Download Magnetotellurics with a remote magnetic reference

GEOPHYSICS,
VOL. 44,
44, NO.1
NO. I (JANUARY
(JANUARY
1979); P.
P. 53-68,
53-68,
16FIGS,
FIGS., 55 TABLES
TABLES
GEOPHYSICS,
VOL.
1979);
16
Magnetotellurics with
with aa remote
remote magnetic
magnetic reference
reference
Magnetotellurics
T. D.
D. Gamble,*
Gamble,* W.
W. M.
M. Goubau,*
Goubau,* and
and J.
J. Clarke*
Clarke*
T.
Magnetotelluric measurements
measurementswere
were performed
performed simultaneously
simultaneouslyat
at two
two sites
sites4.8
4.8 km
km apart
apart near
near Hollister,
Hollister,
Magnetotelluric
California. SQUID
SQUID magnetometers
magnetometerswere
were used
used to
to measure
measurefluctuations
fluctuationsin
in two
two orthogonal
orthogonal horizontal
horizontal comcomCalifomia.
ponents-of
the magnetic
magneticfield,
field. The.
Thedamobtained
each site
sitewere
were analyzed
analyzed using
usingthe
the magnetic
magnetic fields
fields at
at the
the
ponentsof the
data_ohtained atat each
othersite
siteas
asaaremote
remotereference.
reference.In
In this
thistechnique,
technique,one
onemultiplies
multipliesthe
theequations
equationsrelating
relatingthe
theFuurier
Fouriercomponents
components
other
of the
theelectric
electricand
andmagnetic
magneticfields
fieldsby
by aa component
componentof
of magnetic
magneticfield
field from
from the
theremote
remotereference.
reference. By
By averaging
averaging
of
the various
variouscrossproducts,
crossproducts,estimates
estimatesof
of the
the impedance
impedancetensor
tensornot
not biased
biasedby
by noise
noiseare
areobtained,
obtained. provided
providedthere
there
the
areno
nocorrelations
correlationsbetween
betweenthe
thenoises
noisesin
inthe
theremote
remotechannels
channelsand
andnoises
noisesin
in the
the local
localchannels.
channels.For
For some
somedata,
data,
are
conventionalmethods
methodsof
ofanalysis
analysisyielded
yieldedestimates
estimatesof
ofapparent
apparentresistivities
resistivitiesthat
thatwere
werebiased
biasedhy
bynoise
noiseby
byas
asmuch
much
conventional
astwo
two orders
ordersof
of magnitude,
magnitude.Nevertheless,
Nevertheless,estimates
estimatesof
of the
the apparent
apparentresistivity
resistivityobtained
obtainedfrom
from these
thesesame
samedata,
data,
as
usingthe
the remote
remote reference
reference technique.
technique. were
were consistent
consistentwith
with apparent
apparentresistivities
resistivitiescalculated
calculatedfrom
from relatively
relatively
using
noise-freedata
dataatatadjacent
adjacentperiods.
periods.The
Theestimated
estimatedstandard
standarddeviation
deviationfor
for periods
periodsshorter
shorterthan
thanJ3 sec
set was
wasless
lessthan
than
noise-free
percent, and
and for
for 87
87 percent
percentof
of the
the data,
data, was
was less
lessthan
than 22 percent.
percent. Where
Where data
data bands
bandsoverlapped
overlappedbetween
between
55 percent,
periodsof
of 0.33
0.33 sec
set and
and I1 sec,
set, the
the average
averagediscrepancy
discrepancybetween
between the
the apparent
apparentresistivitie,
resistiviticawas
was 1.8
1.8 percent.
percent.
periods
INTRODUCTION
INTRODUCTION
paper(Goubau
(Goubauet
et ai,
al, 1978)
1978) discussed
discussedtwo
two different
different
paper
Inthe
themagnetotelluric
magnetotelluric(MT)
(MT) method,
method,one
oneseeks
seeksthe
the approaches
approachesto
to reducing
reducingthis
thisbias,
bias, namely,
namely, (1)
(1) aa solusoluIn
elements of
of the
the impedance
impedance tensor
tensor Z(w)
Z(o) from
from the
the tion
tion of
of the
the eight
eight simultaneous
simultaneousequations
equationsfor
for the
the imimelements
equations
pedance elements
elements in
in terms
terms of
of crosspowers
crosspowersalone,
alone,
equations
pedance
and (2)
(2) aa solution
solution of
of the
the equations
equations in
in terms
terms of
of
and
ExCw) = ZxxCw)Hx(w) + Zxy(w)Hy(w), (1)
weighted
crosspowers.
Analysis
techniques
for
MT
weighted crosspowers. Analysis techniques for MT
measurementswith
with aa fifth
fifth (electric
(electric or
or magnetic)
magnetic)
and
and
measurements
localreference
referencechannel
channelwere
were also
alsot1iscussed,
discussed.includincludlocal
E,(w) == Zyx(w)Hx(w)
Z,,(w)&(o)
Z,,(oJ)&/(cLJ).
(2)
Ey(w)
++ Zyy(w)Hy(w),
(2)
ing
a
crosspower
analysis
in
which
one
multiplies
ing a crosspower analysis in which one multiplies
equations(I)
(I) and
and (2)
(2) by
by the
the complex
complex conjugate
conjugateof
of
equations(I)
(I) and
and (2),
(2), Hx(w),
H,(o), Hy(w),
H,(o), E.r(w),
E,(w),
equations
InIn equations
the
Fourier
transform
of
the
reference
field.
It
was
and
E,(w)
are
the
Fourier
transforms
of
the
fluctuatthe
Fourier
transform
of
the
reference
field.
It
was
and Ey(w) are the Fourier transforms of the fluctuatconcludedthat
that any
any of
of the
the 44- or
or 'i-channel
5-channel methotls
methods
ing horizontal
horizontal magnetic
magnetic(H)
(Hj and
andelectric
electric (E)
(E) fields
fields concluded
ing
would
work
satisfactorily
provided
that
the
noiseinin
H,(r),
H,(t),
E,(t),
and
E,(r).
If
one
multiplies
H.r(t), Hy(t), E;r(t), and Ey(t). If one multiplies would work satisfactorily provided that the noise
the
various
channels
was
uncorrelated.
These
techequations
(I)
and
(2)
in
turn
by
the
complex
conthe various channels was uncorrelated. These techequations (I) and (2) in turn by the complex conniqueswere
w’eretested
testedon
ondata
dataobtained
obtainedatatGrass
GrassValley,
Valley.
jugate of
of each
each of
of the
the frequency-dependent
frequency-dependentfields,
fields, niques
jugate
Nevada. InIn most
most measurements,
measurements,there
there was
was aa sigsigand averages
averagesthe
the resulting
resulting autopowers
autopowersand
and crosscross- Nevada.
and
nificant
level
of
correlated
noise
found
between
powers
of
the
fields
over
many
sets
of
data,
one
obpowers of the fields over many sets of data, one ob- nificant level of correlated noise found between
some channels.
channels. Most
Most techniques
techniquesyielded
yielded apparent
apparent
tainseight
eightsimultaneous
simultaneousequations
equationsthat
thatcan
canbe
besolved
solved some
tains
resistivitiesthat
thatwere
were biased.
biased.
for the
the impedance
impedanceelements.
elements.As
As isiswell
well known,
known, the
the resistivities
for
autopowersmay
may severely
severely bias
biasthe
the impedance
impedanceestiestiFinally. use
useof
of aa remote
remote magnetometer
magnetometerwas
was proproautopowers
Finally,
mates
if
there
is
noise
in
the
measured
fields
(Sims
posedtotoobtain
obtainreference
referencefields
fieldsH,.,.(t)
H,,,.(r) and
andHur(t)
H,,(t) inin
mates if there is noise in the measured fields (Sims posed
al, 1971;
1971; Kao
Kao and
and Rankin,
Rankin, 1977).
1977). An
An earlier
earlier which
whichthe
thenoise
noiseshould
shouldbe
beuncorrelated
uncorrelatcdwith
withany
anyofthe
of the
etet aI,
Manuscript
received
bythe
theEditor
EditorFebruary
February
10,1978;
1978;revised
revisedmanuscript
manuscriptreceived
receivedApril
April 17,
17, 197R.
1978.
Manuscript
received
by
10,
*University of California. Materials and Molecular Research and Earth SciencesDivision, Lawrence I&xkeley Laboratory,
*Umverslty
ofCahforma, MaterIals and Molecular Research and Earth Sciences Division, Lawrence Berkeley Laboratorv
Berkeley, CA
CA 94720.
94720.
'J'
Berkeley,
OOIS-8033/79/0101-0053$03.00. ©
@ 1979
1979Society
Societyof
ofExploration
ExplorationGeophysicists.
Geophysicists.All
All rights
rightsreserved.
reserved.
0016-8033/79/0101-0053$03.00.
53
53
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54
54
Gamble
Gamble et
et al
al
low Creek
Willow
Creek PeakA
Peak6
FM
F M Repeater
Repeater
MN
E2
EI
Upper
~LaGlorJa
·E3
I
I km--j
FIG. I.
Magnetotelluric measurement
measurement sites
sites in
in Bear Valley,
Valley, California, @ magnetometer;
magnetometer; l• electrode.
electrode.
FIG.
I Magnetotelluric
four
(I) and
and (2) can
can
four fields
fields at
at the
the MT
MT station.
station. Equations
Equations (1)
be
by multiplying them
them in
in turn
tum by H,*,(W)
Hx*r(w) and
and
be solved
solved by
H,*(w)
Hu*r(w) to
to obtain
obtain four
four more
more equations
equations that
that can
can be
be
solved
solved for the
the impedance
impedance elements.
elements. One finds:
finds:
Z;r;r = (ExWir HyH":r - ExH:'. HyH:r) / D, (3)
ZXY
=
(E;rH:rHxH:r - E;rH:r H;rH:r) / D, (4)
Zy;r = (EyH:rHyH:r - EyH:rHyHi,.) / D, (5)
and
and
where
where
D :=HxH:rHyH:r
-HPHjC*HHUH$-- HxH:rHyH:r.
H,H$H,H,*.
D
The bar
bar denotes
denotes an
an average
average over all
all transform
transform points
points
The
given frequency
frequency window, and
and over all
all sets
setsof
within aa given
data. The
The impedance
impedance elements
elements will be
be unbiased
unbiased by
data.
noise provided
provided the
the noise
noise in
in the
the MT
MT array
array is
is uncorreuncorrenoise
fated with
with noise
noise in
in the
the reference
reference channels.
channels.It should
shouldbe
be
lated
noted that
that since
sinceequation
equation(I)
(I) and
and then
then (2) is
is multiplied
multiplied
noted
in tum
turn by
by aa single
single reference
reference field,
field, the
the values
values of the
the
in
impedance elements
elements are
are independent
independent of the
the magnimagniimpedance
tudes and
and phases
phasesof the
the reference
reference fields.
fields. Therefore,
Therefore,
tudes
one does
does not
not need
need aa precise
precise know
knowledge
the gains
gainsor
or
one
ledge of the
phaseshifts
shifts in
in the
the telemetry
telemetry for the
the remote
remote references.
references.
phase
this paper,
paper, aa test
test of the
the remote
remote reference
reference techtechIn this
nique is
is described.
described. In
In Bear
Bear Valley, near
near Hollister,
nique
California, two
two magnetotelluric
magnetotelluric stations
stations were
were set
set up
up
and
E J ., E,,
E., H,,
H x , H,,
H y, and
and H,
Hz were recorded
recorded from
and E,.,
both
both stations
stations simultaneously.
simultaneously. The standard
standard analysis
analysis
techniques
techniques yielded apparent
apparent resistivities
resistivities that
that were
significantly
significantly biased
biased by noise.
noise. Howcv*er,
However, the use
use of
the
the remote
remote reference
reference allowed derivation
derivation of
of apparent
apparent
resistivities
resistivities that
that had
had no
no obvious
obvious bias.
bias. even
even when
when the
the
coherencies
coherencies were as
as low as
as 0.1. Furthermore,
Furthermore, where
the highest
the
highest frequency
frequency band
band and
and second
second highest
highest frequency band
band overlapped.
quency
overlapped, the
the apparent
apparent resistivities
resistivities
agreed to
to within 1.8
I .8 percent.
agreed
percent. The estimated
estimated standard
standard
deviation for the
deviation
the apparent
apparent resistivities
resistivities at
at periods
periods
shorter than
than 3 set
I .3 percent.
shorter
sec was
was 1.3
percent.
MEASUREMENTS
complete MT
Two complete
MT stations
stations separated
separated by 4.8 km
established on
were established
on La Gloria road
road in
in Bear
Bear Valley,
Valley,
1. The Upper
California, at
at the
the sites
sites shown
shown in Figure
Figure I.
station is
La Gloria station
is in
in hilly terrain
terrain where
where the
the geology
geology
consistschiefly of granites,
granites, while the
consists
the Lower La Gloria
station is
is in
in a level
level area
area over
over a zone
zone of low resistivity
resistivity
station
1976), and
and is
is slightly
slightly east
east of a fault
fault that
that
(Mazella, 1976),
separatesthis
this zone
zone from
from the
the granites.
granites. Lower
lower La Gloria
separates
is about
about 2 km west
west of the
the San
San Andreas
Andreas rift zone.
zone.
is
Pb electrodes
electrodes installed
installed by
by Corwin
Cot-win for dipoledipoleThe Pb
dipole resistivity
resistivity monitoring
monitoring were
were used
used for the
the electric
electric
dipole
field measurements
measurements(Morrison et
et ai,
al, 1977).
1977). The localocafield
tion of the
the electrodes
electrodesis
is shown
shown in
in Figure
Figure I. Electrodes
Electrodes
tion
Et and
and E2
E, were
were the
the common
common electrodes
electrodes at
at the
the lower
E1
and upper
upper stations,
stations, respectively.
respectively. III
In the
the subsequent
subsequent
and
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55
Magnetotellurics
analysis,
analysis, the
the electric
electric field directions
directions at
at each
each stastation were made
made orthogonal.
orthogonal. For the
the magnetic
magnetic field
measurements
measurements a dc
dc SQUID
SQUID 3-axis magnetometer
magnetometer
(Clarke et ai,
al, 1976)
1976) at
at Lower La Gloria, and
and an
an
rf SQUID
SQUID 3-axis magnetometer,
magnetometer, manufactured
manufactured by
S. H. E. Corporation,
Corporation, at
at Upper La Gloria were used.
used.
The magnetic
magnetic field sensitivities
sensitivities were approximately
approximately
4 yHrI/2, respectively. The
5 yHz- 1 /2 and
1Oand 1O10m4y
Hz-~‘~, respectively.
10-5yHz-“2
magnetometer
magnetometer at
at each
each site
site was
was used
used as
as the
the reference
reference
for the
the MT
MT signals
signals at
at the
the other
other site.
site.
The MT
MT data
data and
and the
the vertical
vertical components
components of the
the
magnetic
magnetic field fluctuations
fluctuationsat
at each
each site
site were
were recorded
recorded
simultaneously.
simultaneously.A block diagram
diagram of the
the measurement
measurement
electronics
electronics appears
appears in
in Figure
Figure 2. The equipment
equipment at
at
Lower
lower La Gloria was
was battery
battery powered,
powered, while that
that at
at
Upper La Gloria was
was powered
powered by
by a 60 Hz generator.
generator.
Each
Each signal
signal was
was passed
passed through
through a preamplifier that
that
contained
contained a high-pass
high-pass filter to
to attenuate
attenuate the
the largelargeamplitude
amplitude low-frequency signals
signals that
that could
could have
have
exceeded
exceeded the
the dynamic
dynamic range
range of the
the electronic
electronic circuits.
circuits.
Each
Each preamplifier was
was followed by a 60 Hz notch
notch
filter. The signals
signals from Lower La Gloria were transtransmitted
mitted to
to Upper La Gloria by
by FM
FM telemetry
telemetry via a repeater
peater on
on Willow
Willow Creek
Creek Peak.
Peak. At
At Upper
Upper La
La Gloria
Gloria we
passed each of
of the eight MT
MT signals and two vertical
vertical
components
through a four-pole
four-pole
components of
of magnetic
magnetic field through
band-pass
band-passfilter, digitized the
the signals
signalswith 12-bit
12-bit resoresolution, and
and recorded
recorded the
the data
data on
on a nine-track
nine-track digital
digital
recorder.
recorder. Data were acquired
acquired in
in the
the four
four overlapping
overlapping
bands
bands listed
listed in
in Table 1.
1. Band
Band 4 was
was intended
intended to
to include
clude periods
periods from
from 30 to
to 1000
1000 sec,
set, but
but an
an error
error in
setting
setting the
the high-pass
high-pass filter of the
the telemetry
telemetry preampliat the
the remote
remote site
site resulted
resulted in the
the longest
longest period
period
fier at
being
being 100
100 sec.
sec. The times
times required
required for data
data collection
collection
Table
of filter
filter bands,
bands, total
total recording
recording time
time
Table 1. Summary
Summary of
per band,
digitizer sampling
sampling period,
period, and
and the
the numnumband, digitizer
ber
of points
points per
per fast
fast Fourier
Fourier transform
transform
ber of
(FFT).
(FFT).
Digitizer
No. of
Digitizer
Total
points per
sampling
points
recording
sampling
recording
peri ods (set)
(sec)
FFT
(hours) periods
FFT
time (hours)
Filter
band
band
no.
no.
Filter
band
band
(sec)
(set)
I
2
3
4
o.oz-1
0.02-1
0.33-5
0.33-5
3-100
3-100
30-100
30-100
0.54
0.54
4.22
4.22
10.52
14.9
0.005
0.1I
0.
I
10
10
1024
512
512
256
and
periods are
are also
also listed
listed in Table 1.
and the
the sampling
sampling periods
All data
recorded within a 40 hour
hour period, with
data were recorded
only brief
interruptions to change
change gains,
gains, filter bands,
bands,
brief interruptions
and
and batteries.
batteries.
DATA PROCESSING
The CDC
computer facility of the
the Lawrence
CDC 7600 computer
Berkeley Laboratory,
Laboratory, data
data was
was used
used for data
data processing,
graphed on microfilm, and
and the
the records
records
cessing, graphed
visually
inspected. After data
data rendered
rendered meaningless
meaningless
visually inspected.
by
saturation, or magby equipment
equipment failure, amplifier saturation,
netic
passing vehicles
vehicles were
were renetic interference
interference from passing
remaining data
data were arranged
arranged into segsegjected, the remaining
ments
the number
number of points
points shown
shown in
ments containing
containing the
Table 1.
mean value
value and
and linear trend
trend was
was subsub1. The mean
tracted
each segment.
segment. The ends
ends of the
the segments
segments
tracted from each
were
cosine bell window, and
and the
the
were mUltiplied
multiplied by a cosine
fast
transform was
was computed.
computed. The necessary
necessary
fast Fourier transform
crosspower
and autopower
autopower densities
densities were
were calculated
calculated
crosspower and
by mUltiplying
the Fourier coefficients
coefficients for the
the various
various
multiplying the
fields
and averaging
averaging the
the products
products over all
fields together,
together, and
Repeater Stat 1 on
Bandpass
Filters
Bandpass
FII fers
Voltage Controlled
Preamplifiers
and Filters
Preamplifiers
and Filters
OSCillators
Upper La Gloria
Lower La Glorlo
diagram of data
data acquisition.
FIG. 2. Block diagram
acquisition.
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56
56
Gamble
Gamble et
et al
al
Table 2.
2. Number
Number of
of harmonics
harmonics per
per window,
window, and
and numbers
numbers of
of sets
sets of
of data
data segments
segments for
for each
each station.
station.
Table
Band no.
no. II
Band
Period
Period
(sec)
(xc)
Band no.
no. 22
Band
Band
Band no.
no. 33
Band
Band no.
no. 44
Harmonics
Harmonics
per windows
window
per
Period
Period
(sec)
(set)
Harmonics
Harmonics
per window
window
per
Period
Period
(sec)
(aec)
Harmonics
Harmonics
per
per window
window
Period
Period
(sec)
(XC)
Harmonics
Harmonics
per
per window
window
75
7s
0.325
0.325
52
52
3.3
3.3
52
52
32.0
32.0
13
13
53
53
0.45
0.4s
0.63
0.63
0.88
0.88
I1.2
.2
I1.7
.7
2.4
2.4
3.3
3.4
37
37
27
27
I9
19
I4
14
IO
10
77
4.5
4.5
6.3
6.3
X.8
8.8
12
12
17
17
24
24
34
34
49
49
37
41.1
41.1
60.9
60.9
85.3
85.3
77
55
0.023
0.023
0.032
0.032
0.044
0.044
0.062
0.062
0.085
0.089
0.12
0.12
0.16
0.
I6
0.22
0.22
0.30
0.30
0.41
0.41
0.57
0.57
0.79
0.79
38
38
27
27
19
19
14
I-4
10
IO
I7
55
55
37
27
27
I9
19
14
14
IO
10
77
55
44
9
4
4
33
22
Number
Number of
of sets
sets of
of data
data segments
segments
Gloria
Upper La Gloria
476
476
297
74
74
21
21
Lower La Gloria
Gloria
Lower
381
381
297
297
74
21
21
of the
the data
data segments
segments and
and over the
the Fourier harmonics
harmonics
of
contained in nonoverlapping
nonoverlapping frequency
frequency windows
contained
of Q = 3. The center
center period of each
each window,
window. the
the
of
harmonics in
in each
each window, and
and the
the numnumnumber of harmonics
number
segments are
are given in Table
Table 2.
ber of segments
DATA ANALYSIS
ANALYSIS
DATA
Impedance
Impedance tensors
tensors were
were computed
computed for both
both MT
MT
stationsas
as aa function
function of period
period using
using equations
equations(3) to
to
stations
comparisonthe
the impedance
impedance tensors
tensors were
were also
also
(6). For comparison
computed
computed using
using the
the following three
three methods:
methods:(I)
( I) The
The
impedance
impedancetensor
tensorwas
was found
found that
that minimized the
the mean
mean
squareof IiE
E - ZH-I.
Zil/ This
This method
method is
is referred
referred to
io as
as the
ihe
square
standard
standard analysis
analysis since
since itit is
is the
the method
method that
that is
is most
most
commonly used
used (Vowff,
(Vozoff, 1972).
1972). Impedances
Impedances calcucalcucommonly
lated by
by this
this method
method depend
depend on
on autopowers
autopowers of the
the
lated
magnetic
magnetic fields.
fields. As
As aa result,
result, magnitudes
magnitudesof the
the imimpedance
pedancetensor
tensor elements
elements are
are biased
biaseddownward
downward by
by the
the
noise
noise power
power in
in the
the magnetic
magnetic channels.
channels. (2)
(2) Z
Z was
was
computed
computed from
from the
the inverse
inverse of
of the
the admittance
admittance tensor
tensor
Y, where
where YY was
was chosen
chosento
to minimize
minimize the
the mean
mean square
square
y,
of
H -- YE
of IIH
YEI.I. This
This calculation
calculation is
is referred
referred to
to as
as the
the
admittance
admittance method
method which
which biases
biasesthe
the magnitudes
magnitudesof
of
the
the impedance
impedance tensor
tensor elements
elements upward
upward by
by the
the noise
noise
power in
in the
the electric
electric fields
fields (Sims
(Sims et
et al.
al. 1971).
1971). (3)
(3) ZZ
power
was computed
computed ir.
in terms
terms of
of crosspowers
crosspow’ersof
of the
the four
four
was
fields
fields measured
measuredat
at each
each station.
station. As
As we
we have
have shown
shown
(Goubau
(Goubauet
et ai,
al, 1978),
1978). there
there isis sufficient
sufficient information
information
in
in the
the crosspower
crosspowerdata
data to
to enable
enable one
one to
to obtain
obtain estiestimates
matesof
of ZZ that
that are
are not
not biased
biasedby
by the
the noise
noisepower
power in
in
any of
of the
the channels.
channels. We
We refer
refer to
to this
this analysis
analysisas
asthe
the
any
crosspower
crosspowermethod.
method.
For each
each method
method of
of analysis
analysis the
the coordinate
coordinate axes
axes
were
IZ,rYI"tt lZ,,12,
IZy.r1 2 , thereby
thereby
were rotated
rotated to maximize lZ,,l’
aligning
of the axes
axes parallel to the
the strike
strike direction,
aligning one of
if
if such
such a direction
direction existed.
existed. Then
Then the
the off-diagonal elements,
PIY and
and puX,
PW" of
of the rotated
rotated apparent
apparent resistivity
resistivity
ments, psz,
matrix
matrix were computed
computed from the
the expr-essions
expressions
psi, = 0.2 IZ,,l’T.
(7)
&/* = 0.2 IZ,,iZ7’.
(8)
and
and
is the
the period
period in
in secsecare in
in nm,
Rm, T is
where P.ry
ps,, and
and PYX
pus are
where
onds, andZ~y
and Z>, andZ~J'
and ZY, are
are in
in units
units or
of(mVjkmj
y-r.
onds,
(mV/km) y-'.
For the
the standard
standard and
and remote
remote reference
reference analyses,
analyses, the
the
For
and the
the skewnesses
skcwnessesIl(Z,,.
phasesof Z.ry
Z,, and
and ZY.1'
Z,, and
phases
(Z.rJ' +
Z,.,)) I also
also were
were calculated.
calculated.
Zyu!
/I (Zy,r
Z!J?J
(Z&l, - ZJ'Y)
obtain an
an estimate
estimate of the
the noise
noise in
in our
our data,
data, we
we
To obtain
computed the
the coherency
coherency between
between the
the measured
measuredeleceleccomputed
tric field
field E
E and
and the
the electric
electric field
field E"
E,, predicted
predicted from
from
tric
E,, =
= ZH,
ZH, where
where Z was
was obtained
obtained from
from the
the standard
standard
E"
analysis.
The coherencies
coherenciesare
are defined
defined by
by C;
Cj == E;E;t
m
The
analysis.
__~
where i=x,y.
i =x,
For the
the standard
standard
(iEYIE;pIZ)-1!2,
For
(JE,IzIE,012)-1’2, where
analysis one
one can
can show
show that
that E;E;~,
E,E,y, == IE;,,12,
IE~,,I~, so
so that
that
analysis
cj = ()/12/IEi12)1/2
(i = x,u).
(9)
(9)
GRAPHICAL COMPARISON
COMPARISON OF
OF APPARENT
APPARENT
GRAPHICAL
RESISTIVITIES
RESISTIVITIES
The results
resultsfor
for Upper
Upper La
La Gloria
Gloria are
at-csummarized
summarizedin
in
The
Figures33 to
to 9.
9. and
andfor
for Lower
Lower La
La Gloria
Gloria in
in Figures
Figures 10
10
Figures
to 16.
16.Figures
Figures33 through
through66 show
showthe
the apparent
apparentresistiviresistivito
ties as
as aa function
function of
of period
period for
for the
the standard,
standard,admitadmitties
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57
Magnetotellurics
Magnetotellurics
I
I
I
I
I
I
I
I
lOO(I1000
,,
-------
E
F
,
.s100IOC>~
-pyx
---------
'Yx
2>..->>
;.‘If)
z
If)
(l,)
LL
0::
c
c:
0)
(l,)
....
o&
a
a.
a.
I( I10
2
<!
I
I __~~
I __~I __~~L_
I~~--~
_ _L
I
I _ _ L_ _~
I _ _~~r
I
J
0.1
I
0.1
10
100
IO
IIDC1
:‘;
i 31
0.01
Period
(s)
Period
(5)
FIG. 3. Standard
Standard method
method apparent
apparent resistivities
resistivities versus
versus period,
period, Upper La Gloria. Remote
crencc results
FIG.
Remote rel’
reference
results arc
are
indicated by
by dashed
dashed lines.
lines.
indicated
I
I
I
I
I
I
I
I
I
I
I
I
E,
q 1000
P..xy- ____ --
>
I f)
If)
(l,)
-
0::
c
....
(l,)
o
a.
a.
<!
IOI
0.01
I
I
I
0.1
I
I
I
I
I
I
IO
I
I
100
Period
Period (s)
(5)
FIG.
FIG. 4.
4. Admittance
Admittance method
method apparent
apparent resistivities
resistivities versus
versus period,
period, Upper
Upper La
La Gloria.
Gloria. Remote
Remote relkrcnce
reference results
results are
are
indicated
indicated by dashed
dashed lines.
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Gamble et al
58
I-IO, ooc
E
~
I
I
I
I
I
I
I
I
I
I
1000)-
>
Vl
Vl
<lJ
cr
C
<lJ
....
100I-
o
a.
a.
<[
----IC)-
10L-~
____
L-~
__~__- L_ _~_ _L-__~~__~____L-~
0.1
0.01
100
10
I
Period (s)
(s)
FIG. 5. Crosspower
Crosspower method
method apparent
apparentresistivities
resistivities versus
versusperiod, Upper La Gloria. Remote
FIG.
Remote reference
reference results
results are
are
indicated by dashed
dashed lines.
lines.
indicated
EIOOO
I
c:
..,..
>-
~y
-
Pyx
>
Vl
In
QI
a:: 10
c:
QI
d
Q.
Q.
ct
101
10
0.01
0.01
I
I
I
0.1
I
I
I
I
I
I
10
IO
I
I
100
too
Period
Period (5)
(s)
FIG. 6. Remote
Remote reference
reference method
method apparent
apparent resistivities
resistivities versus
FIG.
versus period, Upper La Gloria.
Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/
59
Magnetotellurics
Magnetotellurics
Z;0.8
20.8
cc
Q)
...Q)Q)
ii
.g
2 0.6
u
t::.
X axis
- o
0 Y axis
axis
0.4
0.01
0.1
I
IO
100
Period
Period (5)
(s)
FIG. 7. Coherency
Coherency between
between the
the measured
measuredelectric
electric field and
and the
the electric
electric field
field predicted
predicted by
by the
the standard
standardmethod
method
of analysis.
analysis, Upper La Gloria.
tance,
tance, crosspower,
crosspower, and
and remote
remote reference
reference methods
methods at
at
the
the Upper
Upper La Gloria station.
station.’l The
The apparent
apparentresistivities
resistivities
from
from the
the remote
remote reference
reference method
method are
are repeated
repeated as
as
dashed
dashedlines
lines on
on Figures
Figures 3 to
to 5 to
to facilitate
facilitate comparison
comparison
with the
the other
other methods.
methods. The coherencies
coherencies C
C,x and
and
C,yare
are plotted
plotted in Figure
Figure 7.
C
Comparing Figures
Figures 3 and
and 4, we see
see that
that both
both the
the
Comparing
standard and
and admittance
admittance methods
methods yield resistivities
resistivities
standard
that vary
vary smoothly
smoothly over wide
wide ranges
rangesof periods.
periods. Howthat
both methods
methods yield discontinuities
discontinuitiesin
in PXY
pzu where
where
ever, both
bands overlap
overlap at
at periods
periods of 3 and
and 30 sec.
sec. These
These disdisbands
continuities will be
be discussed
discussed later,
later, and
and it will be
be
continuities
shown that
that they
they are
are not
not caused
caused by
by systematic
systematic errors
errors
shown
in data
data processing.
processing. The standard
standardanalysis
analysis also
also shows
shows
in
a large
large dip in plr
PYX at
at 0.03 set
sec that
that does
does not
not appear
appear in
the
the admittance
admittance results,
results, and
and is
is not
not associated
associated with any
any
anomaly
C Y (Figure
(Figure 7).
7). This dip is
is believed to be
be
anomaly in C,
caused
caused by the
the magnetic
magnetic noise
noise from the
the generator
generator at
at
the
the Upper La Gloria station.
station.
Although
Although the
the apparent
apparent resistivity
resistivity curves
curves from the
the
standard
standard and
and admittance
admittance methods
methods are
are fairly smooth,
smooth,
there
there are
are significant
significant systematic
systematic discrepancies.
discrepancies. The
resistivities
resistivities from the
the admittance
admittance analysis
analysis are
are higher
higher
than
cases exthan those
those from the
the standard
standard analysis
analysis in all cases
cept
cept four
four on
on the
the y-axis near
near 40 set
sec period.
period. By comparing
paring Figures
Figures 3 and
and 4 with Figure
Figure 7 one
one sees
sees that
that
the
the discrepancies
discrepancies generally
generally increase
increase as
as the
the coherency
coherency
Ci
C j decreases.
decreases. The best
best agreement
agreement between
between the
the two
methods
is for periods
periods shorter
shorter than
than 2 sec.
sec. For periods
periods
methods is
‘lThe
The windows at 0.023
0.023 set
sec and
and 0.325
0.325 set
sec contain
contain harmonics
harmonics
outside
the filters,
filters. and
and ordinarily would not
not
outside the
the band-pass
band-pass of the
be
we plotted
plotted the
the apparent
apparent resistivities
resistivities from
be used.
used. How*ever,
However, we
the
the 0.023
0.023 set
sec window to demonstrate
demonstrate the
the narrow band
band nature
nature
of the
the noise
noise in the
the 0.032
0.032 set
sec window. The apparent
apparent resistiviresistivities
ties from the
the 0.325
0.325 set
sec window were used
used only to interpolate
interpolate
a value of
of the
the resistivity to
to be
be compared
compared with the
the result
result at
0.41 set
sec from band
band I.I.
shorter
shorter than
than 3 sec,
set, CoX
C, is
is greater
greater than
than 0.9, and
and most
most
values
values of PXy
psarin
in Figure
Figure 4 are
are about
about 10
IO percent
percent higher
higher
than
than those
those in Figure
Figure 3, although
although the
the disagreement
disagreement
at 3 XC
scc period.
period. For C
does
to a factor
factor of 2 at
does increase
increase to
between
and 0.6, the
the disagreement
disagreement is
is usually
usually
between 0.9 and
of two (for example,
example, py3
PYX between
between 0.06
about
about a factor
factor of
and
periods), but
but can
can be
be much
much larger
larger (for exand 1 sec
set periods),
ample
at 0.032 and
and 9 set
sec periods).
periods). The systematic
systematic
ample PYX
pus at
differences
are attributed
attributed to
to the
the bias
bias errors
errors mentioned
mentioned
differences are
earlier.
earlier.
The apparent
resistivities from
from the
the crosspower
crosspower
apparent resistivities
method
are far more
more irregular
irregular than
than those
those
method (Figure 5) are
from
admittance (Figure
(Figure 4) or standard
standard (Figure
(Figure 3)
from the
the admittance
the crosspower
crosspower analyanalymethods.
random errors
errors of the
methods. The random
sis depend
depend in a complex
complex way on the
the value
value of
of the
the impedsis
of the
the measurement
measurement axes,
axes,
ance tensor,
tensor, the
the orientation
orientation of
ance
and the
the relative levels
levels of
of the
the noises.
noises. However, we
and
believe that
that the
the random
random errors
errors are
are relatively large
large pribelieve
because this
this estimate
estimate of the
the impedance
impedance tensor
tensor
marily because
depends strongly
strongly on
on the
the crosspowcrs
cross powers between
between fields
fields
depends
that may be only slightly coherent,
coherent, such
such as
as E,E,*
ExE:
that
(Goubau et al,
aI, 1978). The best
best results
results from this
this
(Goubau
PXy at
at periods
periods shorter
shorter than
than 1 set,
sec, where
method are
are for plu
method
C
is greater
greater than
than 0.9.
0.9. Here, the
the reAistivities
resistivities from the
the
C,x is
crosspower method
method are
are still scattered
scattered over the
the 10
10 percrosspower
cent range
range of the
the disagreement
disagreement between
between the
the standard
standard
cent
and admittance
admittance resistivities.
resistivities. Note that
that no value of
of apand
parent resistivity
resistivity has
has been
been plotted at
at 0.032 set
sec period
period
parent
is because
because
the crosspower
crosspower method
method (Figure 5). This is
for the
this method
method did not predict
predict real values
values for the autoautothis
powers. Thus, there
there is some
some significant
significant noise
noise in this
this
powers.
though C,
C y is
is higher than
than in the
the adjacent
adjacent
window even though
windows (Figure 7).
windows
Because of
of the large
large random
random errors
errors in the crosscrossBecause
analysis and
and the bias
bias errors
errors in the
the two leastleastpower analysis
squares analyses,
analyses, these
these methods
methods cannot
cannot be used
used to
squares
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Gamble et al
Gamble
60
180
180
150
I
I
I
I
I
I
I
I
I
I
I
1
Phose of Zyx
~O--"""">--C:L
120
90
60
<II
Q)
Q)
'0Q)
30
0
~
Q)
-30
Phase of Zxy
0-
c:
c::[
-60
-9
0.6
r=“-c
Skewness
0.3
0
0.01
0.1
I
10
100
Period
Period (s)
(sl
FIG. 8. Orientation angle
angle 8",
rotated x-axis and
and magnetic
magnetic north, skewness,
skewness, and phase
phase angles
angles versus
versus
es between rotated
period, standard
standard method, Upper La Gloria.
those from the standard
method are
are smaller
obtain
obtain reliable estimates
estimates of the
the apparent
apparent resistivity
resistivity larger, and
and those
standardmethod
Cij are
are less
less than
than 0.9. If
If all resistivities
resistivities for than
when the C
than those
those from the
the remote
remote reference
reference method.
method. This
which C
Cij is
is below 0.9 sec
set were rejected,
rejected, only 11
11 regular
regular ordering
ordering of
of the apparent
apparent resistivities
resistivities demonretained, all at periods
periods longer
longer strates
stratesthat the
the bias
bias error in at
at least
least two of
values
p"", would be retained,
of the
the methods
methods
values for par*
is large
large compared
compared to the random
than
is
random error in any
any of
of them
than 0.5 sec.
sec.
In Figure
Figure 6 the
the apparent
apparent resistivities
resistivities from the
the reis due
due to the use
use
and
that the bias
bias is
and it strongly
strongly suggests
suggeststhat
reference method
method lie on smoother
smoother curves
curves than
than of autopower
mote reference
estimates in the
the least-squares
least-squares methods.
methods.
autopower estimates
those
thosefrom any
any of the previous
previousmethods.
methods. Furthermore,
Furthermore,
The apparent
resistivities at Lower La Gloria from
apparent resistivities
the
the discontinuities
discontinuities and
and disagreements
disagreements where
where bands
bands the
the standard,
standard, admittance,
admittance, crosspower,
crosspower, and
and remote
remote
overlap in Figures
Figures 3 arid
and 4 have
have essentially
essentially been
been elimreference methods
shown in Figures
reference
methods are
are shown
Figures 10 to 13, and
and
inated, suggesting
suggestingthat
that the
the disagreements
disagreementswere caused
caused the
predicted coherencies
coherencies C,
inated,
C", and
and C,
C II
the electric field predicted
by bias
bias errors.
errors. In the
the next
next section,
section, we compare
compare quanquan- are
are shown
shown in Figure
Figure 14. Again, the
the dashed
dashed lines
lines in
titatively the
the results
results from
from different bands
bands where
where the
the Figures
Figures 10
10 to
to 12
12 reproduce
reproduce the remote
remote reference
reference apapbands
bands overlap.
overlap. At periods
periods where
where the
the C
CIj are
are high, the
the parent
parent resistivities
resistivities from Figure 13.
13. At Lower La
remote
remote reference
reference usually
usually agrees
agreeswell with the
the standard
standard Gloria there
there was
was more
more noise
noise than
than at the upper
upper station.
station.
C, and
and CII
C, are
are never
never both
both above
above 0.9. C'"
C, and
and CII
C, are
are
and admittance
admittance methods.
methods. For P"'II
pzN between
between 0.032 and
and C",
and
both
both below 0.5 for periods
periods between
between 5 and
and 10
10 sec.
sec. At
2 sec,
set, the
the apparent
apparentresistivities
resistivities obtained
obtained using
using the
the remote
mote reference
reference lie about
about half-way between,
between, and
and are
are all periods,
periods, the apparent
apparent resistivities
resistivities from the
the admitwithin about
about 5 percent
percent of those
those obtained
obtained with the
the tance
tance method
method (Figure 11)
11) are
are higher
higher than
than the
the correcorresponding
standard
sponding apparent
apparent resistivities
resistivities from the
the standard
standard
standard and
and admittance
admittance methods.
methods.
We produced
produced 64 apparent
apparent resistivities
resistivities from each
each analysis
analysis(Figure 10). Thus, as
as at Upper La Gloria, the
the
method
method of analysis
analysisat Upper La Gloria. In 60 cases
casesthe
the bias
bias errors
errors of the least-squares
least-squaresmethods
methods are
are large comapparent
apparentresistivities
resistivities from
from the
the admittance
admittance method
method are
are pared
pared to
to the
the random
random errors.
errors. When C
CIj is
is lowest, the
the
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Magnetotellurics
Magnetotellurics
relative
relative bias
bias is
is largest.
largest. At a period
period of 9 sec
set the
the relative
relative
bias
bias is
is about
about a factor
factor of 20 for PYX'
pys, and
and about
about a factor
factor
of 100
100 for PXy'
psi/. The peaks
peaks and
and dips
dips in
in the
the apparent
apparent
resisti
vity curves
resistivity
curvesin
in Figures
Figures 10
IO and
and II
11are
are also
also so
so steep
steep
that
that neither
neither least-squares
least-squaresmethod
method accurately
accurately estimates
estimates
the
the apparent
apparent resistivity
resistivity of the
the ground.
ground.
The apparent
apparentresistivities
resistivitiesfrom
from the
the crosspower
crosspoweranalanalysis
ysis at
at Lower La Gloria (Figure
(Figure 12)
12) seem
seem to
to be
be more
more
stable
stable than
than they
they were at
at Upper La Gloria (Figure 5).
For periods
power method
periods shorter
shorterthan
than 20 sec
set the
the cross
crosspower
method
yields
yields apparent
apparent resistivities
resistivities that
that lie between
between the
the two
least-squares
least-squaresresistivities
resistivitiesin
in 50 of 54 cases.
cases.This result
result
indicates
power
indicates that
that the
the random
random errors
errors for the
the cross
crosspower
method
method are
are small
small in
in this
this case
case compared
compared to
to the
the bias
bias
errors
errors of the
the least-squares
least-squaresmethods,
methods, and
and is
is further
further evidence
to power bias
dence that
that the
the au
autopower
bias is
is the
the major
major source
source of
error.
error. At periods
periods between
between 3 and
and 20 sec,
set, the
the crosscrosspower
power analysis
analysis yields
yields dips
dips in
in the
the apparent
apparent resistivity
resistivity
similar to
to those
those of the
the standard
standard analysis,
analysis, but
but about
about
a factor
factor of five smaller.
smaller. Such
Such dips
dips are
are believed to
to be
be
caused
caused by
by correlations
correlations in
in the
the noises,
noises, which bias
bias the
the
estimates
estimates of the
the apparent
apparent resistivity.
resistivity.
180
18C I-
I
I
I
I
61
Table 3. Percent
Percent disagreement in apparent
Table
apparent resistivities
between bands.
Remote
Remote
reference
reference
Bands
Bands
1,2
1.8
4.5
6.3
2,3
3,4
No.
No. of values
values
compared
compared
Standard
Standard
I2
12
4
8
5.9
5.9
41.5
I I.5
11.5
contrast with the
In contrast
the other
other methods,
methods. the
the remote
remote
reference
yields apparent
apparent resistivities
resistivities (Figure
(Figure
reference method
method yields
13) that
that vary
vary smoothly
smoothly over the
13)
the entire
entire range
range of peis low. There
There is
is
riods,
the coherency
coherency is
riods, even
even where
where the
almost
between overlapping
overlapping bands.
bands.
almost no
no disagreement
disagreement between
At periods
than 1
I set,
sec. the
the remote
remote reference
reference
periods shorter
shorter than
apparent resistivities
resistivities agree
apparent
agree with the
the results
results from the
the
crosspower
the random
random scatter
scatter of the
the
crosspowermethod
method to within the
percent). The resistivities
resistivities
crosspower
crosspower results
results (±
(* 10
10 percent).
from the
method are
are biased
biased downward by
by
the standard
standard method
about 10
10 percent
percent near
about
near 1
I set
sec period,
period. and
and by
by more
more than
than
factor of 2 at
at the
the shortest
shortest periods
periods.
a factor
I
I
I
I
150
15C)- - Phose
Phase of Zyx
Zyx
120
I20
I-
90
ex
60
60
(fJ
Q)
Q)
CJ1
Q)
30
0
E
Q)
-30
Phose of Zxy
CJ1
c:
<r
-60
-90
0.6
0.6
Skewness
Skewness
0.3
0.3
0
0.01
L
I
Period (s)
Period
10
100
FIG.
skewness. and
and phase
phase angles
angles versus
versus
FIG. 9. Orientation
Orientation angle
angle Ox
OS between
between rotated
rotated x-axis and
and magnetic
magnetic north.
north, skewness,
period, remote
remote reference
reference method,
method, Upper La Gloria.
period,
Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/
62
Gamble
Gamble et
et al
al
IOl
------
~---~-~'~,~-~~~~~~~~~~
E
d
10
;:..,
>
+II>
II>
Q)
cr:
+-
Pyx
c
Q)
....
/
-----
l-
0
a..
a..
<l:
I __~__L -_ _ _L
I____~
O.I~~
_ _~_ _~_ _~_ _~_ _- L_ _ _ _L-~
0.1
0.1
0.01
Period
Period
100
100
IO
10
I
(~1
(5)
FIG. 10.
method apparent
apparent resistivities
resistivities versus
versus period, Lower La Gloria. Remote
Remote reference
reference results
results are
are
FIG.
10. Standard
Standard method
indicated
by dashed
dashed lines.
lines.
indicated by
100
E
I
.5
;:..,
+.:;
II>
10'
II>
Q)
cr:
c
Q)
....
0
a..
a..
<l:
I
lo.01
I
I
0.1
I
I
I
I
I
I
I
IO
I
I
100
Period (5)
(s)
Period
FIG.
FIG. II.
II
Admittance
Admittancemethod
methodapparent
apparentresistivities
resistivitiesversus
versusperiod,
period, Lower
Lower La
La Gloria.
Gloria. Remote
Remotereference
referenceresults
resultsare
are
indicatedby
by dashed
dashedlines.
lines.
indicated
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63
Magnetotellurics
Magnetotellurics
100,--~---,---,--'----r--,--,----'-~--'----r--'
E
10
S
->.
Pyx
>
/
I f)
If)
Cl>
n:::
c::
1-
Cl>
>0
0.
0.
<[
O.I~~____~~__~____I _ _~_ _~_ _~_ _~I__~____~~
0.01
0.1I
0.
I
IO
10
100
100
Period (5)
(s)
Period
FIG.
12.
Crosspower method
method apparent
apparent resistivities
resistivities versus
versus period,
period, Lower La Gloria. Remote
Remote rel’
rderence
results are
are
12. Crosspower
erence results
indicated
dashed lines.
indicated by dashed
100
E
~
Px y
>-
>
10
I f)
If)
Cl>
n:::
Pyx
c
...
Cl>
0
a.
a.
<[
1
0,01
0.1
100
Period (5)
(s)
Period
FIG.
FIG.
13. Remote
Remote reference
reference method
method apparent
apparent resistivities
resistivities versus
versus period,
period, Lower La Gloria.
Gloria
13.
Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/
Gamble et
et al
al
Gamble
64
64
0.8 0.8
>-
u
0.6
c
Q)
~
~ 0.4
o
u
0.2
I
I
I
J
I
I
I
I
I
01 ~~--~--~--~--~--~--~--~--~~----~~
100
IO
0.01
0.1
10
100
I
0.1
0.01
o
Period (s)
(s)
Period
FIG. 14.
14. Coherency
Coherency between
between the
the measured
measured electric
electric field and
and the
the electric field predicted
predicted by the
the standard
standard method
method
FIG.
analysis, Lower La Gloria.
of analysis,
180
180,
I
I
I
I
I
I
I
I
I
1
150
120
Phose of Zyx
90
90
-11'>
Q)
z
Q)
:
'"O'l
D
Q)
a,
:s
s
60
60
30
30
0
(l)
-O'l -30
c
<!
-60
-90
0.6
0.3
0
0.01
Skewness
0.1
I
10
100
Period
Period (s)
(s)
FIG. 15.
15. Orientation
Orientationangle
angleO,r
0, between
betweenrotated
rotatedx-axis
x-axis and
and magnetic
magneticnorth,
north, skewness,
skewness,and
and phase
phaseangles
anglesversus
versus
FIG.
period, standard
standardmethod,
method. Lower
Lower La
La Gloria.
Gloria.
period,
Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/
65
65
Magnetotellurics
Magnetotellurics
QUANTITATIVE EVALUATION
EVALUATION OF
OF APPARENT
APPARENT
QUANTITATIVE
RESISTIVITIES OBTAINED
OBTAINED USING
USING REMOTE
REMOTE
RESISTIVITIES
REFERENCE
REFERENCE
this section
section we present
present a more quantitative
quantitative analIn this
ysis of
ofthe
expected errors
errors associated
associated with the
the apparent
apparent
ysis
the expected
resistivities obtained
obtained using
using the
the remote
remote reference
reference tcchtechresistivities
is computed
computed for the
the
nique. An average
average disagreement
disagreement is
nique.
apparent resistivities
resistivities at periods
periods where bands
bands overlap,
apparent
of the rms
rms random
random fluctuations
fluctuations is
is oband a measure
measure of
and
tained for the
the resistivities
resistivities within a single
single band.
band.
tained
there are
are three
three
both Upper and
and Lower La Gloria there
At both
of psv
PJ'Y and
and three
three values
values of
of pus
PYJ' in band
band II at
at
values of
values
periods that
that are
are also
also contained
contained in band
band 2. These
These resisresisperiods
are compared
compared with the
the linear interpolation
interpolation of
tivities are
the values
values of
of apparent
apparent resistivity
resistivity in band
band 2. The fracthe
tional discrepancy
discrepancy between
between the
the overlapping
overlapping resistivresistivitional
is computed,
computed, and
and the
the magnitude
magnitude of
of this
this discrepdiscrepties is
ties
ancy is
is averaged
averaged over each
each of the
the three
three periods,
periods, for
ancy
"mean
both axes
axes and
and for both
both stations.
stations, to produce
produce the
the “mean
both
discrepancy" for the
the I2
12 resistivities
resistivities in the
the region
region of
of
discrepancy”
band overlap.
overlap. In the
the same
same way, the
the mean
mean discrepancy
discrepancy
band
is calculated
calculated between
between the
the overlaps
overlaps of bands
bands 2 and
and 3,
is
180
180
150
150120
120-
I
I
I
and bands
bands 3 and 4.
4. The mean
mean discrepancies
discrepancies (percent
(percent
and
disagreements) and the
the number
number of
of resistivity
resistivity values
values
disagreements)
compared to
to obtain
obtain each
each mean
mean discrepancy
discrl'pancy are
are shown
shown
compared
in Table 3 for both
both the
the standard
standard and
and t-emote
remote reference
reference
analyses.
analyses.
mcan discrepancies
discrepancies for the
the remote
remote reference
rcference
The mean
method are
are consistently
consistently smaller than
than those
those for the
the
method
standard analysis.
analysis. The smallest
smallest dt\crepancy
di,crepancy is 1.X
1.8
standard
percent between
between bands
bands 1 and 2.
2. Thi?
This discrepancy
discrepancy is
percent
somewhat smaller than
than the -C2
±2 percent
perL'l'nt uncertainty
uncertainty in
somewhat
apparent resistivity
resistivity that we expect
expect because
because of a i± I1
apparent
gaim. Between
Between bands
bands
percent uncertainty
uncertainty in amplifier gain\.
percent
and 3 and
and bands
bands 3 and
and 4, the
the mean
mean discrepancies
discrepancies arc
are
2 and
of the
the random
random
larger, but they
they are
are still on the
the order
order of
larger,
hy comparing
comparing apscatter seen
seen within a single
single band
band I>)
scatter
parent resixtivities
resistivities at adjacent
adjacent period\.
period,. Because
Because of
of the
parent
good agreement
agreement where the bands
bands o\
()\ erlap,
crlap, errors
errors due
due
good
of the
the Fourier transform
transform are
are bespectral resolution
resolution of
to spectral
lieved to bc
be negligible. As shown
shown in Table I,I, in
band 2 the
the segments
segments are
are IO
10 times
times lollgcr
IOllger than
than those
those in
band
band 1.
Thus, the
the spectral
spectral resolution
resolutioll of the
the harmonics
harmonics
band
I. Thus,
in band
band 2 is
is ten
ten times
times higher
higher than
than the
the resolution
resolution in
in
I
I
I
I
I
I
~
Phase
of
Phose
of Zyx
Zyx
90
go60
60;;
‘(j'j
Q)
a,
Q)
\"
z
ry
0
Q)
a,
:s
E
Q)
a,
-try
30
30-
-30
-30 -
c:
<l:
:
-
0OPhase of Zxy
Zxy
Phose
cr-
-60
-6O- -90
-9oI
0.6
0.60.3
0
0.01
0.1
I
10
100
Period
Period (s)
(s)
FIG. 16.
16. Orientation
Orientation angle
angle 8Bs
between rotated
rotated x-axis
x-axis and
and magnetic
magnetic north,
north, skewness,
skewness. and
and phase
phase angles
angles versus
versus
FIG.
J • between
period,
period, remote
remote reference
reference method,
method, Lower La Gloria.
Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/
Gamble
Gamble et
et al
al
66
66
Table 4.
4. Arrangement
Arrangement of
of data
data from
from bands
bands 11 and
and 22 into
into blocks
blocks to
to estimate
estimate the
the standard
standard deviation
deviation of
of the
the apparent
apparent
Table
resistivity at
at each
each period.
period. Date
Date refers
refers to
to September
September 1977.
1977.
resistivity
Band
Band II
Band
Band 22
Data
Data blocks
blocks
Recording
Recording time
time
PST
PST
I11:55
I:55 AM-l2:OO
AM-12:00 PM
PM
12:Ol
12:01 PM-12:06
PM-12:06 PM
PM
7:30
PM- 7135
7:35 PM
PM
7:30 PM7:36
PM- 7:41
7:41 PM
PM
7:36 PMI:20
1:20 PMPM- I:25
1:25 PM
PM
I:25
1:25 PMPM- I:30
1:30 PM
PM
I:30
1:30 PMPM- I:35
1:35 PM
PM
I:35
1:35 PMPM- I:40
1:40 PM
PM
I:40
PM- I:45
1:45 PM
PM
1:40 PMI:45
1:45 PMPM- I:50
1:50 PM
PM
Date
Date
14
I4
14
I4
14
14
I4
14
I5
15
15
I5
15
I5
15
I5
15
I5
15
I5
Upper
Upper
La
La Gloria
Gloria
Lower
Lower
La
La Gloria
Gloria
2
3
44
55
II
2
:3
44
55
II
Omitted
Omitted
Omitted
Omitted
33
44
I
:2
33
44
I
:2
Data
Data blocks
blocks
Lower
Lower
La
La
La Gloria
Gloria
La Gloria
Gloria
upper
Upper
Recording
Recording time
time
Date
Date
9:25
9:25 AMAM- 9:50
9:50 AM
AM
9:55
IO:42AM
9:55 AMAM-10:42
AM
I I :27
IO:43
10:43 AMAM-II
:27 AM
AM
I4
14
14
14
I4
14
I4
14
I4
14
I5
15
I5
15
I5
15
6:20
PM- 6:57
6:57 PM
PM
6:20 PM7:00
7:00 PMPM- 7:32
7:32 PM
PM
IO:50
I:37 AM
10:50 AM-I
AM-II:37
AM
111:38
I:38 AM12:25 PM
AM-12:25
PM
l2:36
12:36 PMPM- I:13
1:13 PM
PM
I
22
33
.I...
72
II
33
4...
II
22
33
44
i2
I
:3
44
-
band
band 1,
I. and the
the spectral
spectral overlap from narrow
narrow peaks
peaks in
in
the autopower
autopower spectra
spectra of
of the various
various fields
fields is ten
times smaller.
smaller.
The rms errors
errors associated
associated with apparent
apparent resistiviresistivities
Figures
ties within a single
single band
band are
are now estimated.
estimated. In Figures
6 and
and 13
13 (remote reference
reference analysis),
analysis), there
there is
is no
visible scatter
scatter between
between resistivities
resistivities at
at adjacent
adjacent periods
periods
for periods
periods shorter
shorter than
than 3 set
sec (i.e..
(i.e., bands
bands 1 and
and 2). To
estimate
estimate the
the random
random errors
errors in
in this
this range,
range, we recomrecomputed
puted apparent
apparent resistivities
resistivities for each
each period.
period, using
using a
smaller
data segments
segments in the
the determination
determination
smaller number
number of data
of the
the average
average crosspower
crosspower densities.
densities. The original
original data
data
segmentswere sorted
sorted into
into N smaller
smaller blocks,
blocks, thereby
thereby
segments
obtaining N completely
completely independent
independentestimates
estimatesfor the
the
obtaining
apparent resistivity
resistivity at
at each
each period.
period. We computed
computed the
the
apparent
average of the
the N values,
values, pj(j
pj(j = x)',
,v, yx), and
and the
the exaverage
pected deviation
deviation of the
the mean,
mean, defined
defined by
by (Bendat
(Bendat and
and
pected
Piersol, 1971)
1971)
Piersol,
fractional
fractional deviation
deviation of
of both
both cXl,
PXY and
and pus
PYX isis always
always
less
less than
than 5 percent
percent and, for 87 percent
percent of
of the
the data,
data,
is
is 2 percent
percent or less.
less. The average
average of
of aj/pj
uj pj over all
entries
.3 percent.
is I1.3
percent. For
For comparison,
comparison,
entries in Table 5 is
when we performed the same
analy~is on the
the apparent
apparent
same analysis
resistivities
resistivities calculated
calculated by the standard
standard analysis,
analysis, the
average
average of
of the fractional
fractional standard
standard deviation
dcviation was 3.3
percent.
percent. At periods
periods less
less than
than 3 XC.
sec, the expected
expected
deviations
deviations are
are much
much smaller
smaller than
than the
the discrepancies
discrepancies
caused
caused by bias
bias (typically 20 percent)
percent) that
that one
one observes
serves when comparing
comparing these
these results
results with those
those obtained
tained using
using the remote
remote reference
reference analysis.
analysis.
ORIENTATION
ORIENTA
TlON ANGLES, PHASES,
PHASES,
AND
AND SKEWNESSES
SKEWNESSES
Graphs of the
other parameters
parameters that
Graphs
the other
that may
may be
be used
used
modeling the
the resistivity
resistivity of the
the carth
earth are
are now
now examexamin modeling
ined. For Upper La Gloria, Figures
Figures 8 and
and 9 show
show the
the
ined.
orientation angles
angles Ox
Bs between
between the
the rotated
rotated x-axes
x-axes
orientation
- N
] 112
(10) and
and magnetic
magnetic north,
north, the
the phases
phasesof ZJ'Y
Z,., and
and ZyX'
Z,,. and
and
O'j =
(Pii - 7iY / N(N - 1)
the skewness
skewnessas
as aa function
function of period
period for
for the
the standard
standard
the
and remote
remote reference
reference analyses.
analyses. A right-handed
right-handedcoorcoorFor band
band I1 at
at Upper
Upper La Gloria
Gloria N = 5 blocks
blocks were
were and
For
dinate system
system is
is used
used with the
the z-axis
z-axis pointing
pointing down,
down,
used, while for
for band
band I at
at Lower La
La Gloria
Gloria and
and for
for dinate
used,
and the
the complex
complex phase
phase i~
is --ior.
The corresponding
corresponding
band 22 at
at both
both stations
stationsN
N = 44 blocks
blocks were
were used.
used. In
In and
iwt. The
band
resultsfor
for Lower La Gloria
Gloria are
are shown
shown in
in Figures
Figures 15
I5
an attempt
attempt to
to include
include signals
signalsof
of various
variouspolarizations
polarizations results
an
and 16.
16. From
From Figures
Figures88 and
and 99 we
we see
seethat
that at
at Upper
Upper La
La
in each
each of
of the
the N
N blocks
blocks of
of data
data segments,
segments, roughly
roughly and
in
Gloria both
both methods
methodsof analysis
analysis give
give physically
physically reareaequalnumbers
numbersof
of records
recordswere
were selected
selectedfor
for each
eachblock
block Gloria
equal
sonablevalues
values for
for the
the orientation
orientation angle,
angle, phases,
phases,and
and
from two
two different
different recording
recording times
times that
that were
were widely
widely sonable
from
skewness.There
There is
is aa maximum
maximum scatter
scatterof
of about
about ±
? 10
10
separated. Table
Table 44 summarizes
summarizesthe
the recording
recording times
times skewness.
separated.
degreesin
in the
the phases
phasesand
and ±5
+5 degrees
degreesin
in the
the orientaorientaand the
the number
number of
of the
the block
block to
to which
which the
the data
data segseg- degrees
and
mentswere
were assigned.
assigned.There
There are
areno
noentries
entriesfor
for the
the first
first tion
tion angle
angle for
for both
both methods
methods at
at periods
periods near
near 10
IO sec.
sec.
ments
two recording
recordingtimes
times in
in band
band I1at
at Lower
Lower La
La Gloria
Gloria bebe- For
For both
both methods,
methods, the
the phase
phase angles
angles where
wjherebands
bands 33
two
causewe
we had
hadaccidentally
accidentallyremoved
removedaa set
setof
of preamplipreampli- and
and44 overlap
overlap differ
differ by
by about
about55 degrees.
degrees.However,
However, at
at
cause
fiers from
from some
some of
of the
the channels
channelsat
at that
that station.
station.
periods shorter
shorter than
than 0.1
0.1 sec
set the
the standard
standard analysis
analysis
fiers
periods
Table 55 lists
liststhe
the percentage
percentageexpected
expecteddeviation
deviation of
of yields
Table
yields aa scatter
scatter of
of about
about ±i33 degrees
degrees in
in orientation
orientation
the mean
mean resistivity,
resistivity, 100
100 uj
aj/cj,
function of
of angle
the
Pj, asas aa function
angle whereas
whereasthe
the remote
remote reference
referenceyields
yields no
no visible
visible
period for
for both
both stations.
stations. We
We see
see that
that the
the expected
expected scatter.
period
scatter.At
At Lower
Lower La
La Gloria
Gloria the
the standard
standardand
and remote
remote
l~o
Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/
67
67
Magnetotellurics
Magnetotellurics
reference
reference methods
methods yield very similar values
values for the
the
phase
phase angles,
angles, with scatter
scatter increasing
increasing with period
period up
up
to
to about
about ±5
*5 degrees
degrees for periods
periods longer
longer than
than 10
10 sec
set
(Figures
(Figures- 15
!5 and
and ]{i)~
16). The standard
standard analys{&analysis yield&yields
values
values of orientation
orientation angle
angle and
and skewness
skewness that
that differ
by
by 20 degrees
degrees and
and 0.2 respectively
respectively between
between bands
bands 2
and
and 3, while no
no disagreements
disagreementsare
are apparent
apparent for the
the
remote
remote reference
reference method.
method. There
There are
are also
also consistent
consistent
differences
differences between
between the
the two methods.
methods. For example,
the
the orientation
orientation angle
angle at
at short
short periods
periods determined
determined by
by
the
the remote
remote reference
reference method
method is
is about
about 52 degrees,
degrees,
while by
by the
the standard
standardmethod
method it is
is about
about 65 degrees.
degrees.
SUMMARY
SUMMARY AND
AND DISCUSSION
DISCUSSION
The technical
technical feasibility
feasibility of performing
performing MT
MT soundsoundings
ings using
using a remote
remote magnetometer
magnetometeras
as a reference
reference has
has
been
been demonstrated,
demonstrated, and
and the
the results
results from
from this
this method
method
are
are shown
shown to
to be
be substantially
substantially better
better than
than those
those obobtained
tained using
using the
the conventional
conventional MT
MT technique.
technique. Smooth
Smooth
curves
curves of apparent
apparent resistivities,
resistivities, orientation
orientation angles,
angles,
phases,
phases,and
and skewnesses
skewnessesas
as functions
functionsof period
period for both
both
stations
stations were
were obtained,
obtained, even
even at
at periods
periods where
where the
the
coherencies
coherencies determined
determined from
from the
the standard
standard analysis
analysis
were as
as low as
as 0.1. In bands
bands I1 and
and 2 (periods
(periods <3
<3 sec)
set)
an
an estimate
estimate of 1.3 percent
percent was
was obtained
obtained for the
the mean
mean
percentage
percentageerror
error associated
associatedwith random
random variations
variations in
the
the apparent
apparent resistivities.
resistivities. At periods
periods where
where bands
bands I
and
and 2 overlapped,
overlapped, the
the resistivities
resistivities obtained
obtained for the
the
two bands
bands agreed
agreed to
to within an
an average
average percentage
percentage
uncertainty
uncertainty of 1.8
1.8 percent.
percent.
By comparing
comparing apparent
apparent resistivities
resistivities from
from the
the re-
mote
analysis with apparent
apparent resistivities
resistivities
mote reference
reference analysis
from the
impedance and
and admittance
admittance analyanalythe standard
standard impedance
of the
the bias
bias
ses,
the significance
ses, we demonstrated
demonstrated the
significance of
ermfSleast squares
squares methods,
methods, Andy
and- showed
showed.
errors in these
these !east
there is
is bias
bias from noise
noise in both
both electhat,
that, in
in general,
general, there
bands I and
and 2, where
where
tric
channels. In bands
tric and
and magnetic
magnetic channels.
the
was between
between 0.7 and
and 0.9,
0.9, the
the dominant
dominant
the coherency
coherency was
bias
noise in the
the magnetic
magnetic channels,
channels, and
and
bias was
was from noise
the order
order of 20 percent.
percent. At Lower La
was
was typically of the
as low as
as 0.1,
0.1,
Gloria, where the
the coherencies
coherencies were
were as
the
analysis apparent
apparent resistivities
resistivities at
at pethe standard
standard analysis
sec were biased
biased downward by more
riods
riods near
near 10
10 set
magnitude, while the
the apparent
apparent
than
orders of magnitude,
than two orders
resistivities
the admittance
admittance method
method were biased
biased
resistivities from the
magnitude. The apparent
apparent reupward
one order
order of magnitude.
upward by one
is ununsistivities
for the
the crosspower
crosspower analysis
analysis (which is
resistivities
biased
autopower noise)
noise) had
had random
random errors
errors that
that
biased by autopower
the two least-squares
least-squares
often
the bias
bias errors
errors of the
often exceeded
exceeded the
methods.
methods.
The results
the remote
remote reference
reference analysis
analysis are
are
results for the
autopowers and
and by noises
noises that
that
unbiased
noise in autopowers
unbiased by noise
are
the distance
distance separating
separating the
the
are not
not correlated
correlated over the
reference
magnetometer and
and the
the base
base station.
station. The
reference magnetometer
systematic errors
errors caused
caused by long
long range
range
possibility
possibility of systematic
the noises
noises cannot
cannot be
be ruled
ruled out
out entirely,
correlations
correlationsin the
but
that the
the use
use of the
the remote
remote reference
reference
but it is
is believed that
greatly
the likelihood of such
such systematic
systematic
greatly reduces
reduces the
errors.
errors.
As an
to a remote
remote magnetic
magnetic reference,
reference,
an alternative
alternative to
one
using a remote
remote telluric
telluric array.
array. Howone could
could consider
considerusing
ever, there
are two reasons
reasons why telluric
telluric arrays
arrays may
there are
Table
from the remote reference
reference
Table 5. Expected standard
standard deviations,
deviations, 100 (Ti/
aj/pj,Pi' of mean apparent
apparent resistivities from
method.
method.
Upper
UpperLa
La Gloria
Gloria
Period
Period
(sec)
(see)
0:03
0.03
0.04
0.04
0.06
0.06
0.08
0.08
0.12
0.12
0.16
0.16
0.22
0.22
0.30
0.30
0.41
0.41
0.57
0.57
0.79
0.79
0.33
0.33
0.45
0.45
0.63
0.63
0.88
0.88
1-.2
!.2
1.7
1.7
2.4
2.4
3.4
3.4
100 (TXY/PXY
0.4
0.5
0.5
0.2
0.3
0.3
0.5
0.5
0.4
0.7
0.6
0.04
0.04
1.2
1.2
1.2
I .2
2.2
2.2
0.8
0.8
1.2
1.2
1.2
1.2
LV
1.0
L{)
1.1
1.1
0.8
0.8
1.3
1.3
Lower La
La Gloria
Gloria
Lower
100 (Tux/PyX
100 (TXY/PXY
100 (Tyx/ PYX
35
3.5
Z.O
2.0
0.7
1.3
1.3
1.1
1.1
0.8
1.6
I .6
1.9
1.9
0.9
0.7
0.7
1.3
1.3
1.8
1.8
0.4
1.2
1.2
1.0
1.o
0.9
1-.4
i.4
0.9
2.7
2.7
1.7
1.7
2.3
2.3
0.8
0.5
0.9
0.7
1.3
1.3
1.1
1.1
1.8
1.8
1.2
1.2
1.3
1.3
1.5
1.5
0.8
0.8
0.5
0.5
0.5
0.5
0.7
i.i
i.i
1.5
1.5
1.2
1.2
2.0
0.8
0.8
0.8
0.8
2.1
2.1
0.7
0.7
1.4
1.4
0.6
0.6
0.9
0.9
4.4
4.4
2.2
2.2
1.6
1.6
1.6
1.6
1.0
1.0
3.0
3.0
0.9
0.9
1-.3
i.3
1.4
1.4
3.4
3.4
2.6
2.6
Downloaded 15 May 2010 to 95.176.68.210. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/
66
68
Gamble et
et al
al
Gamble
proveto
tobe
beless
lessre
reliable
asaareference
referencethan
thanaamagnetic
magnetic
prove
liable as
held reference.
reference. First.
First, itit has
hasbeen
beenour
ourexperience
experiencethat
that
field
thereisisoften
oftenmore
morenoise
noisein
inthe
theelectric
electricmeasurements
measurements
there
thaninin the
the magnetic.
magnetic, although
althoughthis
this was
wasnot
not the
the case
case
than
theLa
La Gloria
Gloria stations.
stations.Second.
Second.the
theelectric
electricfield
field atat
atatthe
thesurface
surfaceof
of the
theearth
earthproduced
producedby
by aagiven
given magnetic
magnetic
the
field isis highly
highly dependent
dependenton
on the
the geology.
geology. The
The referreferfield
ence must
must be
be able
able to
to respond
respondin
in different
different directions
directions
ence
as the
the polarization
polarization of
of the
the incident
incident magnetic
magnetic field
field
as
changes. IfIf the
the apparent
apparentresistivity
resistivity isis highly
highly anisoanisochanges.
tropic, the
the electric
electric field
field response
responsetends
tendsto
to lie
lie in
in the
the
tropic.
direction of
of the
the highest
highest apparent
apparent resistivity.
resistivity, and
and aa
direction
higher level
level of
of random
randomerror
error isis produced
producedby
by aa given
given
higher
level of
of random
random noise.
noise.
level
The use
useof
of aaremote
remotemagnetic
magneticreference
referenceshould
shouldenenThe
able one
one to
to carry
carry out
out aa magnetotelluric
magnetotelluricsurvey
survey in
in an
an
able
areacontaminated
contaminatedby
by cultural
cultural magnetic
magneticand
and electric
electric
area
noises. provided
provided that
that the
the reference
reference isis sut1iciently
sufficiently
noises.
distantto
to insure
insurethat
that any
any possible
possiblebias
bias errors
errorsdue
due to
to
distant
correlatednoises
noisesare
aresmall
smallcompared
comparedwith
with the
therandom
random
correlated
errors. Clearly.
Clearly, the
the minimum
minimum separation
separationdepends
dependson
on
errors.
both the
the correlation
correlationlengths
lengthsof
of the
the noises
noisesand
andon
on the
the
both
lengthof
of time
time over
over which
which the
thedata
dataare
areaveraged.
averaged.The
The
length
upperlimit
limit on
onthe
theseparation
separationisisset
setnot
notonly
only by
by practipractiupper
cal problems
problemsof
of telemetry
telemetry but
but also
alsoby
by the
the coherence
coherence
cal
lengthof
of incoming
incomingmagnetic
magneticsignals.
signals.When
When the
thesepasepalength
ration becomes
becomes greater
greater than
than the
the coherence
coherence length.
length,
ration
the random
random errors
errorswill
will increase.
increase.
the
The use
useof
of aa remote
remote reference
reference may
may enable
enable one
one to
to
The
test the
the validity
validity of
of the
the assumptions
assumptionsusually
usually made
made in
in
test
magnetotellurics:for
for example.
example, that
thatthe
the incident
incidentfields
fields
magnetotellurics:
are plane
plane waves.
waves. and
andthat
thatthe
the electric
electric fields
fields are
are adeadeare
quatelydetermined
determinedby
by measurements
measurementsof
of the
the potential
potential
quately
difference between
between widely
widely separated
separatedelectrodes.
electrodes.The
The
difference
planewave
wave approximation
approximationcould
couldbe
betested
testedby
by measurmeasurplane
ing the
the apparent
apparentresistivities
resistivitiesas
as aa function
function of
of time
time in
in
ing
an auroral
auroralzone
zone(where
(where source
sourceeffects
effects are
are likely
likely to
to be
be
an
largest)over
over ground
groundwhere
where the
the true
true resistivity
resistivity isis bebelargest)
lieved to
to be
be constant.
constant.One
One could
couldexamine
examine the
the effects
effects
lieved
of electrode
electrode placement
placementon
on the
the apparent
apparentresistivity
resistivity by
by
of
measuringapparent
apparentresistivities
resistivitiesas
asaa function
functionof
of elecelecmeasuring
trode position.
position. Furthermore.
Furthermore, the
the remote
remote reference
reference
trode
technique should
should allow
allow one
one to
to monitor
monitor long
long term
term
technique
changes
in
the
apparent
resistivity
at
a
given
site
to
changes in the apparent resistivity at a given site to
greater accuracy
accuracythan
than has
has previously
previously been
been possible.
possible.
greater
Finally, the
theadditional
additionalcost
costof
of the
thesecond
secondmagnetomagnetoFinally.
telluric station
stationisis believed
believed to
to be
be easily
easily justified
justified ecoecotelluric
nomically. in
in view
view of
of the
the advantages
advantagesof
of the
the remote
remote
nomically.
referencetechnique.
technique.First.
First. apart
apartfrom
from data
datarejected
rejectedin
in
reference
preliminary screening.
screening.all
all of
of the
thedata
datacollected
collectedwere
were
aapreliminary
usedto
tomake
makereliable
reliable estimates
estimatesof
of the
the apparent
apparentresisresisused
tivities. even
even when
when the
the coherencies
coherenciescomputed
computedby
by the
the
tivities.
Second, the
the
standardmethod
method were
were as
as low
low as
as O.
0. I.I. Second.
standard
simultaneousoperation
operationof
of the
themagnetotelluric
magnetotclluricstations
stations
simultaneous
obviouslydoubles
doublesthe
thesurveying
surveyingrate
ratecompared
comparedwith
with aa
obviously
single station.
station. Thus.
Thus. the
the remote
remote reference
reference technique
technique
single
may substantially
substantiallyreduce
reducethe
thetime
time necessary
necessaryto
to survey
survey
may
given area.
area.
aa given
ACKNOWLEDGMENTS
ACKNOWLEDGMENTS
We are
are grateful
grateful to
to Mr.
Mr. Melendy
Melendy and
and Mr.
Mr. DeRosa
DeRosa
We
for granting
grantingus
usaccess
accessto
to their
their land.
land. We
We are
are indebted
indebted
for
to Professor
ProfessorH.
H. F.
F. Morrison
Morrison and
and his
his students
studentsfor
for the
the
to
loanof
of equipment
equipmentand
andfor
for invaluable
invaluableassistance.
assistance.ProProloan
fessor Morrison
Morrison and
and Dr.
Dr. K.
K. Yozoff
Vozoff kindly
kindly made
made
fessor
helpful comments
commentson
on the
the manuscript.
manuscript.This
This work
vvorkwas
was
helpful
Basic Energy
Energy Sciences
Sciences
supportedby
by the
the Divisions
Divisions of
of Basic
supported
and of
of Geothermal
Geothermal Energy.
Energy, U.
U.S.
Department of
of
S. Department
and
Energy, and
and by
by the
the U.
U.S.G.S.
under grant
grant number
number
Energy.
S. G. S. under
14-08-0001-G-328.
14-08-000l-G-32S.
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