It was established that the total absolute magnetic flux crossing the core- mantle boundary has been a constant of the core motion for the last 50 years. This provides a scalar constraint that could be added to the geometric modelling procedure. The GSFC 8 8/80 model is being evaluated. The absolute magnetic flux linking the CMB to that model was plotted as a function of time during the span covered by the data, and increasing truncation level. The inclusion of the standard error of each Gauss coefficient derived from the statistics of fit in the GSFC 9/80 model is useful. The magnitude and sense (upwelling or downe welling) of vertical fluid motion adjacent to the core-mantle boundary was calculated using the model. Standard errors were found to be sufficiently small at all but one or two of the 40 or more critical points of B sub r. They do not nearly overlap the value gamma u/gamma r = 0. It is concluded that the core is upwelling and downwelling at an observationally detectable level

Benton, E. R.

English

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for any use made thefeor."
E
Quarterly Status and Technical Progress Report #9
(Covering the Period 1 January 1982 to 31 March 1982)
(E82-10JIO) INHESTIGATIGN Of GEOMAGNETIC	 N82-245E4
FIELD FOHECASTIhG ANL 1LU11; LibAMICS CF THE
C09E Vuarteriy rtoyress helort, 1 Jan. - 31
mar. 1982 (CoioLado Univ.) 7 F
	
Unclas
HC AU2/8F Ail	 CSCI O8G 63/43 OU31J
NASA Contract NAS5-25957 (MAGSAT)
Investigation of Geomagnetic Field Forecasting
and Fluid Dynamics of the Core
Principal Investigator: Edward R. Benton
Department of Astro-Geophysics, University of Colorado
Boulder, Colorado 80309
RECEIVED
APR 9, /??-Z-
1 April 1982
	
SIS1 902'661 -036
T Y/°r
2'
1. roblems
Several contractual problems were identified at the beginning
of this quarter. As a result a letter (dated 29 January 1982 to
Mr. Alton Payne, NASA-GSFC) was sent requesting a re-allocation of
existing contract funds, a supplement to the contract of $5,000,
and a one month extension in time. It is our understanding that
the requested changes have been approved, except that the time
extension is for three months (making the new termination date
26 November 1982). This resolves all problems completely.
2. Approach
In the paper by Voorhies and Benton (1982) referred to in
section 5 below, we established that the total absolute magnetic
flux crossing the core-mantle boundary has indeed been essentially
a constant of the core motion for the last 50 years. This strongly
supports the theoretical hypothesis that the core moves like a
perfect conductor in the short term. Moreover, it provides one
scalar constraint that could be added to the geomagnetic modelling
procedure. For example, MAGSA'1 data at 1980, provides a value, Po,
for the absolute magnetic flux linking the core-mantle bouniary (CMB).
In preparing the magnetic model for the next set of world charts,
one could require the model to produce that same value of absolute
magnetic flux across the CIS. However, one scalar constraint is
hardly enough to make any significant impact on the modelling
procedure, so Wij now ask if there are other constraints available.
W^ .	 A new approach to constraining secula , variation is in its
initial,st8ges of development. The idea is a simple extension of
r	 3	 }
flux conservation. At the top of a perfectly conducting core, every
null-flux contour (i.e., the curves on which B r = 0) moves with
the fluid. Therefore, the number and topology of these curves are
short-term invariants of the motion. Furthermore, the magnetic flux
through each patch of surface area on the CMB bounded by a null-flux
curve must also be a constant of the motion. At the present time
there are two or possibly three resolved magnetic equators on the
CMB for a truncation level of N a 8 (which appears to be about the
largest value that can reliably be chosen for extrapolation to the
core). These two or three "tr.agnetic loops" are small features,
whose location and flux values are presumably determined by the
high-order gauss coefficients. It may be possible to adjust some
of those coeffi(7ients so as to satisfy the above constraints.
We have begun this line of inquiry by evaluating the magnetic
flux through the two magnetic equators near Africa and South America
using a variety of magnetic models (refit to the MAGSAT data
appearing in MGST 6/80, IGS 65, and GSFC 12/66--the latter model
being evaluated at 1960, 1950, 1940, and 1930). It was no surprise
to find that the magnetic flux through these small loops was not
especially constant. The flux values are only of order 1 to 2% of
that linking the entire CMB, ;end, in contrast to P o (which remained
constant to something better than 0.1%), these small scale magnetic
fluxes were predicted to vary by up to of order 25%. This implies
that there is indeed good reason to impose the constraints provided
by perfect conduction in the core. It will, necessarily, require
changing some of the high order coefficients (which are, of course,
those leant well determined by the data). This development seems
{
I #	 - ti
to hold some promise, but we do not yet know how to adjust the
coefficients so as to satisfy the constraints.
3. Accomplishments
Much of our effort during this quarter has gone into revising
and casting into final form the three MAGSAT-related papers cited
in section 5 below. These are now in press for the issue of
Geophysical Research Letters being edited by Dr. R. A. Langel.
In addition, we have begun an evaluation of the new GSFC 9/80
model, which looks very good to us. Figure 1 below is a plot of
the absolute magnetic flux linking the CMB according to that model,
as a function of time during the span covered by data, and increasing
truncation level. The largest value of N at which flux is very
nearly conserved throughout the twenty year period is N - 8. This
reconfirms one of the conclusions reached in the paper by Benton,
Estes, Langel, and Muth (1982). We are not surprised to find a
lack of convergence setting in above N - 10, because the high order
coefficients of the secular variation are simply not, as yet,
sufficiently well determined at the earth's surface to permit
trustworthy extrapolation to the core-mantle boundary.
4. Significant Results
Ine of the most useful aspects of GSFC 9/80 is the inclusion
of the standard error of each Gauss coefficient derived from the
statistics of the fit. Even though those errors represent only
F
	
	
lower bounds to the true errors, it nevertheless does provide some
way to gauge whether or not a result derived from the model can
If
possibly be trusted (if the lower bound errors aro too large t____
obviously a result must be discarded as insignificant; it is
necessary, but unfortunately not sufficient, to have small error bars
before accepting a result).
A graduate research assistant, Coerte V. Voorhies, has used
GSFC 9/80 to calculate the magnitude and sense (upwelling or
downwelling) of vertical fluid motion adjacent to the core-mantle
boundary by the techni ..c 3iscovered independently by Whaler (1980)
and Benton (1981). This gives 3u/ar = (3B r /at ) /B r at the critical
points of Br (i.e., where 3B r /ae rind 3B r /a^ 3 0), where u is the
vertical motion and au / 8r < 0 (> 0) at an upwelling (downwIl:ng).
Also calculated were the standard errors of B r , aBr / at, and au/3r,
for truncation levels N = 7, 8, 9, 10. The interesting finding is
that the standard errors are sufficiently small at all but one or
twc of the 40 or more critical points of B r , that they do not
nearly overlap the value 3u/3r = 0. This is in direct conflict with
the results obtained by Whaler ( 1980) using the 1965 TGRF and its
secular variation ( she considered only 19 extreme of Br , and found
that the standard deviations overlapped the value zero; so her
conclusion was that the outer part of the core is quiescent in the
vertical). In contrast, we conclude that the core is upwelling and
downwel .ling at an observationally detectable level. This result
needs bolstering ' vt we think it sufficiently important to merit
publication ( knowledge of au / 3r forms the starting, point for the
two methods of determining core motions from magnetic measurements
described in Benton, 1981).
5. Publications
In press for April 1982 Geophysical Research Letters and
supported, in part, by this contract:
a. Benton, E. R., Estes, R. H. , Langel, R. A. and Muth, L. A.,
"Sensitivity of Selected Geomagnetic Properties to Truncation
Level of Spherical Harmonic Expansions".
b. Benton, E. R. and Coulter, M. C., "Frozen-Flux Upper Limits
to the Magnitudes of Geomagnetic Gauss Coefficients, Based
on MAGSAT Observations".
c. Voorhies, C. V. and Benton, E. R., "Pole-Stren.o th of the
Earth from MAGSAT and Magnetic Determination of the Core
Radius".
6. Recommendations
None.
7. Funds Expended Through 28 February 1982:
8. Data Utility
The new model GSFC 9/80, which is the basis for much of our
recent progress is extremely well suited to our purposes.
S
ORIGINAL PAGE 13
OF POOR QUALM
4 2 4 i
13
40
12
11
12
38
I 1
10
10
93 9
u 36
8	 _ 8
7
Z	 6–	 6
.-	
5—	 - a
34--
a.
4	 4
32
30
28 L-L-1960 1965	 1970	 1975	 1980
FIGURE 1. ABSOLLTE MAGNETIC FLUX, P(b,t;N), LINKING EART'H'S CORE AS A
FUNCTION Of TIME, t, ANN TRUNCATION LEVEL, N. AS CALCULATED FROM GSFC 9/r•+J
ASSLM M- AN INSULATING MANTLE. AND CURE RADIUS h - 3485 K,M.
.-A


Investigation of geomagnetic field forecasting and fluid dynamics of the core

The magnetic determination of the depth of the core-mantle boundary using MAGSAT data is discussed. Refinements to the approach of using the pole-strength of Earth to evaluate the radius of the Earth's core-mantle boundary are reported. The downward extrapolation through the electrically conducting mantle was reviewed. Estimates of an upper bound for the time required for Earth's liquid core to overturn completely are presented. High order analytic approximations to the unsigned magnetic flux crossing the Earth's surface are also presented

  
 
 
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MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT 
CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED 
IN THE INTEREST OF MAKING AVAILABLE AS MUCH 
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https://ntrs.nasa.gov/search.jsp?R=19820013812 2020-03-21T08:23:17+00:00Z
i
 
E82^ 101,62tRe iM,c ^ of early a^^ , .^ ,,, ,,;
	 ` 
Quarterly Status and Technical Progress Report #7
(Covering the Period 1 July 1981 to 30 September 1981!
(282-10162) IN VESTIGkTION OF GEoKkGV9TIC
1182-21686
FIELD loRECASTING AND FLUID DINAQICS of THE
CORE Quarterly Status Technical Progress
	
unclas
adoReport, t Jul. - 30 Sep. L01981 (ColorCSCL 08G G3/43 00162U niv.) 14 P HC k02/11
NASA Contract NAS5-25957 (MAGSAT)
Investigation of Geomagnetic Field Forecasting
and Fluid Dynamics of the Core
Principal Investigator: Edward R. Benton
Department of Astro-Geophysics, University of Colorado
Boulder, Colorado	 80309
RECEIVED
OCT 1 - , /,??/
1 October 1981	
S!S 902.6
7-Yoe- JT-7
2a) Magnetic Determination of the Depth of the Core-
Mantle Boundary Using MAGSAT Data
The pole-strength of earth, P(r,t), defined in equation 1
of Progress Report #6 has been the focus of further study durinq
this reporting period. A slightly different approach has been
taken in using this quantity to evaluate, magnetically, the
radius of the earth's core-mantle boundary. In Figure A of
the last report we plotted the change in pole strength (in
megawebers) between 1965 and 1980 at various radii within
the earth, the radius at which it is zero being the "magnetic
core radius". However, Figure A does not reveal just how small,
relatively, this absolute change in P is, so in Figure 1 below
we plot, instead the dimensionless ratio of pole strength at
1980 to that at 1965. The magnetic core radius is then where
the ratio takes on the value 1. A further refinement is that
both data sets have been treat-d in the same way. The so-called
definitive model of Barraclough, Harwood, Leaton, and Malin
(BHLM) selected for 1965 was a fit to a massive data set at
a truncation level N=8, so instead of simply truncating MGST
6/80 from its fitting level of 13 back to N=8 (as done in the
previous Figure A), we have now utilized calculations kindly
made, at our request by Drs. R.A. Langel (GSFC) and Ron Estes
(BTS) which re-fit the data used for MGST 6/80 to various
l 
LI
;r
3
3
truncation levels, among them h=8. This refinement makes no
significant changes in the value of the magnetic core radius
compared to that found previously.
An important addition to our approach is the calculation
of one standard deviation error estimates for P(r,t) for the
1965 BHLM model. The approximate a's of the Gauss coefficients
(.n nT) at r=a are given by Hide and :Malin (1981) as
a(g-) = a(hn) = 0.56(n+l)	 (1)
The resulting standard deviation of the pole-strength integral
P is then calculated from
a (P 1 ) _ {	 (0.56) 2 (n+l)[(^Pm)2 + (aPm) 2 ] }	 (2)
	n=1 m=0	 agn	 ahn
Here P 1 designates P at time t 1=1965 and eac:i of the partial
derivatives is an integral. To obtain the total one sigma
error bar for the ratio P 2 /P 1
 (where P 2
 is P at 1980) we re-
quire error bars for the MGST 6/80 model fit to the MAGSAT
data. These have just been acquired from Dr. Ron Estes.
Since
a ( P 2 ) 2	 a ( P 1 ) 2 1-
2	 1
	
Cy
 
(P1)
	
P1 a (P2) 2
..	 11 + F	 ,l }	 (3)
12/66, and made extensive calculatic
-INN
r
4
we expect that the relatively smal. fitting errors in MGST
6/80 will be dominated by those in the BHLM model so no
appreciable change will be required. In any event, these
error estimates have to be regarded as lower bounds on true
errors since they do not account for instrument errors and
errors associated wi th extrapolation through the mantle
(assumed to be an insulator).
As a partial check on these error bars we also used a
random number generator to perturb each gn , hnseparately
by up to + 0.56(n +1) 1`nT and then calculated P(b,1965) where
b = 3485 km. Repeating this for 5 different random sets gave
differences in P 1 from the value for BfiLM that were in every
case within the error shown on Figure 1. We, therefore, be-
lieve the minimum errors associated with the data fitting
process have been reliably determined.
The basic curve of Figure A relied on two main field
models only so that, by design, secular variation played
only an indirect role (no role whatsoever in MGST 6/80 and
only to bring the 20 years of data for BHLM to the common
central epoch of 1965). One still wonders whether the
closeness of the magnetic core radius, so determined, to
the seismic core radius might not be fortuitous. A further,
indepen3ent test is therefore highly desireable. Accordingly,
we have chosen another high quality main field model, GSFC
^t
b) Downward Extrapolation through the Electrically
Conducting Mantle
In Progress Reports #1, 2, and 4 reference was made to
work in progress designed to account for the effects of in-
duced electric currents in the man t le (due to non-zero mantle
conduction) for the downward ext:--polat on of magnetic fields
from earth's surface to the core-mantle boundary. The formu-
lation was completed some months ago, but relatively little
numerical evaluation and application of the methodology had
been made. During the present reporting period (and with
financial assistance from an NSF Grant, no NASA funds having
been used) the application aspect of this work has been
tackled by Dr. Kathryn A. Whaler who visited Boulder for
5 weeks during June and July 1981. The approach used was
to choose several selected radially symmetric conductivity
models for the mantle and then numerically integrate the
magnetic diffusion equations. Some conclusions are described
in Section 5 below.
c) Estimate of an upper bound for the time required
for earth's liquid core to overturn completely
An approach has been developed for estimating an upper
bound on how long it takes earth's core to overturn. While
bearing some similarity to recent work of Busse and Proctor,
.r
6
which gives methods for bounds on dynamo action, our approach
is different in a vital way. These previous results require
evaluation of magnetic volume integrals over the core which
cannot generally be done since we have no real information
on the structure of the magnetic field within the dynamo
region. Thus, the results are of theoretical interest, but
of limited practical value.
Our approach reduces the problem to one of magnetic
surface integrals over spheres within the core. These,
too, cannot be directly calculated, but the integrals in
question are the analytic continuation of the same quanti-
ties over spheres within the mantle, where we do have mag-
netic information, so it seems likely that numerical esti-
mates of interest can be inferred.
Without going into much detail, we assert that it is
possible to prove, in a straightforward fashion that for
some spherical surface of radius r in the core, bounded
away from the inner core-outer core boundary and the core-
mantle boundary,
2 Tr Tr
	
2 T it	
2	
n	
f	
I ( V (rBr) } 2r2sinodlldQ,
lu(r,e,^,t) jrsineded^ 	 ° o 0
	
fo 0	 (rB•V ( rBr)IMAX
(4)
Here no - 1/Uoao is the (constant) magnetic diffusivity of
the core, and MAX denotes the largest value achieved on the
3
sphere of radius r. Because u is the vertical fluid motion
ir
7
(whose surface average is zero for incompressible flow, as
much fluid moving upwards as downwards), Jul integrated
over the spherical surface measures the unsigned flux of
fluid volume (m3 s-1 ) across that surface (just as
I
27t ^r
1 IBr (r,64 ,01r2 sinOdOd^ measures the unsigned magnetic
'o 0flux crossing the sphere of radius r).. Thus, when the total
liquid core vol qie is divided by the left-hand integral
we obtain the overturning time for the core. Now, the two
quantities on the right are both continuous functions of radius
everywhere and moreover, they can be evaluated in the mantle,
and estimated in the inner core. In fact, within the insul-
ating mantle the numerator integral can be evaluated exactly
as
2 T
r)o 1
	 f 7 1V(rBr ) 2r2sin9dedQ
0 0
4rra2n I I (n+l) 3 ( a ) 2n+2 ^gm ) 2 + (hm ) 2 1	 (5)
°n=1m=o	 r	 n	 n
where a is the radius of the earth. Thus, the radial dependence
of the Numerator is readily exposed. It but remains to tabulate
rB • Q(rBr ) on the spherical surface in the mantle and evaulate
the maximum value at various depths.
Although both the numerator and the denominator in (4) are
expected to increase rapidly with depth in the mantle, their
ratio should be a rather mild function of radius. It, therefore,
becomes possible to extrapolate into the core (since both functions
8and their ratio remain continuous across the core-mantle
boundary) and estimate a lower bound on the volume flux
integral (which upon inversion gives an upper bound on
the overturning time).
This work is being jointly funded by this NASA contract
and an NSF grant, and we intend to use the MAGSAT data for
evaluation.
3. Accomplishments
a) Magnetic determination of the depth to the core-
mantle boundary using MAGSAT data
A major accomplishment of this reporting period is the
completion of a body of calculations (by Mr. Coerte V. Voohies,
a Graduate Research Assistant beinu supported by this contract)
revealing both the radial and time dependence of Dole-strenqth,
P(r,t), within the earth. Figure 1 summarizes some of the
results. In this figure, the ratio of P evaluated at the MAGSAT
epoch to P evaluated at various previous epochs (1930, 1940,
1950, 1960, 1965) is disp layed as a function of death within
the mantle (considered to be an insulator). The models used
are MGST 6/80 (re-fit to N=8) for 1980; S11LM for 1965; and
GSFC 12/66 for 1 0,30, 1940, 1950, 1960 (truncated back from
10 to 8, and compared with a re-fit to the data of MGST 6/80 to
N=10 followed by truncation back to N=8). Minimum direct use
of secular variation was entailed in the curve labeled 1965.
1
9For the curves usinc VS w 12 /66, the secular variation and
secular acceleration coefficients were used not only as part
of the data fitting pi•ocess, but were also used subsequently
to construct Gauss coefficients at the desired epochs.
The final truncation level of 8 chosen was based on the
belief that it i3 the optimum va l ue for evaluating the pole-
strength integral a'_ vario^:s levels down to the core-mantle
boundary. Choosii(,+ smalls N excludes too much magnetic
flux, wher.e,^,G	 ?.argvr. N results in downward extra-
polation .,id ?,ence anipl : f ication) of too much noise because
of tb,- rel%tivel y larger uncertainties in the hi gher order
Gauss coefficients.
Further details will be described in a paper beinq
prepared for the MAGSAT issue of Geophysical Research Letters
being edited by Dr. R.A. Langel. Here we call attention to
the fact that each curve compares a previous magnetic model
with MAGSAT, and that every curve passes throunh the value 1
within a few per cent of the accurate seismically determined
core radius of 3485 km. The somewhat peculiar shape of the
curve for 1930, compared to that for later epochs is believed
to be due to its increased dependence on the secular variation
and secular acceleration coefficients compared to the later
curves. The error bars on the curve for 1965 are those des-
cribed in the preceding section. Given the size of the !mini-
mum) error, we conclude that this technique finds the core
I10
radius, magnetically over a span of 35 years with acceptable
accuracy, the mean of the five determinations beinq only
11 km (or about 0.3%) larger than the seismic core radius.
This significant result builds our confidence in (a) the
short term validity of the frozen-flux assumption in the
core, (b) the adequacy of treating the mantle as an insulator,
(c) the accuracy of the main field models MGST 6/80 for 1980,
BHLM for 1965 and GSFC 12/66 for 1960, and (d) the validity
of the secular variation and secular acceleration coefficients
in GSFC 12/66 for limited interpolation backward in tii«e (while
remaining well within the span covered by data).
b) Higher order analytic approximation to the unsigned
magnetic flux crossinc- earth's surface
The principal investigator and Ms. M. Christine Coulter
(a Graduate Research Assistant being supported by this con-
tract) have collaborated so as to obtain an improved analvtic
approximation for P(a,t) compared to that given in the last
Progress Report, the result beinq
P(a,t) = -4na 2 g 0 {1 + 1[(C;1)2 + (111)21
61G1G1 + H 1 It 1 1 + 1- ( G 0 ) 2 + E [ ( G2 1 2 + (H2 ) 21
	2 1 3	 1 3	 16 2	 32	 2-	 2
+ 15JI3 [G2G2 + H 2 H 2 - 1 GO + 3 [(G 1 ) 2 + ( H1)2132 2 4	 2 4	 2 3	 4	 3	 3
+4 [ ( G3) 2 + (H3) 2 1 + 256 (G 4 ) 2
+ 175[(G2)2 + (H2)21 + 875 [(G4 ) 2 + (H4)21},
	
M 4	 4	 M 4	 4
where Gn = gn/yl'
11
This reveals the fact that, at earth's surface (and undoubtedly
elsewhere too), P is a (quadratically) non-linear functional
of normalized Gauss coefficients.
In the next step it is hoped to extend this approximaticn
to situations where there is more than one magnetic equator,
and then to use the result to help understand the morphology
of the geomagnetic field during polarity transitions. Initial
conversations with Prof. Michael Fuller (Univ. of California at
Santa Barbara) suggest that the above sort of analysis, when
properly extended, can contribute needed constraints for
modelling reversals.
c) Downward extrapolation through the electrically
conducting mantle
The preliminary results revealed by the computations of
Dr. Whaler referred to above are as follows: (a) For all
but the most extreme conductivity profiles, the correction
to main field Gauss coefficients for mantle conduction is
insignificant throughout the mantle. (b) The correction
to secular variation coefficients is probably marginally
significant, but the dependence on conductivity profile is
surprisingly weak; thus it is more important to correct SV
models than main field models for mantle conduction if they
are to be extrapolated downward, but the choice of conductivity
profile is of minor concern. (c) Regardless of the conductivity
profile chosen, the spectral power in the secular variation is
I12
decreased for all harmonic orders except 1, 2, 4 and the
largest corrections occur for a constant conductivity pro-
file. (d) The correction for mantle conductivity does not
preferentially amplify the mall wave length structures,
since the sign of the correction depends upon the ratio
of aecular acceleration (gn) to secular variation (4m
which can be either positive or negative.
4. Significant Results
By comparison, in a consistent fashion, of the magnetic
pole-strength of the earth at earlier epochs with the value
determined by MAGSAT, it has been demonstrated that the
radius of earth's core can be found magnetically with accep-
table accuracy, provided the optimum truncation level N=8
is chosen for the spherical harmonic models.
5. Publication
Edward R. Benton "Inviscid Frozen-Flux Velocity Components
at the Top of Earth's Core From Magnetic Observations at Earth's
Surface. Part I. A New Methodology", Geophysical and Astro-
physical Fluid Dynamics 18, 157-174, 1981.
6. Recommendations
None
7. Funds Expended through August 31, 1981
$50,143.
L
13
S. Data Utility
The MAGSAT and GSFC magnetic models, as they are currently
being produced, continue to be the main data source for this
project, and they are eminently suited to our purposes. We
expect to utilize the new GSFC 9/80 and 7/81 models in our
continuing work.
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Progress in the development, testing, and evaluation of kinematic geomagnetic forecast models and their utility in magnetic prediction of the core-mantle boundary of the Earth and in determination of the core radius is reported. The GFSC 9/80 model, which uses MAGSAT data, was determined to be of high quality

General Disclaimer 
One or more of the Following Statements may affect this Document 
 
 This document has been reproduced from the best copy furnished by the 
organizational source. It is being released in the interest of making available as 
much information as possible. 
 
 This document may contain data, which exceeds the sheet parameters. It was 
furnished in this condition by the organizational source and is the best copy 
available. 
 
 This document may contain tone-on-tone or color graphs, charts and/or pictures, 
which have been reproduced in black and white. 
 
 This document is paginated as submitted by the original source. 
 
 Portions of this document are not fully legible due to the historical nature of some 
of the material. However, it is the best reproduction available from the original 
submission. 
 
 
 
 
 
 
 
Produced by the NASA Center for Aerospace Information (CASI) 
https://ntrs.nasa.gov/search.jsp?R=19820024935 2020-03-21T06:27:37+00:00Z
q4
v
.1 c w E aH
n,
00 ld
°h 4
Quarterly Status and Technical Progress Report #10
(Covering the Period 1 April 1982 to 30 June 1982)
NASA Contract NAS5-25957 (MAGSAT)
Investigation of Geomagnetic Field Forecasting
and Fluid Dynamics of the Core
Principal Investigator: Edward R. Benton
Department of Astro-Geophysics, University of Colorado
Boulder, Colorado 80309
1 July 1982
RECEIVED
JUL 7 , 1912-
SIS 1902 6
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(R82
-10389) !NV?STI3P InN CF GQ^MsGN°TIr
FIELD FCRACAS"ING AN!' FLUIr DYNM`SICS OF '"HIP
CORE Quarterly Status T clinical rrogress
Report, 1 A p r. - 31 Jun. 1982 (?'olorado
Univ.)	 5 p HC A"21!I y
 P^ 1	 C3CL 08G G3/43
^b2-32811
Uric'. as
CC 369
1. Problems: None
2. Approach
a. Conventional Kinematic Geomagnetic Forecast Models for Epoch 1980
Task a of this contract calls for the construction of two conven-
tional kinematic geomagnetic forecast models for epoch 1980, based on
pre-MAGSAT data. The two models selected for this purpose are the
definitive model of Barraclough, Harwood, Leaton and Malin (1978), desig-
nated herein as IGS 65, and the model of Cain, Hendricks, Langel, and
Hudson (1967), designated as GSFC 12/66. The first of these draws on data
from the period 1955 to 1973 and gives main field and secular variation
coefficients for epoch 1965 to ore er and degree N - 8. The second model
is based on data from the period 1j00 to 1966 and includes Gauss coeff-
icients of the main field, secular variation and secular acceleration
for epoch 1960, to order and degree N - 10. These two models were
selected as among the best pre-MAGSAT models, based in part on their
successfully tested ability to predict the radius of earth's core-mantle
boundary magnetically, when compared with appropriate models of MAGSAT
data (Voorhies & Benton, 1982).
We have used all of the available coefficients for the main field
and time variations in these models to forecast the main field coeffici-
ents furward in time to epoch 1980 by straightforward expansion in Taylor
series. We intend to include the resulting tables of these kinematic
forecast coefficients in the final report.
It is known that, generally, magnetic models tend to deteriorate
in accuracy rather rapidly when they are extrapolated outside the time
interval during which the model is constrained by observations. For
IGS 65 there was a 7 year extrapolation (from 1973 to 1980) but for
GSFC 12/66 the extrapolation is over the 14 year interval from 1966
to 1980. It must be expected then that the IGS 65 model would give
the better kinematic forecast at 1980. The following approach to test
this supposition has been developed and implemented. MAGSAT data for
epoch 1980 (more accurately 1979.85) were re-fit to the same fitting
levels as in IGS 65 and GSFC 12/66 (Benton, Estes, Langel, and Muth,
1982). Then the difference between these re-fitted MAGSAT models
(designated MGSTRF) and the pre-MAGSAT models was formed and contoured
at earth's surface to reveal the locations and magnitudes of the
discrepancies. The main results are described under Accomplishments.
We regard Task a as essentially complete.
b. Evaluatiott of Magnetic Model GSFC 9/80
An approach has been developed and partially implemented for
evaluating one aspect of the quality of the new geomagnetic model
designated GSFC 9/80 (Langel, Estes, and Mead, 1981). This sort of
work was not explicitly contemplated at the time this MAGSAT investi-
gation was planned, but it is, nonetheless, thought to be worth doing
as part of this project.
1
The work described by Voorhies and Benton (1982) strengthens
our belief that, in the short run (i.e. on the time scale of decades),
earth's core moves like a perfect conductor while the mantle can
simultaneously be treated as a perfect insulator. That physics implies
that the magnetic flux crossing each patch of area on the core-mantle
boundary bounded by a zero contour of vertical magnetic field should
be a constant of motion. By simple addition, so is the total unsigned
magnetic flux crossing the entire core-mantle boundary. This provides	 4
a criterion against which to test geomagnetic main field and secular
variation models. As elaborated below under Accomplishments, we have
completed a set of computations of flux through patches for both the
IGS 65 model and the GSFC 9/80 model; we find that the GSFC 9/80 model
conserves flux both patchwise and in toto, substantially better than
does IGS 65.
Another basis for evaluating a model is to ask how accurately
it locates, magnetically, the core-mantle boundary, whose radius is,
of course, very well-known from seismology. In Voorhies and Benton,
1982 this question was answered for GSFC 12/66 and IGS 65 by comparing
each of them with an appropriate (i.e. consistent) MAGSAT model. We
have now used the main field, secular variation, and secular acceler-
ation of GSFC 9/80 alone and found the core radius magnetically to
an accuracy better than that obtained by Voorhies and Benton (see
elaboration below).
3. Accomplishments
a. Conventional Kinematic Geomagnetic Forecast Models
Six important contour maps have been produced to help determine just
how inadequate is our ability to forecast geomagnetic time evolution
a decade or so into the future. The first set of three maps plots
contours (for a truncation level N T = 10) of ABre AB69 AB  at earth's
surface where, for example,
AB 
	 Br1MGSTRF	 Br I GSFC 12/66
and the re-fit to MAGSAT data is for a fitting level NF=10, so as to
be consistent with GSFC 12/66. The epoch of MGSTRF is 1979.85 and that of
GSFC 12/66 has been brought forward to 1980. Maximum differences are
two negative cells, located beneath the Indian Ocean and of magnitude
2396 and 2144 nT. Thus, although GSFC 12/66 does a good job over
the 30 year interval 1930-1960 of determining the radius of earth's
core-mantle boundary when compared to MAGSAT models for 1980, it makes
errors of over 2,000 nT, compared to MAGSAT, when extrapolated 14 years
beyond the end of the interval constrained by data. Maximum values of
JAB E1 1, JAB I are comparable but somewhat smaller, 1510 nT and 1499 nT,
respectiveiv.
2
The other three contour maps are for the differences ABr , AB a, ABA
where now
AB  a Br I MGSTRF - Br I IGS 65.
Fitting and truncation levels are N =NT
 8 and the epoch of MGSTRF is
1979.85, while IGS 65 has been brouNht forward to 1980. Maximum
values of JAB i, JAB6 J ,IAB,4 1	 are, as expected, substanti&V y
smaller over Ehe 7 year exttapolation frodr 1973 to 1980, namely, 661 nT,
420 nT, and 346 nT, respectively.
b. Evaluation of Maeetic Model GSFC 9/80
The results summarized in Figure 1 of the last Progress Report (#9)
have also been obtained for the model IGS 65. Although not yet drafted
into final form, it is apparent from the rough figure that total flux
crossing the core-mantle boundary is not nearly so well conserved by
this model as for GSFC 9/80.
Calculations of the magnetic flux through individual patches on the
seismic core-mantle boundary bounded by null-flux curves have been
completed for a truncation level of N=8. At that truncation level there
are five magnetic equators (North polar, Pacific, Main, South American,
African) so there are five independent flux conserving constraints
that ought to be satisfied.F :o r model IGS 65, for the five epochs
1955, 1960, 1965, 1970, 1975 we find deviation from constancy expressed
as an overall percentage variation for the various patches as follows:
North Polar (131%); Pacific (91%) ; Northern Magnetic Hemisphere
(0.53%); South American (8.7%);African (9.6X). In contrast, for the
model GSFC 9/80 for the five epochs 1960, 1965, 1970, 1975, 1980, we
find: North Polar (86X); Pacific (15.7X); Northern Magnetic Hemisphere
(0.35%); South American (2.5%); African (7.9X). In each case, GSFC 9/80
satisfies these frozen-flux constraints substantially better than does
IGS 65.
To check on how well GSFC 9/80 determines the core radius, magnetically,
a rather complete set of calculations ha s been made. The total absolute
magnetic fluxes crossing the spheres of radius ratio r/a = 1, 0.9, 0.8, 0.7,
0.6, 0.58, 0.56, 0.54, 0.52, 0.50 have been calculated at epochs 1960,
1970, 1980 for the complete range of truncation levels from N = 1 through
N	 13. The best value for core radius is achieved for N T =T8 by
finding the value of r at which the unsigned flux in 1980 was the same as
at 1960. That value is 3463 km, only 22 km (or 0.63%) below the accurate
seismic radius of 3485 km. Comparisons at shorter time separations (1960
to 1970, 1970 to 1980) give substantially poorer results (3215 km and
3670 km, respectively). We attribute this to dominance of round-off
error from subtracting two large numbers which are not sufficiently
different when the time interval is only 10 year:.
4. Signific:nt Results
A basis for evaluating geomagnetic models of the main field and its
secular variation (plus U gher time derivatives if they are part of the
model) has been developed. One asks (a) how well does the complete
model locate the core-mantle boundary magnetically, using Lite technique
3
of Hide (1978), and (b) how well does the model conserve magnetic flux
crossing patches of area on the core-mantle boundary bounded by
null-flux curves (Backus, :.968)? Calculations in progress strongly
suggest that the recent geomagnetic model GSFC 9/80 for the 20 year
period 1960-1980 is an extremeii nigh quality model from this viewpoint.
For example, when truncated to N-8, then back at the two extremes of its
data interval (1960 and 1980), it conserves total absolute magnetic
flux across the sphere of radius r-3463 km, which is only 22 km (or 0.63%)
below the seismic core radius of 3485 km.
5. Publications: None
6. Recommendations: None
"^. Data Utility: The modelling effort at GSFC is indispensable to
this project and the data products received to date have been out-
standing. The high quality found in the model GSFC 9/80 is, no doubt,
due in part to the treatment of observatory anomalies, but also to
the insertion of highly accurate MAGSAT data.
4


An additional approach is being taken to address the problem of how to decide where to truncate spherical harmonic representations of geomagnetic data. The idea is to simply evaluate some aspect of interest at successively higher levels of truncation and then to chose that value of truncation level (N) which gives the most reasonable appearance of convergence. The preliminary determination of the onset of relative numerical stability at a truncation level of N=7 in two independent studies is thought to be a potentially significant result of practical value for field modeling. It requires further substantiation and explanation before dissemination

  
 
 
N O T I C E 
 
THIS DOCUMENT HAS BEEN REPRODUCED FROM 
MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT 
CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED 
IN THE INTEREST OF MAKING AVAILABLE AS MUCH 
INFORMATION AS POSSIBLE 
https://ntrs.nasa.gov/search.jsp?R=19810013912 2020-03-21T14:05:59+00:00Z
Principal Investigator: Edward R. Benton
Department of Astro-Geophysics, University of Colorado
Boulder, Colorado 80309 RECEi vEo
JAN 9 1 1q81
151 902.6
M-034
1 January 1981
	
Type _-'r
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•.^ ^` `'^ J	 Quarterly Status and Technical Progress Report #4
(Covering the Verioe, 30 September 1980 'to 31 December 1980)
(Ey i -1U i1'1) INVESTIGAT.IUN OF GEOMAGNETIC; 	 N81-22443
F,=D FOHECASIING AND FLUID DYNANICS CF TOO
O)BE 1uarterly Status Toc1jiiicdl Froyres ,
Report, 30 Sep. - 31 Dec. 198U (Colorado	 Ut►Clas
Univ.) 5 p HC A02/mF AU1	 CSCL 066 u3/43 UU107
NASA Contract NA85-25957 (MA ;SAT)
Investigation of Geomagnetic Field Forecasting
and Fluid Dynamics of the Core
tr	 2
1. Pro b
The first problem mentioned in Progress Report 12 Mack
f of a graduate research assistant to work on 	 project) iE> be-
ing solved by the appointment of Miss Margaret Coulter as a
one-half time Graduate Research Assistant beginning 15 January
19'31.	 With her dual	 bachelors degree in Physics and
R
Mathematics from the University of California-Berkeley in 19800
she appears very well qualified to assist this project.
No new scientific obstacles have arisen, but a financLa1-
contractual problem exists because the total costs of the
Principal Investigator's trip to Goddnrd Space Flight Center
to attend the recent MAGSAT Investigatic:ns Status Meeting
(4,5 December 1980) was $712 . 22 1 whereas the contract budget
for travel is $500.00 ( for the entire 32-month duration of
the contract).	 A separate letter to the Contract Administrator
i (Mr. Perry W. Beilke of ONR-Albuquerque) requesting permission
to reallocate funds Within the contract so as to cover, fully,
the cost of this trip, is expected to resolve this problem.
Permission (and funds) for foreign travel to the proposed
MAGSAT session at the IAGA meeting in Edinburgh (July-August
1981) also needs to be requested.
2. Approach
No changes have occurred in the approaches described in
earlier Progress Reports. However, a new approach is being
F:	 taken to the thorny questi on of how best to decide where to
truncate spherical harmonic representations of geomagnetic data.
The idea is simply to evaluate some aspect of interest (two
^,.	 examples are given below) at successively higher levels of
truncation and then to choose that value of truncation level,
N ? Vaich gives the most reasonable appearance of "convergence."
This approach cannot be defended on rigorous mathematical
grounds but is, in our view, the only sensible one to adopt for
'`	 practical purposms.
.	 3
3.	 Accomplishments,
a. Truncation Level Study. Two examples of the deter-
mination of truncation level mentioned above have been initiated
and partially completed. Firstly, Dr. Robert. t. Lanqel a has
at the request of the P.I., tit a selection of MAGSAT dota
(from 5,6 November 1979) at the following tnincation levels
(here N is mathematical degree and order); 517,9,11,13,14,17.
For reference to the results, see the letter from Langel to
Benton dated 29 September 1980 toaether with its attached
table (this wa,^ distributed to all MAGSA.T workers in the field
modeling group). The interesting result of these calculations
is that nearly all of the computed Gauss coefficients up through
order and degree 7 show no further change greater than 1 nT as
higher degree and order spherical harmonics are added to the
representation, but rather more substantial, changes occurred
between N = 5 and N - 7. The conclusion appears to be that
if one is only interested in a relatively low order and degree
representation of the da,-a, N = 7 may be an appropriate place
to truncate because the zAdition of higher order terms do not
significantly affect the coefficients up through order and
degree 7.
It remains to explain why this stability first sets in at
N = 7 rather than at some other value of N. To come to better
grips with that question, further calculations (at lower N, and
filling in some of the missing higher N values) are needed; the
P.I. has requested such calculations from Mr. Ron Estes (Business
and Technolgical. Systems, Inc,),
A second truncation level result has been obtained in an
entirely different context. Rather than focussing on the
dependence of individual Gauss coefficient: on truncation level,
we (the P.T. with the collaboration of Dr. Lorant A. Muth)
have just obtained initial results for the number of critical
points of the vertical magnetic field (places where 9B r/a9 and
3Br /90 simultaneously vanish) on the core-mantle boundary.
These points are of vital importance for the method of evaluating
L M-00
r 4
cor ps fluid motions described in Progress Report #2. As the
truncation level N is increased from 5 to 12 in the 1975 main
field model of Barraclough, Harwood, Leaton and Maiin, we find
the number of cr3 deal points N  varies as fc^^ ::octsz
N	 5	 6	 7	 8	 9	 10	 11	 12
Nc . O	 25	 s l	 39	 56	 72	 98	 113
Maximum stability (corresponding to the smallest change in Nc)
appears to be in the vicinity of N = 7 In this calculation,
clearly a complicated weighted sum of Gauss coefficients is
involved, yet a similar result to the other one is obtained.
These two calculations bear further bolstering, and will be
the subject of some further effort.
b. Downward Extrapolation Through the Electrically
Conducting Mantle. We have virtually finished the study of how
one corrects for mantle conduction the vacuum extrapolation of
the poloidal geomagnetic field downward to the core-mantle
boundary. The problem is described in progress Report 02.
What has been accomplished since is the evaluation of the integral
in equation (5) of that report for a variety of mantle conduc-
tivity profiles. The results confirm the, conjecture rAde on
page 6 of that report, namely, that the effective conductivity
is not a strongly sensitive function of°the poorly known actual
conductivity at the mantle base.
No graphics are yet available, but following a;'other week
or two of work, we will begin preparing a manuscript for publi-
cation (to be included, we hope, with the next Progress Report)
under the title:
"A perturbation solution for extrapolation to the
core of the polodal geomagnetic field and its
secsalar variation"
ti
5
4.	 Significant  Results
The preliminary determination of the onset of relative
numerical stability at a truncation leve ^ :)` '	 7 ^',n two
independent studies is thought to be a potant1ally signifi-
cant result of practical value for field modeling. It requires
further substantiation and explanation before dissemination.
Publication
The 32-page manuscript entitled "lnvicnid, Frozen-Flux
Velocity Components at the Top of Earth's Core from Magnetic
Observations at Earth's Surface: A New Methodology," included
with Progress Report #3, has been accepted for publication,
probably in the July 3;981 issue of Geophysical and Astrophysical
Fluid Dynamics. The editor has requested that it b y Part 1 of
a two-part paper, where the second part will give numerical
results of applying the techniques to data (a suggestion we
intend to implement).
S. Recommendations
None.
8.	 Data Utility
The Principal Investigator found the discussions of the
MAGSAT data set at the December Investigators Meeting both
interesting and useful As a result, several reques is for
auxiliary data are in process. Dr. Joseph Cain's polar plots
of the MAGSAT orbits, Dr. Masahisa Sugiura I s tabulation of Dst
during the MAGSAT mission, and microfilm MAGSAT fine altitude
latitude plots (from r. Kent Hills) are all being acquired.


The discovery of simple, theoretically sound upper limits for geomagnetic moments (dipole, quadrupole, etc.) provides a significant use of MAGSAT data, establishes useful constraints for future magnetic models, and bears strongly on the probable time required before the next polarity reversal can occur. The field models of MAGSAT data are of prime use and are highly suitable as supplied to date

  
 
 
N O T I C E 
 
THIS DOCUMENT HAS BEEN REPRODUCED FROM 
MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT 
CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED 
IN THE INTEREST OF MAKING AVAILABLE AS MUCH 
INFORMATION AS POSSIBLE 
https://ntrs.nasa.gov/search.jsp?R=19810012884 2020-03-11T17:59:33+00:00Z
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Quarterly Status and Technical Progress Re port #5
(Covering the Period 1 January 1981 - 31 March 1981)
0.0.9 11
(E81-10093)	 INVES116AIlON OF .;EOMhGNLTIC
FIELD FOnECASTIN6 ANC FLUID CYHAMICS OF TdE
CORE L)uarterly Status 'technical Progress
Report, 1 Jan. - 31 liar. 1981 (Colorado
Uuiv.) o p HC A02/1F AJ1	 CSCL 06G G3/43
N81-21413
Unclas
00i^93
NASA Contract NAS5-25957 (MAGSAT)
Investi qation of Geomaonetic Field Forecastina
and Fluid Dynamics of t he Core
RE CE: IVEU
APR 6 , f?i r
SIS19G2.6
/Y1- c36
7-We ff
Princi pal Investi qator: Edward R. Benton
Department of Astro-Geovhysics, University of Colorado
Boulder, Colorado 80309
- t
1 April 1981
21. Problems
N7 new problems have arisen. Moreover, it has been learned
that what was thought to be a problem (the fact that the domestic
travel contract budget of $500 was exceeded in making the trip
for the December 1980 MAGSAT Investigations Meetinq at GSFC, see
Progress Report $4) is not such a Problem after all because of
the government Policy allowing
 automatic reallocation to cover
such an excess up to a limit of $500. Therefore, official
permission to exceed the contract bud get is not being requested
of NASA.
2. Approach
New approaches are being developed in two areas of interest,
(a) use of MAGSAT data alone to evaluate theoretical upper limits
to the present dipole and quadrupole magnetic moments of the
earth, and (b) use of MAGSAT data to provide constraints on future
geomaqnetic field models.
a. Upper Limits to the Present Dipole and Quadrupole Moments
of the Earth. Several Possible global measures of the strength
of the geomagnet exist (such as ma gnetic dipole moment, mean
square surface field intensity, magnetic ener gy outside the core,
etc.), but most of these can change quite rapidly (in a matter of
decades to centuxies). However, the "total oole-strength" of the
earth (Bondi & Gold, 1950) defined as
2 71	 71
P(rc ,t) E J	 f I B r ( r c * e Apo# t) I r c 2 sined6do 	 (^.)
0	 0
where r  is the core radius, should, theoretically, only vary on
the several-thousand-year time scale fcr ohmic dissipation in the
core.
We intend to make a careful evaluation of P from MAGSAT data
above, but will also introduce a new way of doin g so. Use of
Stokes' theorem and the absence of magnetic monopoles PeriAts (1)
3to be re-expressed as a contour intearal of a magnetic vector
potential, A, around null-flux curves, C o , on the core-mantle
boundary:
P(rc ,t) = 2 f.
-
A(rc16,0,t)•ds	 (2)
o
This form is more convenient, numerically, than (1) and is also
less sensitive to truncation level, since spherical harmonic
se-ies for A converge more rapidly than those for B. Recently,
Hide and Malin calculated P from (1) at 1965 and obtained
P(rc ,1965) = 3.60.101 m2.
By repeating this at 1980, using (2), we can (i) test the above
new methodology, (ii) do away with a Possible dependence of P on
secular variation models (since MAGSAT data are essentially
instantaneous in time), and (iii) compare P at 1965 with P at
1980.
We will also re-evaluate P at earlier epochs (up to a century
or so ago) from existing geomaqnetic models to verify that P is a
slowly varying function of time (results of Hide and Malin suggest
that P can perhaps be estimated to within less than 1% with
geomaqnetic field models truncated beyond dearee N = 7).
Assume, for the moment, that P is constant in the near term.
Shen we can obtain an upper limit to the dipole moment of the
earth, as follows. Rearranqe the field lines crossinq r = r 
into an axial, purely dipolar configuration (without omitting any
field lines or introducing new field lines). Calculate the
dipole moment of the resultinq field, calling its Gauss coefficient
G 1 0 . Stated another way, the upper limit dipole moment (G10re3)
is achieved by that pure dipolar maanetic field with the same
total pole strengtb as the real earth. A useful "dipolarity
index" for the earth is, then, the ratio
C
( g 1 0 ) 2 + ( q 1 1 ) 2 + (h 1 1 ) 2] ' /  G l 0 .
a
4 ^e ^
4For 1965 this ratio was about 808, i.e., the actual dipole
strength was about 808 of its theoretical upper limit. The idea
extends simply to hiqher order moments as well (e.q., at 1965,
the quadrupole index was about 488).
b. Field Modelling Constraints from MAGSAT. If the total
pole strenqth of the earth is, indeed, nearly constant in time,
then field models should be improved by incor porating this fact
as a constraint. The accurate determination of P from MAGSAT
data will provide the correct value of P to utilize.
We have also decided how to search for other constraints.
As defined above, P is an integral on the core-mantle boundary
and therefore is contributed to, significantly, by all of the
retained spherical harmonics (although the work of Hide and Malin
does indeed reveal encouraginq tendency to convergence). It is
suspected (thouqh not yet proven) that the total pole-strength
as observed from earth's surface, r = re,
2 
r	 7/'
P(re .t) = J	 J I Br.(re,©,C,t) r e 2sin©dadu	 (3)
0	 0
althouqh not constrained in theory to vary as slowly as does
P(rc ,t), will n.,)netheless either be nearly constant or change
smoothly in time over the near term. Then, its constancy or
evaluated time change (usinq both pre-MAGSAT and MAGSAT models)
can be used to constrain P(r e ,t) at some future epoch. Since
truncated series for Br converge so much more satisfactorily at
r = re than at r = rc , this constraint will be felt much more by
the lower order harr*.onics.
Procedures similar in spirit have also been thought out in
terms of magnetic enerqy (of internal origin) stored outside
earth's core and outside the earth. This provides two further
constraints of a global, integral character.
53. Accomplishments
The accomplishments durinq this reporting period fall into
several categories.
a) Conceptualization of the new approaches to important qeo-
magnetic issues outlined in 2 above.
b) Completion of the revision to a paper which will be
published in Geophysical and Astrophvsical Fluid Dynamics this
summer under the title: "Inviscid, Frozen-Flux Velocity Components
at the Top of Earth's Core from Macnetic Observations at Earth's
Surface: A New Methodology." This constitutes a major theoretical
step forward for this prr;^^;t. Dart 2, dealing with an application
of data to the method, is to be a focus of work durin g
 the
remainder of this project.
c) Preparation of the first half of a paper proposed in the
last proqress report: "Rapid Diffusion of the Poloidal Geomagnetic
Field Through the Weakly-Conductinq Mantle: A Perturbation
Solution." The second half of this paper requires numerical work
that will be addressed during the next six months.
d) The truncation level study described in the last report
has been formalized, somewhat, and advanced. It is now intended
to examine five geomagnetic properties in a four-way collabora-
tion between Langel, Estes, Muth, and Benton. The work is
expected to be complete in time to present at the MAGSAT and the
IAGA meetings in Edinburgh.
e) Three abstracts have been prepared and submitted for
the IAGA meetings:
i) "Total Pole-Strength of the Earth from MAGSAT and
Upper Limits to the Low Order Geomaqnetic Moments" by E. R. Benton,
M. C. Coulter, and C. V. Voorhies.
ii) "Dependence of Several Geomaqnetic Properties on
Truncation Level of Spherical Harmonic Expansions," by E. R.
Benton, R. H. Estes, R. A. Lanqel, and L. A. Muth.
iii) "A Test for the Presence of Significant Vertical
Motion in the Upper-most Layer of Earth's Core" by E. R. Benton.
W.
64. Significant Results
The discovery of simple, theoretically-sound upper limits
for geomagnetic moments (dipole, quadrupole, etc.) provides a
significant new use for MAGSAT data, establishes useful constraints
for future magnetic models, and bears strongly on the probable
time required before the next polarity reversal can occur.
5. Publication
One sent by editor to the printer; three abstracts submitted.
6. Recommendations
None.
8.	 Data Utility
The field models of the MhiGSAT data are of prime use in this
investigation and are highly suitable as su pplied to date.
['


Investigation of geomagnetic field forecasting and fluid dynamics of the core

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