Schering bridge (described by Charles, et aZ.,

1966) was used to perform the measurements. A cylindrical sample about !;(

inch thick and 1-3/4 inch in diameter was placed between two micrometer

electrodes with secondary foil electrodes assuring more intimate contact.

Capacitance and loss measurements are considered accurate to ± 1% and ± 3%,

respectively, except for the highest loss measurements at the highest fre­

quency which are correspondingly ±5% and ± 10% (Wes t phal , personal com­

munication). Magnetic measurements (still in progress) utilized a coaxial

sample holder with a built-in series capacitor.

Measured and Derived Results

Tables 1, 2, and 3 contain the measured values of sample density,

moisture content (% weight on awet weight basis and % by volume), frequency

varying from 100 Hz to as high as 62 MHz, the relative dielectric constant,

and dielectric loss tangent. In addition, the derived quantities of resis­

tivity, conductivity, propagation velocity, attenuation factor, and atten­

uation in db/m are listed. Calculations of these parameters were made by

applying appropriate equations appearing earlier in this report in the

Theoretical Propagation of Electromagnetic Waves. The computer FORTRAN

TABLE 1. DIELECTRIC PROPERTIES OF HAWAIIAN RED DESERT SO IL AS A

FUNCTION OF FREQUENCY WITH VARY ING MOISTURE CONTENT.

RUN 1 DENSITY MOI STURE CONTENT FREQ DIELECTRIC LOSS RE SI S COND VELOCI TY ATT FACTOR ATTEN(G/CM3 ) %WE IGHT %VOLUME (HZ ) CONSTANT TANGENT (OHM-M) (MHO/ M) (M/jASEC ) (W I) (DB/M)O. 7627 0.0 0. 0 1. DE 02 3. 43 0.0878 5. 97E 08 1. 68E-09 161.83 1. 70E- 07 1. 48E-0 6

1. DE 03 3.07 0. 0772 7. 58E 07 1. 32E-08 171. 09 1. 42E-06 1. 23E-051. DE 04 . 2. 78 0.0700 9. 24£ 06 1. 08E-07 179.82 1. 22E-05 1. 06E-041. DE 05 2. 54 0"0460 1. 54E 06 6. 50E- 07 188. 19 7. 68E- 05 6. 67E-041. 0E 06 2. 414 0. 02815 2.65E 05 3. 78E-06 193. 07 4. 58E-04 3. 98E-039.5E 06 2. 353 0.0180 4. 47E 04 2. 24E- 05 195. 57 2: 75E-0 3 2.39£-021.8E 07 2.343 0.0157 2. 71E 04 3. 68E-05 195. 98 4.53E-0 3 3. 93E-02

RUN 2 DENSI'P-' MOI STURE CONTE NT FREQ DIELECTRIC LOSS RE SI S COND VELOC ITY ATT FACTOR ATTEN(G/CM ) %WE IGHT %VOLUME (HZ) CONSTANT TANGENT (OHM~M) (MHO/ M) (M/,At SEC ) (W I ) (DB /M)0.8634 16.7 14. 4 1. 0E 02 1462 3.02 4.07E 04 2. 46E-05 5.43 8. 36E-05 7. 26E-04

1. DE 03 ' 142. 3 3. 91 3. 23E 04 3. lOE·05 15. 85 3. 08E-04 2.6 7E-031. OE 04 34.4 1.93 7 2. 70E 04 3. 71E-05 40.56 9. 44E-04 8. 20E-0 31. OE 05 15. 25 O. 798 1. 48E 04 6. 77E-05 ' 71. 96 3. 06E-03 2.66E -021. DE 06 7. 02 0. 492 5. 20E 03 1. 92E- 04 110. 12 1. 33E- 02 1. 15E-Ol9. 5E 06 4. 95 0. 279 1. 37E 03 7. 30E-04 133.57 6. 12E-02 5 . 31E-Ol1. 8E 07 4.5 1 0.224 9.89E 02 1. 01E- 03 140.40 8. 91E-02 7. 74E~01

RUN 3 DE NSITY MOISTURE CONTE NT FREQ DIELECTRIC LOSS RE SI S COND VE LOC ITY ATT FACTOR ATTEN(G/CM3) %WElGHT 7,VOLUME . (HZ ) CONSTANT TANGENT (OHM-M) (MHO/M) (M/p,SEC) (W I ) (DB/M)0.8 730 21. 7 18. 93 1. OE 02 10560 2. 305 7. 38E 03 1. 35E- 04 2.20 1. 87E-04 1. 63E- 03

1. DE 03 940 4. 43 4.3 2E 03 2. 32E- 04 5. 88 , 8. 54E-04 7. 42E-0 31. 0E 04 68. 0 7.25 3.65E 03 2.74E -04 17. 84 3. 07E-03 2. 67E-0 21. OE 05 21. 6 2. 67 3. 12E 03 3. 21E-04 46. 52 9. 36E-03 8. 13E- 021.0E 06 12. 0 0.827 1. 81E ,03 5. 52E-0 4 80.80 2.80E -02 2. 43E- Ol9.5E 06 6. 88 0. 389 7.07E 02 L 41E-03 112. 34 9. 97E - 02 8.66E - Ol1. 8E 07 6.25 0. 322 4.96E 02 2. 02E- 03 118. 51 1. 50E-Ol 1. 30E 00

RUN 4 DENSITY MOI STURE CONTENT FREQ DIELECTRIC LOSS RE SIS COND , VELOCI TY ATT FACTOR ATTE N(G /CM3) %WEIGHT %VOLllM):: , (HZ) CONSTANT TANGENT (OHM-M) (MHO/ M) (M/ ).L SEC) (WI ) (DB / M)1. 1370 37. 0 42. 1 1. OE 03 47000 ' 5. 37 7. 12E 01 1. 40E-0 2 0. 77 6. 78E-03 5. 89E-0 2

1. OE 04 1364 20. 66 6. 38E 01 1. 57E -02 2.47 2. 43E-02 2. 11E-Ol1. OE 05 170. 2 17. 22 6. 13E 01 1. 63E- 02 7. 61 7.79E-02 6. 76E-Ol1. OE 06 60. 0 5. 51 5. 44E 01 1. 84E-02 21. 32 2. 46E-Ol 2. 14E 009.5E 06 30. 7 1. 467 4. 20E 01 2.38£-02 45. 96 6.86E -Ol 5. 96E 001.8E 07 25. 8 1. 016 3.8 1E 01 2.62E - 02 53. 63 8. 83E-Ol 7. 67E 00

RUN 5 DENSIb) ~:U:ll~WTE G;,°Wo1~ &l¥)Q DIELECTRI C LOSS RE SI S(£?8PM)

VELOCITY ATT FACTOR ATTEN(G/CM CONSTANT TANGENT (OHM- M) (M/~SEC ) (M- ) (DB/M)1. 2133 41. 8 50.8 ,1. OE 03 21880 9.25 8.88E 01 1. 13E-0 2 0.89 6.31E-03 5. 48E-0 2

1. OE 04 1287 17. 63 7. 92E 01 1. 26E- 02 2. 74 2. 17E-02 1. 88E- Ol1.0E 05 135.4 17.73 7. 49E 01 1. 34E-02 8.42 7. 05E- 02 6. 13E-Ol

49.0 6. 84E 01 1. 46E-02 23. 86 2. 19E-Ol 1. 90£ 00 N1. OE 06 5. 36 f-"

9.5E 06 27. 0 1. 317 5. 32E 01 1. 88E- 02 50. 12 5.91E -Ol 5. 13E 001. 8E 07 24. 7 0.840 4. 81E 01 2. 08E- 02 56. 22 7. 33E-Ol 6. 37E 00

~~~i~~'~~~~~;iJ:£tioio1i:-;it_ "dkl~I " -"''' _'~~ota~.-_s;;;;oo;lK :a:;;;:;;::;:

TABLE 2. DIELECTRIC PROPERTIES OF LOW DENSITY HAWA IIAN BASALT AS A

FUNCTION OF FREQUENCY WITH VARYING MOISTURE CONTENT.

RUN 1 DENSI TY MOI STURE CONTENT FREQ DIELECTRIC LOSS RE SIS COND VELOCITY ATT FACTOR ATTEN(G/CM3) %WEIGHT %VOLUME (HZ) CONSTANT TANGENT (OHM-M) (MHO/M) (M/~SE C) (M- 1) (DB/M)1.4001 0.0 0.0 1. 0E 02 5.89 0.0915 3.34E 08 3. 00E-09 123. 48 2. 32E-0 7 2. 02E-06

1. OE 03 5. 60 0.0360 8.92E 07 1. 12E- 08 126. 75 8.92E-07 7. 75E-061. OE 04 5.50 0.0203 1. 61E 07 6. 21E- 08 127. 91 4.99E-06 4.33E-051. 0E 05 5.46 0. 0196 1. 68E 06 5. 95E-07 128. 38 4.80E-05 4.17E-041.0E 06 5. 27 0.0360 9.47E 04 1. 06E-05 130.66 8. 65E-04 7.5 2E-039.5E 06 4. 87 0. 0656 5. 92E 03 1. 69E-04 135. 87 1. 44E-02 1. 25E-011.8E 07 4. 69 0. 0740 2.88E 03 3. 48E-04 138. 43 3. 02E-02 2.62E -016.2E 07 4.47 0.0875 7. 41E 02 1. 35E-03 141. 76 1. 20E-01 1.04E 00

RUN 2 DENSI r MOI STURE CONTENT FREQ DIELECTRIC LOSS RE SI S COND VELOC ITY ATT FACTOR ATTEN(G/ CM ) %WE IGHT %VOLUME (HZ) CONSTANT TANGENT (OHM-M) (MHO/M) (M/)lS EC) (M- 1) (DB/ M) .1. 4008 0.04 0. 06 1. OE 02 7. 22 0. 280 8. 89E 07 1. 12E-08 110. 59 7.80E-07 6. 78E- 06

1. OE 03 6. 15 O.102 2.87E 07 3. 49E-08 120. 82 2. 65E-06 2.30E -0 51. OE 04 5. 66 0.0427· 7. 44E 06 1. 34E- 07 126. 07 1. 06E-0 5 9. 24E-051. OE 05 5. 42 0.0292 1. 14E 06 8.80E-07 128.85 7.1 2E-05 6. 18E- 041.0E 06 5. 19 0.0402 8.62E 04 1. 16E-05 131. 66 9. 59E-04 8. 33E-039. 5E 06 4. 78 0.0692 5.72E 03 1. 75E-04 137.13 1. 50E-0 2 1. 31E-011. 8E 07 4. 58 0.0800 2. 73E 03 3. 67E-04 140. 07 3. 22E-0 2 2. 80E- 01

RUN 3 DENS Ir MOI STURE CONTENT FREQ DI ELECTRIC LOSS RESIS COND VELOCITY ATT FACTOR ATTEN(G/CM ) %WE IGHT %VOLUME (HZ ) CONSTANT TANGENT (OHM-M) (MHO/M) (M/}lSEC) (W 1) (DB/M)1. 4381 2. 63 3.79 1. 0E 02 6550 4.41 • 6.22E 03 1. 61E-04 2.23 2.25E- 04 1.95E-03

1. OE 03 1091 3. 09 5. 33E 03 1. 88E-0 4 6. 23 7. 33E-04 6. 37E-031. OE 04 2.47 2.402 3.03E 03 3.30E-04 14. 22 2. 95E-03 2. 56E-0 21. OE 05 43. 1 2.366 1.76E 03 5. 67E-04 34. 21 1.22E-02 1. 06E-0 11. OE 06 13. 97 1. 254 1.03E 03 9. 75E-04 70. 34 4. 30E-02 3. 74E-0 19. 5E 06 7. 55 0.510 4.91E 02 2. 03E-03 105.98 1.35E -01 1. 18E 001. 8E 07 6. 81 0.395 3. 71E 02 2. 69E-03 112.86 1.91E- 01 1.66E 00

NN

...... 'aIM"" •

TABLE 3. DIELECTRIC PROPERTIES OF HIGH DENSITY HAWAII AN BASALTAS A FUNCTION OF FREQUENCY WITH VARYING MOISTURE CONTENT

RUN 1 DENSITY MOISTURE CONTENT FREQ DIELECTRIC LOS S RE SIS COND VELOCITY ATT FA~IOR ATT EN(G/CM3) %WE IGHT %VOLUME (HZ ) CONSTANT TANGE NT (OHM-M) (MHO/M) (M/jASEC) (M) (DB/ M)2.6671 0.0 0.0 1. OE 02 12.94 0.207 6. 71E 07 1. 49E-0 8 82.96 7. 76E-07 6. 74E-0 6

1. OE 03 11.18 0.0891 1. 80E 07 5. 54E-08 89. 63 3. 12E-06 2. 71E- 051. OE 04 10. 33 0. 0490 3.55E 06 2. 82E-07 93. 31 1. 65E-05 1.43E-0 41. OE 05 9.73 0.035 1 5.26E 05 1.90E-06 96.16 1. 15E-04 9. 96E-041. OE 06 9.44 0.0269 7. 08E 04 1. 41E- 05 97. 63 8. 65E-04 7.5 26-039. 5E 06 9.07 0.0232 8. 99E 03 1. 11E-04 99.61 6. 95E-03 6 . 04E ~ 02

1. 8E 07 8.95 0.0223 5.00E 03 2. 00E-04 100.27 1. 26E-02 1. 09E-016.0E 07 8. 90 0. 0219 1. 54E 03 6.5 1E-04 100. 55 4. 10E-02 3. 5/E- 01

RUN 2 DENSI~ MO ISTURE CONrENT FREQ DIELECTRIC LOSS RE SIS COND VELOCITY ATT FACTOR ATTEN(G/CM ) %WE IGHT %VOLUME (HZ) CONSTANr TANGENT (OHM-M) (MHO/M) (M/,lJ SEC) (W l ) (DB/M)2. 6757 0. 32 0.86 1. OE 02 99. 2 O. 956 1.90E 06 5.28E -0 7 27. 59 9. 13E-0 6 7. 93E-05

1.0E 03 50.3 0.563 6.35E 05 1. 58E-06 40.82 4. 04E-05 3. 50E- 041. OE 04 27. 1 0.482 1. 38E 05 7. 27E-0 6 56. 10 2. 56E-04 2. 22E- 03i ..os 05 15.4 0.329 3. 55E 04 2. 82E-05 75. 46 1. 33E-03 1. 16E-021. OE 06 11. 41 O. 166 9.49E 03 1. 05E- 04 88.51 5.85E·03 5. 08E- 029.5E 06 9.88 0.0803 2. 38E 03 4. 19E-04 95. 37 2.·51E-02 2. f8E-011. 8E 07 9.58 0.0688 1.52E 03 6.60E-04 96.8 7 4. 01E-02 3.48E-01

RUN 3 DENSI'F MOISTURE CONTENT FREQ DI ELECTRIC LOSS RESI S COND VELOCITY ATT FACtOR ATTEN(G/CM ) or.WE IGHT %VOLUME (HZ) CONSTANT TANGENT (OHM- M) (MHO/ M) (M/}4SEC) 01- ) (DB/M)2. 6772 0.38 1. 00 1. OE 02 275.5 1. 845 3.54E 05 2.83E-06 14.5 2 2. 58E-05 2.24E -04

1. OE C3 79. 2 1. 218 1.86E 05 5. 37E-06 29. 70 1.00E-04 8. 69E-041. OE 04 30.83 0. 807 7.22E 04 1. 38E- 05 50.55 4. 39E- 04 3. 81E-031.0E 05 16.45 0. 477 2. 29E 04 4.3 7E - 05 72.05 1.97E-03 1. 71E- 021. OE 06 11. 78 O. 180 8. 48E 03 1. 18E-04 87. 06 6. 44E-03 5. 60E-0 29. 5E 06 10.18 0.0855 2. 17E 03 4.60E-04 93. 94 2. 71E-02 2.36E-0 11. 8E 07 9. 85 0.0734 1. 38E 03 7. 24E-04 95.52 4. 34E-02 3.77E-Ol

~J1:~~~~~wm~~~~~~~~~~!!!· - - ---

NVI

24

language "E" notation is used Ln. Tab les 1, 2, and 3 to express a number in

exponential form. Accordingly, the l etter E is synonymous with "times 10

to the power of," e .g . 5.97E 08 = 5.9 7 x 10 8 . Graphical presentation of the

dispersive nature of the dielectric constant, conductivity, and attenuation

are seen in the appendix, Figures 8 through 16, with moisture content as a

parameter. Plots of most of the relative dielectric constant and loss tan­

gent data have already be en published by Iglesias and Westphal (1967).

Soil measurement run 3 was made with the soil in an "as received" con­

dition, whereas in run 4, distilled water was us ed in the wetting. Other

"moist" soil measurements (runs 2 and 5) and all "moist" rock measurements

(runs 2 and 3) were made with the 10.55 ohm-m salt solution.

The magnetic permeability of the packed soil sample as received was

only 1.024± 0.01 at 10 KHz and the magnetic loss tangent was unmeasureable

~0.004). Therefore, further magnetic measurements of the soil will not be

made since the magnetic losses can be neglected for propagation purposes

compared to the electric losses even in dry samples for frequencies less

then 100 MHz (Westphal, personal communication). Only the static permea­

bility of the rocks has thus far been measured and since it is less than 1.1,

magnetic losses are expected to be low.

Discussion

The laboratory dielectric measurements presented herein in tabular

and graphical form illustrate the wide variation in electrical properties

found in naturally occurring materials. It is not the intention of this

report to discuss in detail the dielectric phenomena exhibited in these

data; the reader is referred to von Hippel (1954b) and Keller and Frisch­

knecht (1966) as sources of this information. A cursory observation of

the data, however, discloses certain aspects which be ar mentioning with

regard to the propagation characteristics.

Most important, although expected, is the relation between attenuation

and moisture content. Except with soil run 4 using distilled water, all

measurements of a sample at a given frequency resulted in larger attenuation

(db/ m) with increasing moisture content. That soil run 4 shows larger

losses than run 5 is quite surprising since the conductivity of distilled

water is nearly two orders of magnitude (Malmberg and Marylott, 1956) less

25

than the s alt solution used in run 5. Yet, the conductivities of the

water-soil mixture in run 4 are gr eat er than the corresponding values in

run 5 even though more water is present in the latter. Distilled water

would certainly become conductive upon picking up residual salts in the

soil. Also the effects of interfacial polarization would be different

with these two solutions. A theory of interfacial polarization in water­

dielectric interphases was presented by Friche and Curtis (1938) and has

been measured in soils (e. g. Smith-Rose, 1934) and in rocks, (e. g. Keller

and Licastro, 1959; Howell and Licastro, 1961). This process often

results in a mixture of two dielectrics having a dielectric constant

much larger than that of either constituent. The effect is especially

striking at low frequencies and when the amount of the higher conductive

component, e .g. , ground wate~ is increased. As the tables and graphs

clearly show, interfacial polarization can result in dielectric constants

of moist samples at low frequencies that are many thousand times larger

than dry specimens. Values of relative dielectric constant, hence pro­

pagation velocity, show large dispersion in the rocks even when the

sample has as little as 1% moisture cont ent , e .g. high density basalt

run 3 in Figure 14. Comparison of the dielectric constant or velocity

values in low density basalt run 3 with <: 4% moisture by volume and

soil run 2 with almost 15%water by volume indicates that interfacial

polarization is larger in the rock sample. No reliable method of es­

timation of propagation velocity through this rock in a higher water­

saturated condition has been found, but interfacial polarization would

definitely be apparent at higher frequencies. A value of 27 m/~sec

(the value inferrred from the in situ measurements made at the Pahala

shaft) at 35 MHz would not seem totally unreasonable at high moisture

saturation. Oven-dried samples show relatively small dispersion in the

dielectric constant, thus electromagnetic waves at different frequencies

propagate with more nearly equal velocities under dry conditions.

Dispersion in the attenuation, also in the conductivity and resis~

tivity, is seen to be related to moisture content in just the opposite sense

as the dielectric constant. That is, these parameters are more nearly con­

stant with frequen~y when the material has the largest moisture content. On

the other hand, the largest frequency dependance is evident in the oven-dried

samples.

I&

1...1..1.'1.'...~~

~~~

~

26

The general tendency for a ,di e l ect r i c property of a given sample, under

various moisture conditions, to converge with frequency is noted in the

plotted results. Many of the conductivity and attenuation dispersion curves

as plotted with log-log coordinates lie very close to straight lines, e.g.~

conductivity of soil run 1 in Figure 9. This suggests the fitting of much

of the experimental data by equations of the power form,

bP = af

where p is the dielectric property

f is the frequency

a is the y value at unit frequency and b is the slope of the log plots.

THEORETICAL HYDROGEOLOGIC MODEL STUDIES

To estimate the theoretical limitations of the 35 MHz radio system in

sounding the ground water depths in Hawaii, some simple earth models must

be considered. The problem is first to determine hydrogeologically prac­

tical models and second to infer in s itu electromagnetic properties from

laboratory measurements.

Structurally speaking, horizontally layered models offer ease in math­

ematical treatment and are often the best approximation to flat lying sedi­

mentary sequences or lava flows. Common features of the volcanic sequences

in Hawaii are buried soil and ash beds, lava tubes, joints, etc. (Stearns

and MacDonald, 1946), but for the purposes of this study, the layers are

assumed to be homogeneous and isotropic. The near subsurface column is di­

vided into a vadose zone above the water table and a phreatic zone below.

The vadose zone may further be sub-divided into regions of soil water, inter­

mediate water, and capillary water just above the water table. The phreatic

zone will be considered as totally water saturated and the water table will

be assumed to represent a sharp transition. That is to say, the transition

from relatively unsaturated rock to total saturation takes place in a ver­

tical distance of much less than a quarter wave length, approximately <:lm

in rock. It will be assumed that the vadose zone is in relative equilibrium;

excess water having been drained downward by gravity. Such a condition

27

would frequently exist in semi-arid r egions on Hawaii. Water remaining in

the soil or intermediate zones would therefore be that of the so-called

specific retention of the soil or rock expressed as the percentage of the

total volume. It is the value of specific retention, especially in the in­

termediate zone, which is most critical when selecting a model to estimate

the in situ electromagnetic properties above the water table.

The specific moisture retention in soi l whi ch supports plant growth

is considered to lie within two limits: the wilting point and the field

capacity. Experimentally these limits may be measured in the laboratory

by applying certain air pressures to a water - s at ur at ed soil sample. For

Hawaiian soils (Thorne, 1950) and more specifically for Hawaiian red desert

soil (Ekern, personal communication), it has been found that pressures of

15.0 bar and 0.15 bar set the respective limits . The wilting point in an

ash soil occurs at approximately 30% water by dry weight, whereas, the

field capacity is approximately 60% moisture by dry weight. These limits

roughly correspond to runs 3 and 5 of the laboratory soil dielectric re­

sults. Extrapolations to 35 MHz in Figures 8 and 10, yield an expected

range in relative dielectric constant of 6 to 23 and in attenuation of 2 to

10 db/m for soil in si tu .

Many field sounding tests were made where no soil cover was present.

In these locations, the moisture content i n the intermediate zone, i. e. the

entire zone above the water table, is by far the most important factor in

determining radio sounding limitations . The model is simply a two-layered

one with the intermediate layer being underlain by a completely water-sat­

urated semi-infinite layer. No values of the in si t u specific retentions

of volcanic rocks are known to exist in the literature. However, certain

other measurements enable an estimate of a value. Recent petrographic

analyses of Hawaiian rocks (MacDonald and Katsura, 1962) list negative or

free water content as totaling less than 1% by weight except in one sample

which measured less than 2%. In situ values are larger than this since the

samples were removed from a high relative humidity environment thought to

exist only a short distance beneath the surface. Electrical resistivity

soundings on the island of Hawaii (Zohdy, 1966) have indicated the presence

of surface lava flows with resistivities lying in the range 2,000 to 10,000

onm-m (conductivity range 5 x 10- 4 to 10- 4 mhos/m) . These results are es­

sentially DC values and comparison with the results in Figures 12 and 15

28

when extended to lower frequencies show that only the low density basalt

run 3 would fall in this range. Keller, et aZ (in press) measured two dis­

tinct DC resistivity zones above the water table on the island of Hawaii

surrounding the Kilaeua Caldera. Recent near surface flows had a resistiv­

ity of 50,000 to 100,000 ohm-m and older rocks below measured about 1,000

ohm-m. The highly resistive zone was interpreted as originating from rockhaving much of its water driven off by heat trom adjacent molten rock and

would therefore represent an anomalous condition. Subsequent laboratory

measurements on basalt samples resaturated with water yielded an empirical

relation between moisture content by volume and the rock resistivity/water

resistivity ratio. Accordingly, the 1,000 ohm-m layer would contain about

3 to 10% water by volume for the effective water resistivity range 1 to 10

ohm-m. Returning to the M.l.T. results, the low density basalt run 3,

Table 2 is the only rock measurement having a water content in this range.

Actually, a water concentration larger than the approximately 4% in thisrun would seem more appropriate from Keller's results since the resistivity ·

of the water was 10.55 ohm-m. From the available DC resistivity data,

however, we conclude that of the laboratory measurements this one most

closely approximates the expected environment above the water table in

Hawaii. For deriving a theoretical range for ground water soundings,

Figures 11 and 13 yield a 35 MHz relative dielectric constant of 6 and an

attenuation of 2.4 db/m.

Having derived values for the dielectric properties to be expected at

35 MHz above the water table, it remains to estimate those at and below this

level. To do so requires estimating the dielectric constant of totally

water-saturated rock and this, as discussed earlier, can not accurately be

done owing to the effects of interfacial polarization. Many dielectric mix­

ture formulas are availabl e to describe the resultant dielectric constant

but they predict values which are less than observed because of this effect.

However, to set a lower limit on the relative dielectric constant, consider

the mixture formula given by Wiener (1910) for a two component system. The

complex relative dielectric constant of a mixture (K*m) consisting of com­

ponents with values K*l ' and K*2 is given by

(28)*K2 -1

---} + q (---)*K2 + u

*Kl -1

( *Kl + u

* -1K m= p

*K + Um

29

where p and q are respectively the ratios of the volumes of the components

to the total volume, hence ,

p + q = 1

u is a geometrical parameter allowed to vary from 0 to co. The largest

dielectric constant is predicted for u =co for which equation 28 reduces

to

* * * 'K m -1 = P (K 1 -1) + q (K2 -1 ) (29)

Assuming a low density basalt (porosity approximately 40%) which is com­

pletely saturated with ground water (K' e = 78) and assuming K' e = 10 in

solid basalt, equation 29 yields ~40 as the resultant r elative dielectric

constant . Thus, the value is expected to be at least this large in the

phreatic zone and at the water table. It is not necessary to estimate the

attenuation below the water table since energy loss upon reflection can be

determined to a first approximat ion at 35 MHz from the dielectric constant

contrast.

Sufficient parameters have now been estimated to determine the theo­

retical electromagnetic losses for a 35 MHz wave reflected from tke ground

water table. First, consider a model having K' e = 6 and attenuation 2. 4

db/m throughout the entire vaoose zone (i. e.,basalt of density 1.44 g/cm 3 ,

porosity approximately 40%, and 3.8% water content by volume) below which

the phreatic zone consists of the same material but totally wat er - s at ur at ed

(K 'e > 40) . Using this model and equations 14, 18, 25, 26, and 27, the

losses are listed in Table 4 for a plane electromagnetic wave entering the

surface at normal incidence (8 "=0°) and returning after reflection from

the water table 25 m below. Evaluating the reflection coefficients using

equations 20, 21, 22, 23, and 24 does not significantly alter the results

hence the reduced form (equation 25) is used ·to compute values of tRI.Considering a simple three layer model constructed by placing a soil

cover (attenuation 2 to 10 db/m) upon the two layers in model 1 generally

further increases the losses expected at given depths. Hence, the depth

limit is probably less than 25 m in either case since the loss in Table 4

(162 db) exceeds the rated performance of the 35 MHz system by 7 db. An

echo would return approximately 0.4 ~sec after transmission and would be

30

TABLE 4. THEORETICAL LOSSES FOR 35 MHz RADIO WAVES REFLECTED FROM THEGROUND WATER TABLE IN HAWAII AT 25 M DEPTH (MODEL 1)

SOURCE OF LOSS

SURFACE PENETRATION (IRI =0.42)

OUTGOING

RETURNING

FREE SPACE

ATTENUATION (2.4 db/m)

WATER TABLE REFLECTION (IRI =0.44)

TOTAL

ECHO LOSS (db)

1

1

33

120

7

162

detectable only under the most ideal antenna matching arrangements. In

fact, since the transmitted pulse can never terminate in practice at the

0.24 psecpulse duration, more sophisticated equipment would be needed to

detect shallow water table echoes. Raising equipment above the surface,

e.g., in a helicopter would be one way of separating outgoing pulse and

ringing from the returning echo. Doubling distance increases free space

loss by 6 db and other losses remain the same. Still, the value of such an

arrangement to sound the depth to ground water in Hawaii is questionable

since maximum penetration would probably be less than 25 m even with ideal

equipment and ideal geologic conditions.

In the interest of other radio sounding applications i n the VHF band

(30-300 MHz) consider model 1 when material above the water table has no

free water content and has the dielectric properties of oven-dried low

density basalt (run 1, Table 2). The 35 MHz properties (Figures 11 and 13)

of this material are K'e = 4.5 and attenuation = 0.57 db/m. In such a

model, losses approximately equal to the 35 MHz system performance occur

when sounding the water table at a depth of about 90 m. A similar model

may be constructed with dry high density basalt (run 1, Table 3) overlying

31

like material which is water-saturated. The estimated reflection loss at

the water table would be 18 db in this case ( I RI ':::' 0.13) . Even so, a de­

tectable echo could theoretically be observed from the water table at a

depth of almost 200 m. An additional layer of dry volcanic ash covering

either the low or high density dry basalt models could be easily penetrated

since the loss at 35 MHz would be only approximately 0.06 db/m.

In passing, attention is directed to the measurements at lower fre~

quencies listed and plotted for the low density basalt sample, run 3 (Table

2 and Figure 13). Assuming these data represent the electrical properties

above the water table in the dry areas in Hawaii it is quite evident that

depths of many hundred meters could theoretically be sounded even at fre­

quencies as high as 0.1 MHz.

32

CONCLUSIONS

Field measurements and theoretical hydrogeologic model studies uti­

lizing laboratory dielectric measurements of rock and soil samples under

varying moisture conditions indicate that attenuation due to moisture pro­

hibits VHF water table soundings to depths;C 2S m in Hawaii. Radio wave

attenuation in this frequency range is estimated to be greater than 2 db/m

through material above the water table even when les s than 4% moisture by

volume is present. To detect shallow water table reflections would require

more sophisticated equipment than that now being used to sound several

kilometers of glacial ice thickness. Although the VHF range does not appear

too promising for sounding purposes in Hawaii it is evident that losses at

lower frequencies, even though above audio range, do not prohibit soundings

to depths of many hundred meters. Thus, techniques employing frequencies

above those commonly used in electromagnetic soundings (low or sub-audio)

may prove valuable in the semi-arid regions in Hawaii.

Results obtained in Hawaii do not preclude usefUl VHF soundings though

rocks in other dry areas. In fact, since the quartz in sandstone aquifers

is less hydrophilic than that of basalt glasses (Keller, personal communi­

cation) loss es would be expected to be less. Further laboratory measure­

ments on various rocks and soils under known moisture conditions and in a

wide frequency range should prove valuable in determining the feasibility

of such soundings.

Judging from the losses measured in oven-dried volcanic rocks and ash,

it is suggested that VHF pulse techniques might prove useful in remote

sounding the lunar sub-surface. The presence or absence of moisture would

again appear to be the crucial factor determining the success of such pro­

bings . It is interesting to note that Cook (1960) has suggested the use

of VHF waves to probe the atmospheres of the major planets.

33

ACKNOWLEDGEMENTS

I wish to thank C. R. Bentley of the University of Wisconsin

Geophysical and Polar Research Center for the generous use of the

35 MHz radio sounding equipment. J. C. Clough accompanied the equip­

ment to Hawaii and was very helpful in performing the field tests.

Able assistance in carrying out the field program was also given by

C. Lao of the University of Hawaii Water Resources Research Center

and S. P. Bowles of the Honolulu Board of Water Supply. The experi­

ments on the Island of Hawaii could not have been accomplished with­

out the cooperation extended by individuals representing the Naalehu

Dairy, Hawaii Agricultural Company, Hawaiian Ocean View Estates, and

Parker Ranch. The use of a vehicle from the University of Hawaii Land

Study Bureau is also appreciated.

The dielectric measurements on Hawaiian rocks and soils were made

by W. B. Westphal at the Massachusetts Institute of Technology Labora­

tory for Insulation Research.

I also extend my gratitude to D. C. Cox, L. A. Palmer, W. M. Adams,

L. S. Lau, and P. C. Ekern among others who provided helpful discussion

and encouragement during the conception and execution of the radio

sounding project. The project was supported by federal and state

funds as a portion of the matching proposal, "Geophysical Bxp l.qrati.on

for Hawaiian Ground Water", U. S. Office of Water Resources Research

project number B-005-HI.

34

REFERENCES

Charles, R. E., K. V. Rao, and W. B. Westphal, A capacitance bridgeassembly for dielectric measurements from 1 Hz to 40 MHz , Labora­t ory f or I nsulat i on Res~arch~ MIT~ Tech . Rept . 201 ~ 26 pp., 1966.

Cook, J. C., Proposed monocycle pulse VHF radar for airborne ice andsnow measurements, Transacti ons of t he American I ns t itute ofElectrical Engineers~ Pt . 1 (Communications and Electronics),79, 588-594, 1960.

Davis, S. N. and R. J. M. DeWiest, Hydrogeo logy~ 463 pp. , John Wileyand Sons, New York, 1966.

Evans, S., Progress report on radio echo sounding, Polar Record~

13~ 85,413-420, 1967.

Friche, H. and H. J. Curtis, The dielectric properties of water-di­electric interphases, J. Phys. Chem. ~ 41 ~ 729-745, 1938.

Howell, B. F., Jr. and P. H. Licastro, Dielectric behavior of rocksand minerals, Am. Mineralogis t~ 4 6~ 269- 288, 1961.

Iglesias, J. and W. B. Westphal, Supplementary dielectric-constantand loss measurements on high-temperature materials, Laboratoryfo r I nsulat ion Research~ MIT~ Tech. Rept. 203~ 119 pp., 1967.

Jakosksy, J. J., Exp l orabion Ueophuei-ee , 2nd ed., pp. 441-442, TrijaPub. Co., Los Angeles, 1950.

Jiracek, G. R. and C. R. Bentley, Dielectric properties of ice at30 Mc/s, J. Glacio l . ~ 6~ 319, 1966.

Keller, G. V. and F. C. Frischknecht, Electrical Methods in Geophysi ­cal Prospecting~ 517 pp., Pergamon Press, New York, 1966.

Keller, G. V. and P. H. Licastro, Dielectric constant and electricalresistivity of natural state cores, U. S . Geol. Surv . BuZZ . 1 052H~

257-285, 1959.

Keller, G. V., J. I. Pritchard, C. J. Zab l ocki , and L. A. Anderson,Evaluation of geological effects on magneto-telluric signals re­corded at the Hawaiian Volcano Observatory, in press . .

Macdonald, G. A. and T. Katsura, Relationship of petrographic suitesin Hawaii, in The Crust of the Paci f i c Basis~ edited by G. A.Macdonald and H. Kuno, pp. 187-195, Geophysical Monograph No.6,AGU, Washington, 1962. .

Malmberg, C. G. and A. A. Maryott, Dielectric constant of water from0° to 100° C, J . .Res. Nat . Bur . Std. 56~ No.1, 1-8, 1956.

McPetrie, J. S., The reflection coefficient of the earth's surface forradio waves, J . I ns t. Eleo. Eng. (London)~ 82~ 214, 1938.

Smith-Rose , R. L., Electrical measurements on soil with alternatingcurrents, J . I nst. Elec . Eng . (London)~ 75~ 221-237, 1934.

Stearns, H. T. and G. A. Macdonald, Geo logy and Ground-water Resourcesof t he I s land of Hawaii~ Bull. 9, Hawaii Division of Hydrography,363 pp., 1946 .

Thor ne , M. D., Moi s t ur e characteristics of some Hawaiian soils, Soi lSci . Soc . Am . Froc . (l949)~ l4~ 38- 41 , 1950.

University of Hawaii Land Study Bureau , De tai led Land Classi f i cat i on ­I sland of Hawaii~ LSB Bulletin No.6, 758 pp., 1965.

35

von Hippel, A. R. Ced.), Dielectric Materia ls and Applications~ p. 361,The Technology Press of MIT and John Wiley and Sons, New York,1954a.

von Hippel, A. R., Dielectrics and Waves ~ 284 pp., John Wiley andSons, New York, 1954b .

Wiener 0., Zur Theorie de Refraktionskonstanten, Ber i chte uber di eVerhandlungen der Koniglich Sachsischen Gese l l schaf t der Wi s sen­chaften zu Leipsig~ Mathematisch-physikalische Klasse, 62, 256­268, 1910.

Zohdy , A. A. R., Preliminary report on the resistivity methods on theislands of Oahu and Hawaii, U. S . Geological Survey open fi le~

41 pp., 1966.

APPENDIX

39

U0::.....UW...JWo

10'

• RUN I• RUN 2~ RUN 3• RUN 4• RUN 5

108104 105 106

FREQUENCY (HZ)

FIG. 8 RELATIVE DIELECTRIC CONSTANT OF HAWAIIAN RED DESERT SOIL AS AFUNCTION OF FREQUENCY WITH MOISTURE CONTENT AS A PARAMETER.(REFER TO TABLE 1 FOR MOISTURE CONTENT IN VARIOUS RUNS.)

40

• RUN I• RUN 2• RUN 3• RUN4• RUN 5

•

-~<,(/)

0I~

>- 165I->I-U::::>0z

IerG0u

10-9 L-...L....JL....J....L....L.LJ.J..L..-....L-..L....L..Ju..u.u---'--..I......L-I-U-LU---l-..L...L.J...J..U.u.---I-.J-l..u...uL.L.L.---I-...J-L...L..LL.LLI.-~

10 2

FREQUENCY (HZ)

FIG. 9 DIELECTRIC CONDUCTIVITY OF HAWAIIAN RED DESERT SOIL AS A FUNCTIONOF FREQUENCY WI TH MO ISTURE CONTENT AS A PARAMETER. (REFER TO TA­BLE 1 FOR MOISTURE CONTENT IN VARIOUS RUNS.O

41

1.0

- 161

~<,

. lD0-z0I-<t:::>zwl-I-<t

• RUN I• RUN 2• RUN 3• RUN 4• RUN 5

FREQUENCY (HZ)

FIG. 10 ATTENUATION (db/m) IN HAWAIIAN RED DESERT SOIL AS A FUNCTIONOF FREQUENCY WITH MOISTURE CONTENT AS A PARAMETER. (REFERTO TABLE 1 FOR MOISTURE CONTENT IN VARIOUS RUNS.)

42

• RUN 1• RUN 2• RUN 3

1,010 2 104 105 106

FREQUENCY (HZ)108

FIG. 11 RELATIVE DIELECTRIC CONSTANT OF LOWDENSITY HAWAIIAN AS A FUNC­TION OF FREQUENCY WITH MOISTURE CONTENT AS A PARAMETER. (REFERTO TABLE 2 FOR MOISTURE CONTENT IN VARIOUS RUNS.)

43

• RUN 1• RUN 2• RUN:3

-~ 1(J4<,en0:r:~->-

105I-

>I-U:>0z

1060

U

169 L--.J.-L.-LJI....U.LLl...---L....L...L.L..LJ...I..ll.-.......L-L...J-J...1.JL.I...U-----I-J......L..LJ...LLLL_..L......J.--LJ...u..u.L-...L-.L.....L-1...LUcll.----'

102

FREQUENCY (HZ)

FIG. 12 DIELECTRIC CONDUCTIVITY OF LOW DENSITY HAWAIIAN BASALT AS A FUNC- ~TION OF FREQUENCY WITH MOISTURE CONTENT AS A PARAMETER. (REFERTO TABLE 2 FOR MOISTURE CONTENT IN VARIOUS RUNS.)

44

10

- 161::E<,m0

z102

0~~::>ZW~

103..-~

• RUN I.. RUN 2• RUN 3

106 ~....L-.L..L.L.L.LI..I.L----L..""""""'....L.LJL..I..LI-~----L..L.LJ....u..u._~.....L.L..LL.ll.L---L.-.L.....L..L.L.U~----L.....L.J.-L.L.I.uL----l

102

FREQUENCY (HZ)

FIG. 13 ATTENUATION (db/m) IN LOW DENSITY HAWAIIAN BASALT AS A FUNCTIONOF FREQUENCY WITH MOISTURE CONTENT AS A PARAMETER. (REFER TOTABLE 2 FOR MOISTURE CONTENT IN VARIOUS RUNS.)

45 .

• RUN 1• RUN 2• RUN 3

U0::....UW...JWo

FIG. 14 RELATIVE DIELECTRIC CONSTANT OF HIGH DENSITY HAWAIIAN BASALT ASA FUNCTION OF FREQUENCY WITH MOISTURE CONTENT AS A PARAMETER.(REFER TO TABLE 3 FOR MOISTURE CONTENT IN VARIOUS RUNS.)

104 10~ 106

FREQUENCY (H Z)108

46

-~<,en0J:~->-....>....o::>cz0 IO-u

• RUN I• RUN 2• RUN!

104 105 106

FREQUENCY (HZ)

FIG . 15 DIELECTRIC CONDUCTIVITY OF HIGH DENSI TY HAWAIIAN BASALT AS AFUNCTION OF FREQUENCY WITH MOISTURE CONTENT AS A PARAMETER.(RE FER TO TABLE 3 FOR MOISTURE CONTENT IN VARIOUS RUNS .)

. i

47

10 1

1.0

- 10-1

~<,mQ-Z0~<t:JZW~~<t

• RUN I• RUN 2• RUN 3

104 . 105 106

FREQUENCY (HZ)

10-6L..-.....................,...LU.I..L..-..L-L..L.I....I....I..I..u.--'--.&...L..JL..LLJ.u.--'--..L-I-LL.L.L.LL---L.....t-L..I...I..I..J..LI.---'-....L.L...a..u.uJ.-~

102

FIG. 16 ATTENUATION (dbjm) IN HIGH DENSITY HAWAIIAN BASALT AS A FUNCTION 'I' :OF FREQUENCY WITH MOISTURE CONTENT AS A PARAMETER. (REFER TO "TABLE 3 FOR MOISTURE CONTENT IN VARIOUS RUNS .) ~

'i<l'l~d~

jji~,

~~~I