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NASA Technical Memorandum 104541

Geomagnetic Model Investigations

for 1980-1989: A Model for

Strategic Defense Initiative

Particle Beam Experiments and

A Study in the Effects of Data Types

and Observatory Bias Solutions

R.A. Langel, T.J. Sabaka,

and R.T. Baldwin

April 1991

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https://ntrs.nasa.gov/search.jsp?R=19910012341 2019-02-21T13:45:03+00:00Z

NASA Technical Memorandum 104541

Geomagnetic Model Investigations

for 1980-1989: A Model for

Strategic Defense Initiative

Particle Beam Experiments and

A Study in the Effects of Data Types

and Observatory Bias Solutions

R.A. Langel

NASA-Goddard Space Flight Center

Greenbelt, Maryland

T.J. Sabaka and R.T. Baldwin

ST Systems Corporation

Lanham, Maryland

National Aeronautics and

Space Administration

Goddard Space Flight Center

Greenbelt, MD

1991

TABLE OF CONTENTS

1 °

2.

3.

4.

5.

6 °

7

8

9

i0

ii

12

13

14

15

16.

17.

18.

Abstract

Introduction ............................................... 1

The GSFC(5/89-X) Series .................................... 1

Observatory Data ........................................... 4

Post 1980 Land and Selected Aeromagnetic and Marine

Survey Data .............................................. 5

Project Magnet White Sands and Remaining Post 1980

Marine Survey Data ....................................... 7

DE-2 Satellite Data ........................................ 7

Data Distribution .......................................... 8

Methodology ............................................... I0

The GSFC(5/89-X) Model .................................... 15

Discussion of GSFC(5/89-X) ................................ 18

The GSFC(4/89-X) Series ................................... 27

Discussion of GSFC(4/89-X) ................................ 29

References ................................................ 39

Tables .................................................... 41

Appendix A: Listing of Internal Field Static and

Secular Variation Terms and, When Available, Their

Estimated Uncertainties for GSFC(4/89-X) and

GSFC(5/89-X) Series ..................................... 73

Appendix B: Listing of External Field Static Terms,

Dst Multiplier Terms, and Their Estimated

Uncertainties for GSFC(5J89-X) Series ................... 87

Appendix C: Listing of Observatory Vector Biases and

Their Estimated Uncertainties for GSFC(4/89-X) and

GSFC(5/89-X) Series ..................................... 89

Figures ................................................... 197

iii

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ABSTRACT

Two suites of geomagnetic field models were generated in response

to a request from Dr. David Chamberlain of Los Alamos Laboratories at

White Sands Missile Range in New Mexico concerning Strategic Defense

Initiative (SDI) research. The first suite, denoted as the GSFC(5/89-X)

series, is a progression of five models which incorporate MAGSAT data

and data from a sequence of batches as a priori information. The batch

sequence is: post 1979.5 observatory data, post 1980 land survey and

selected aeromagnetic and marine survey data, a special White Sands area

survey by Project Magnet with some additional post 1980 marine survey

data, and, finally DE-2 satellite data. These models are of 13th degree

and order in their main field terms and degree and order i0 in their

first derivative temporal terms. A first degree model for the external

field with terms proportional to Dst, is included. The second suite,

denoted as the GSFC(4/89-X) series, consists of four models based solely

upon post 1983.5 observatory and survey data. They are of degree/order

i0 in main field and 8 in a first degree Taylor series. Certain models

also include three vector biases for each observatory where possible.

The models in this suite differ to the extent that these biases were

either not modeled, applied but not adjusted, or applied and adjusted.

A comprehensive error analysis was applied to both series, which

accounted for error sources such as the truncated core and crustal

fields, and the neglected Sq and low-degree crustal fields. Comparison

V
of the power spectrum of the MGST(10/81) model (Langel and Estes, 1982)

with those of the GSFC(5/89-X) series shows good agreement, which

attests to the validity of the modeling technique and the data used.

Except for model 5, the GSFC(5/89-X) series agrees reasonably well with

the IGRF85 model, a test that propagation of the MAGSAT model to 1985 is

not badly in error. However, discrepencies in secular variation

coefficient differences suggest a small possibility of systematic error

in the DE-2 data. Inter-comparison of the GSFC(4/89-X) power spectra

seems to imply that the inclusion of observatory biases generally

reduces the level of high frequency noise introduced to the system, even

over the case in which a comprehensive error analysis is incorporated.

Finally, a comparison between the power spectra of the two series

reveals the need for additional data, such as Magsat, to supplement that

of observatories and surveys in order to establish the baseline or

static field, and the need for adequate model expansion to negate the

effects of signal aliasing.

vi
i. Introduction

Twoseries of geomagnetic field models were produced in May of 1989

at Goddard Space Flight Center (GSFC) for Strategic Defense Initiative

(SDI) research at White Sands Missile Range in New Mexico. The first

series utilized a Magsat a priori model to fix the model fields at 1980

and to provide a basis for determining observatory biases (Langel et

al., 1982). The second series did not incorporate Magsat data, but was

restricted to post 1985 data. The two classes of models allow

investigation of the value of propagating the very accurate field

description from Magsat data nearly ten years into the future versus the

accuracy of using only data nearly cotemporaneous with the model epoch.

These models were undertaken at the request of Dr. David Chamberlain of

Los Alamos Laboratories for use in a particle beam experiment. At the

same time, they were of interest as a means of exploring the properties

of a newly upgraded observation data set and as an opportunity to

explore the differences between models derived with somewhat different

assumptions and procedures.

2. The GSFC(5/89-X) Series

The first series consists of a sequence of four models, each of

which is obtained by reducing a new batch of data from a particular

source while using the model resulting from the previously reduced
batches as both the starting and the a priori model. The series is

denoted by GSFC(5/89-X), where X indicates the sequential number of the

model.

Magnetic observatory measurements made after 1979.5 were processed

in the first batch, which resulted in the GSFC(5/89-1) model. The

GSFC(5/89-2) model was obtained by reducing all post 1980 land and

selected aeromagnetic and marine survey data, with respect to the

GSFC(5/89-1) model as a priori information. Because model accuracy was

essential at the White Sands location, a special Project Magnet

aeromagnetic survey of the area was made in the spring of 1989. The

survey consisted of over 180,000 actual vector measurements, which were

decimated and appropriately weighted for inclusion in the model. This

survey, together with the remaining post 1980 marine survey data,

comprised the third batch, which used the GSFC(5/89-2) model as an a

priori estimate, giving the GSFC(5/89-3) model. Finally, 5100 scalar

measurements made between 1981 and 1983 by the Dynamics Explorer-2

satellite, DE-2, were processed with the GSFC(5/89-3) model as a priori.

This final model is the GSFC(5/89-4), which reflects all the magnetic

data included in the series.

In an attempt to produce as accurate a field model as possible over

the White Sands Missile Range, a regionally biased model, denoted as

GSFC(5/89-5), was also generated. It used the GSFC(5/89-3) model as a

priori while reducing for a second time both the Project Magnet White

Sands survey and the Tuscon observatory data, since it is in close
proximity. Hence, these data are weighted heavily in the resultant

model.

The parameter space of the models is comprised of a 13th degree and

order spherical harmonic expansion (195 terms) for the internal magnetic

field, with an associated first degree Taylor series temporal expansion

over the first i0 degrees (120 terms), a ist degree and order spherical

harmonic expansion (3 terms) for the external magnetic field, and four

disturbance storm time (Dst) terms, for a total of 322 model parameters.

When observatories provided three magnetic field components for three or

more years, then three vector biases were modeled, which account for

local crustal and induced fields (Langel et al., 1982; Langel, 1987).

The Magsat satellite supplied over 55,000 high-accuracy scalar and

vector magnetometer data concentrated near the year 1980 as a basis for

the model used as a priori for the GSFC(5/89-1) model (Langel and Estes,

1985). Since the model epoch for the series is 1980, the Magsat data

provide a stiff constraint on the static terms of the model. Hence, the

major effects of the other data sources are adjustments in the temporal

terms. No a priori information was used for observatory bias parameters

in the GSFC(5/89-1) model, but biases (listed in Table I) from the

GSFC(II/87) model (Langel et al., 1988a), based on DE-2 satellite data

at 1982, were used as the starting model.
3. Observatory Data

Because magnetic observatories provide measurements at stationary

locations through time, they are particularly useful in resolving the

temporal change in the magnetic field. Data from 196 observatories, in

the form of annual means centered on half years, spanning the years

1979.5 to 1989, were included in the series of models. The time spans

for the individual observatories are listed in Table i. A total of 3835

magnetic field components were measured over this time by the various

observatories, which include 131 X, 131 Y, 1266 Z, 1149 D, 4 I, 1146 H,

and 8 B components. These were converted to 1252 X, Y, and Z components

for processing. Vector biases were determined for 165 of the

observatories.

The uncertainty estimates (standard deviations) assigned to the

observed X, Y, and Z components are listed in Table 1 for each

observatory. Effects of unmodeled field sources, such as the neglected

crustal and Sq fields, and the truncated core field, are accounted for

in the measurement weighting scheme by use of the correlated weight

matrix method developed by Langel et al. (1989) and summarized in

Section 8. Usin 8 the approximation described in that section, the

equivalent standard deviations for these unmodeled fields are 404 nT for

the Z, and 285 nT for the X and Y components for observatory data.

However, when modeling vector biases (Langel et al., 1982), these error
contributions may be omitted at that particular observatory, slnce the

biases in fact account for local unmodeled fields.

4. Post 1980 Land and Selected Aeromagnetic and Marine Survey Data

The post 1980 land and selected aeromagnetic and marine survey data

described in this section were statistically analyzed, i.e. uncertainty

estimates were assigned to either the raw or averaged observations,

using two methods (for a more detailed description see Langel et al.,

1988b): (i) a combination of measurement-source criteria, which

isolates systematic error resulting from common instrument and human

error, and spatial distribution criteria, which isolates errors germane

to a particular global region, with the greater of the two uncertainty

estimates being used for the observation siena; and (2) an analysis for

linearly distributed data in which an average value and associated

standard deviation are assigned to each of a series of segments of a

line of observations. The average values are the data used for field

modeling with the observation sigma taken to be the standard deviation

of the data from that line segment. For each segment the data is

rejected if taken during a period of magnetic disturbance or if the data

is not sufficiently contiguous. {NOTE: In later uses of this data, and

in data sets described in the next section, the standard deviation was

replaced by the standard error of the mean for that line segment of

data.}
°

This data set is sub-divided into 8 surveys, each of which

represents a hopefully homogeneous statistical entity. Specifically,

the post 1980 land survey data, analyzed by method i, is divided into a

1980.0 to 1982.5 sub-set and a 1982.5 to 1987.5 sub-set. The

aeromagnetic data is comprised of two collections of Project Magnet

data, each of which is sub-divlded into two time spans. The first

collection is divided into a 1980.0 to 1982.5 sub-set and a 1982.5 to

1987.5 sub-set. In order to obtain a decimated set of averaged data,

these sub-sets were first processed using method 2. The uncertainty

estimates for these averaged data sets were subsequently assigned using

method i. The second collection is divided into a 1984.0 to 1985.0 subset and a 1985.0 to 1986.0 sub-set, which were analyzed by method 2

only. The final group of data consists of total-intensity marine

measurements, which were analyzed in a similar fashion to the first

collection of Project Magnet data. This group is divided into data

residing in the 1980.0 to 1982.5 time interval and the 1982.5 to 1987.5

time interval.

Because the survey data do not generally repeat in spatial

position, biases cannot be resolved, as is the case for observatories.

Hence, the effects of unmodeled field sources must be incorporated into

the survey weighting scheme. The measurement count, the average time of

observation, and the average assigned standard deviation, which includes

an estimate of contributions for unmodeled field sources (see Section

8), are listed in Table 2 for each component present in each of the

surveys.
5. Project Magnet White Sands and Remaining Post 1980 Marine Survey Data

The special Project Magnet White Sands survey and the remaining

post 1980 marine survey data were statistically analyzed using method 2

described in the previous section. However, as noted previously, the

standard error of the mean from each linear segment was assigned as the

observation uncertainty or sigma of the mean rather than the standard

deviation of the various measurements about the mean. The White Sands

survey was considered homogeneous, while the marine surveys were subdivided into 7 groups depending on time of observation: from the years

1980, 1981, 1983, 1984, 1985, 1986, and 1987. As with the previous

survey data, the effects of unmodeled field sources were incorporated

using the correlated weight matrix. The measurement count, the average

time of observation, and the average assigned standard deviation are

listed in Table 3 for each component present in each of the surveys.

6. DE-2 Satellite Data

The Dynamics Explorer-2, DE-2, satellite was equipped with a threeaxis fluxgate magnetometer with which vector measurements were made.

However, limits in the accuracy of attitude determination preclude the

use of such data for main field modeling, even after an attempt was made

at in-flight calibration (Langel et al., 1988a). The associated
computed and corrected scalar data, which is invariant to spacecraft

orientation, are of sufficient quality for use in field modeling.

Hence, 5100 scalar data points collected between September 30, 1981 and

January 6, 1983 were included in this study. These data are described

by Langel et al. (1988a). An uncertainty of 26 nT was assigned to all

the data, and the correlated weight matrix used. The scalar measurement

count, the average time of observation, and the average assigned

standard deviation are listed in Table 4.

A listing of names of the files containing the various observation

data sets included in this study is given in Table 5. These files

currently reside on the GSFC IBM-3081 mainframe under the MVS-TSO

operating system.

7. Data Distribution

A series of global distribution plots of the observatory data used

in this study are given by year since 1980 in Figures i-I0. These data

are concentrated towards the earlier years, having an average time of

1983.2. The coverage is far better for the years 1980 through 1987,

although it is typically concentrated in Europe, sparse in the southern

hemisphere, and practically non-existant in the oceans.

The Project Magnet survey distributions are given in Figures 11-16

for each of the years 1981 through 1985 and 1989. Many of the flight

lines for the 1981-1985 surveys cover ocean areas, complementing the
observatory data and helping to establish global control. Note the

concentrated distribution of data over the White Sands region in the

1989 plot.

Figures 17-24 show the global distribution of the various marine

surveys analyzed in this study. The plots are by year from 1980 through

1987. Though the uniformity of coverage varies over time, most of the

major ocean basins are sampled to some extent. The mid to northern

Pacific and the northern Atlantic basins have particularly good coverage

while a paucity of data exists in the southern Pacific and the Arctic

basins. These surveys, however, provide the most extensive control in

the ocean regions.

The post 1980 land survey data distributions are also plotted by

year from 1980 to 1987 and are given in Figures 25-32. Like the

observatories, the surveys are typically concentrated in Europe and are

sparse in the southern hemisphere. They also provide additional

coverage in Asia, Africa, and South America, which supplements the

observatory data. Note, however, that North America and Australia are

essentially void of any land survey coverage in this study.

A distribution plot of DE-2 satellite measurements is not given in

this paper, however, one may be found in Langel et al. (1988a). Their

plot shows a uniform, global coverage that should provide satisfactory

control over regions not covered by any of the aforementioned sources.
8. Methodology

The model was derived using the method described by Cain et al.

(1967), Tarantola and Valette (1982), Langel et al. (1982), and Langel

(1987). The Bayesian least squares estimation equations are as follows:

6_n+l = (ATWA + 0_I)-I[ATW6yn + 0_l(pa-Pn)] (i)

where

_n+l is the vector of parameter adjustments at the (n+l)th

iteration,

_n is the vector of adjusted parameters at the nth iteration,

_y is the vector of residuals, i.e. measured data minus

predicted value from the previous iteration,

A is the partial derivative matrix of the measurements with

respect to the parameters,

W is the weight matrix for the measurements,

n a is the a priori parameter covariance matrix,

_a is the a priori estimate of the parameters,

and the vector of adjusted parameters at the (n+l)th iteration is:

_n+l = _n + O_n+l (2)

i0
In the GSFC(5/89-1)model, for parameters other than observatory

biases, _a was taken to be the coefficients and na as the associated

covariance matrix of a model produced with 55013 Magsat data points.

The starting model, _o, was also taken to be this model. For the

observatory biases, Qa was taken to be zero, while _o comprised the

GSFC(II/87) model based on DE-2 satellite data (Table I). In subsequent

models, _a and _o were taken to be the coefficients and Qa as the

associated covariance matrix of the previous model for all parameters,

including observatory biases.

In an effort to account for unmodeled field sources, the

observation covariance matrix is assumed to have the following form:

W-1 = V d + A*V.(A*) T + A**V**(A**)T (3)

where

W-I

Vd

A*

A**

V.

is the observation covariance matrix

is the diagonal observation noise covariance matrix

is the partial derivative matrix of the measurements with

respect to the parameters corresponding to the internal field

model expansion up to degree n*

is the partial derivative matrix of the measurements with

respect to the parameters corresponding to the internal field

above n* up to some n**, above which noise dominates

diagonal variability matrix for parameters corresponding to

internal field degrees up to n*

ll
V** diagonal variability matrix for parameters corresponding to

internal field degrees above n* up to n**

Note that the last two terms on the right-hand side of equation (3) are

sometimes referred to collectively as the "inverse correlated weight

matrix", since inclusion of these terms accounts for the correlation

between the data observations. The parameters corresponding to internal

field degrees up to n* include neglected crustal and Sq terms, and for

degrees above n* up to n** the parameters include truncated core and

crustal terms. Hence, estimates of both V, and V** are needed to

incorporate this weighting scheme. Consider the function:

n

R n = (n + I) E [(gnm) 2 + (hnm)2 ] (4)

m--0

which was introduced by Mauersberger (1956) and by Lowes (1966, 1974).

Rn is the mean square value over the Earth's surface of the magnetic

field intensity produced by harmonics of the nth degree. Now Rn is

known or can be estimated. Thus, the following may be adopted as an

estimate of the diagonal terms of the V matrices:

an 2 = Rn / ((2n + i) (n + i)] (5)

12
Note that there is an estimated Rn spectrum corresponding to each of the

field sources, i.e. core, crust, Sq, etc. Analytic expressions have

been determined for each of these spectra (Langel et al., 1989):

Core: R n = (1.349 X 109 ) (0.270) n

Crust: R n = (20) (0.9999387) n (6)

Sq: R n computed from the model of Malin (1973)

Thus, W-I may now be computed. This formulation still does not account

for unmodeled temporal change parameters, which might be important for a

ten year period.

Note that W -I is a full matrix with dimensions N by N, where N is

the number of data points reduced in the particular model. Hence, for

large observation data sets, i.e. Magsat, this computation becomes

unmanagable. An approximation is adopted to facilitate the method. The

approximation is not as satisfactory as the full calculation, but it

does provide more realistic error estimates than when the effects of

neglected terms are completely ignored.

The approximation is to neglect the off-diagonal elements of the

A**V**(A**) T term in equation (3) giving:

W -I = U + A*V,(A*) T (7)

13
where U is a diagonal matrix which includes V d and the diagonal elements

of A**V**(A**) T. Langel et al. (1989) have shown that this approximation is quite acceptable for satellite data, however, it tends to be

less accurate for closely spaced survey data. The resulting expressions

for the modeled core field, Q, and its associated covariance matrix, V_,

are

= [(A*)TU-IA*]-I (A*)Tu-I_y n (8a)

V_ = [(A*)TU-1A*]-I + V* (8b)

In previous sections estimates for the data standard deviation,

including unmodeled parameters and fields, were given and the reader

referred to this section for an explanation of how those estimates were

obtained. The estimate was taken by consideration of equation (3). If

the second term on the right is neglected and only the diagonal terms

from the third term considered we have

V d' = V d + diag[A**V**(A**)T]. (9)

The quoted data standard deviations were derived from (9) by taking the

rms of the terms corresponding to the particular data type and

component.

14
9. The GSFC(5/89-X) Model

The field is assumed to be curl free and representable by a

potential function in the form of the usual spherical harmonic series:

V = a

n* n

_ (a/r) n+l [gnCOSm_ m _ + hmsinm_]P (cos@)

n=l m=0 n

n** n

+ a E F. (r/a)n[<cosm_ + smsinm_]Pn m(cOso)n

n=l m=O

(i0)

where a is the mean radius of the earth (taken to be 6371.2 km), r, 8,

and # are the standard spherical coordinates, and the Pnm(COS@) are the

Schmidt quasi-normalized form of associated Legendre functions of degree

n and order m. The magnetic field is then given by

B = -VV (ii)

Theoretically, (i0 and (ii) hold only if n* and n** go to infinity and

when the region of validity is source free. The measured internal B

contains contributions from both the Earth's core and from its crust; n*

is chosen so that V represents fields from the core but not the crust,

to our best estimation. Langel and Estes (1982) concluded that the core

field dominates for n < 13 and the crustal field for n > 15 so, as from

Langel et al. (1980) and Langel and Estes (1982), we have chosen n* =

13. Because DE-2 and Magsat pass through regions of field aligned

15
currents, the source-free assumption does not strictly hold. However,

these currents have little effect on the field magnitude (Langel, 1974),

so the procedure for Magsat data was to use component data equatorward

and scalar data poleward of 50 ° geomagnetic latitude. Only scalar data

were used from DE-2.

The main contribution to the external portion of B comes from the

equatorial ring current, with contributions also from magnetopause and

magnetotail currents. Near the Earth, fields from these sources tend to

be aligned mainly along the dipole axis and are well described when

n**=l. However, unlike the field from the core, the external fields

vary considerably with both universal and local time. The hourly Dst

index is commonly taken to be an indicator of the relative change of

these fields with universal time, and the local time variations are

generally small during magnetically quiet periods. The following

relationship was determined between the degree one external terms and

Dst from Magsat data:

ql 0 ffi18.7 - 0.63 Dst (nT) (12a)

qll I -l.1 - 0.07 Dst (nT) (12b)

sll = -3.1 + 0.17 Dst (nT) (12c)

16
The gl 0 internal coefficient is also affected by the presence of time

varying external fields and can be expressed as a constant term

representing the contribution from the Earth's core plus a Dst related

term:

gl 0 - -29986.6 - 0.17 Dst (nT) (13)

This formulation differs from that used previously by Langel et al.

(1988a) in which the external variation in the gl 0 coefficient is

proportional to the ql 0 coefficient. Transformation between the two

formulations is effected by the use of equation (12a) as a function of

Dst. These external and Dst multiplier terms listed above are part of

the model derived from MAGSAT and used as a priori to the GSFC(5/89-X)

series.

The temporal variation in the internal field is modeled using a

first degree Taylor Series expansion about the epoch e:

gnm(t) - gnmCe) + gnm(e) (t - e) (14)

where t is the evaluation time. The secular variation is considered

negligible at and above n = ll for this analysis.

A listing of the GSFC(5/89-X) series model parameters and, when

available, their estimated errors is provided in the appendices.

Specifically, the static and secular variation components and errors of

17
the internal field Gauss coefficients are listed in Appendix A, the

static component and error of the external field Gauss coefficients and

the Dst multiplier terms and errors are listed in Appendix B, and the

observatory vector biases and errors are listed in Appendix C. Note

that Appendix C does not include the GSFC(5/89-5) bias listing.

A "global" file is generated for each observation-batch processed

by the modeling software. It contains the updated model and associated

covariance, parameter space, and batch information. Table 6 lists the

names of the global files currently residing on the GSFC IBM-3081

mainframe under the MVS-TSO operating system which were generated for

each of the GSFC(5/89-X) series models.

i0. Discussion of GSFC(5/89-X)

Each of the GSFC(5/89-X) series model analyses were examined for

internal consistancy. Firstly, the data weighting remained fixed

through each iteration on a particular batch of data. Hence, solution

convergence was realized after only a few iterations. Secondly, the

total weighted residual variance was found to decrease with iteration

number in all analyses. Hence, the estimator was generally able to

extract the signal from the data, allowing it to determine a valid

search direction for the model adjustment. Furthermore, the weighted

residual variances for each observed magnetic component type decreased

with iteration number in all analyses, thus indicating that each

component type contained observable signal.

18
An inter-comparison was also made between successive members of the

series to assess the effects of each new batch of data on the parameter

space of the model. In order to facilitate a quantitative comparison,

coefficient differences between successive models were computed for the

internal field at various times. In general, the coefficient behavior

is as expected: (i) the static terms vary only slightly with the

appending of new data because of the volume of Magsat data already

reduced, while the secular variation terms are more significantly

influenced by the new data, (2) the percent change in coefficients

increases with increasing spherical harmonic degree, since the higher

degrees are more sensitive to noise levels in the data, and (5) the

variation in static terms generally increases as the difference between

the model epoch and the time of comparison increases.

Specifically, the comparison between GSFC(5/89-1) and -2 at year

1980 showed a static coefficient change of < 5Z for all terms except the

g134 term, which changed by 18Z. As noted, the change in secular

variation coefficients generally increases with increasing spherical

harmonic degree. The coefficient differences at year 1980 between

GSFC(5/89-2) and -3 again indicate a general static change of < 5% and a

secular variation change that roughly increases with increasing degree.

Where large percentage changes in coefficients do occur, e.g. 395Z for

_84 and 237Z for _i08, it is for coefficients very small in magnitude.

Hence, the effects of the two survey data batches on the model parameter

space are about the same. The coefficient comparison between GSFC(5/89-

19
3) and -4 at year 1980 reveals that most of the static change is < 5Z,

but, at the higher degrees, there are several coefficients that change

by more than that, i.e. 35I for h13 II, 45Z for h138, and 28Z for g1212.

The change in secular variation coefficients is much greater overall

than those observed in the previous comparisons, the largest being 77!IZ

for 4101 and 8119Z for _96. Again, however, all of the high percentage

changes occur for coefficients which are very small, so that the real

change is small in spite of the large percentage. Evidently, the DE-2

satellite data exert a much stronger influence on the model parameter

space than the survey data.

Plots of the first three spherical harmonic degrees (first 15

coefficients) through time for each of the models in the series were

superposed along with the IGRF85 model (Figures 33a-i). The attendant

error bars for GSFC 5/89-4 were also included. A similar suite of plots

(Figures 34a-i) were made with the GSFC 5/89-4 model subtracted from

each model, which allows a more detailed comparison between models.

Though the observation information reduced in the IGRF85 model may be a

subset of that used in the GSFC(5/89-X) series, the methodology differs,

so the inclusion of the IGRF85 coefficient plots provides an independent

check of this new series of models.

Examination of the plots indicates that models GSFC(5/89-1), -2,

and -3 are quite close. In fact, they are hardly distinguishable in

Figures 33a-i and are generally closely grouped in Figures 34a-i. These

models will be collectively referred to as "G" models. As previously

20
noted, the bunching of the G models is a result of their secular

variation being largely determined by observatory data. Model

GSFC(5/89-5) is often considerably different than the G, the IGRF85, and

the GSFC(5/89-4) models. This is to be expected since this model was

"forced", by data distribution and weighting, into close agreement with

the 1989 White Sands data. On the other hand, GSFC(5/89-4), hereafter

called D because of the inclusion of DE-2 data, sometimes shows fairly

close agreement with the G models (g2 l, g22 , h22, g32, h32, g33, and

h33), sometimes diverges significantly from the G models (gl 0, g20, g30'

g3 I, and h31), and sometimes is in between (gl I, hll, and h21). The

secular variation of this model is modified over that of the G models by

the presence of data from the DE-2 satellite. Though speculative, we

note that the fact that the n=0 terms in model D all diverge

significantly from the G models may possibly indicate a systematic bias

in the DE-2 data.

As noted earlier, inclusion of the IGRF85 in Figures 33 and 34

gives an independant verification that nothing radical has gone wrong.

Except for the GSFC(5/89-5) model, the series appears to be in

reasonable agreement with the IGRF85 model, a least over the first three

degrees. Only a slight shift is present in the static terms, and the

linear secular variation terms agree in sign and are close in magnitude.

It should be noted at this point that the parameter space of the IGRF85

model is different from that of the GSFC 5/89-X series, being a 10th

degree spherical harmonic expansion for the internal field with a linear

21
Taylor series representation for secular variation over the first 8

degrees. Thus, the effects of aliasing alone in the IGKF85 model would

be expected to produce some discrepencies.

The plot patterns also confirm the expected behavior of the

GSFC(5_89-X) series. For instance, all the plots for a particular

coefficient radiate from a point at year 1980 and do not diverge

appreciably over the next 9 years, except for the GSFC(5/89-5) model.

The error bars for GSFC(5/89-4) also exhibit the same behavior. We note

that for most of the coefficients plotted, the GSFC(5/89-1) and -2 and

-3 models lie outside the error bars for the -4 model, which reflects

all the data. This could indicate that the actual temporal change is

not well modeled by a linear time function, could simply indicate that

the global coverage of the observatory and survey data is inadequate, or

could reflect some as yet undetected bias in the DE-2 data. Conversely.

the comparison between GSFC(5/89-1), -2, and -3 coefficient plots

reveals very little difference. This indicates that the survey data and

observatory data are in very good agreement and that the GSFC(5/89-1)

model, which reduced all post 1979.5 observatory data, is dominant in

the determination of the secular variation terms.

It is clear that if there is any fundamental difference between

models it is between the secular variation of models -3 and -4. Table 7

displays the differences between both the main field and secular

variation coefficients of these models. It also shows the appropriate

for comparison, i.e. a 2 = (a3)2 + (a4) 2. For comparison, another column

22
gives the "degree sigma of the difference", which is defined as the

standard deviation of the coefficient differences for a particular

spherical harmonic degree. One would expect q and the degree _ to be of

comparable value if the parameterization of the models is accurate and

if the models are derived from independant data populations.

Examination of the Table shows that the differences between the main

field coefficients is negligible, much smaller than the G. This

reflects the fact that the predominant data set determining these

coefficients at their epoch, 1980, is from Magsat and is common to both

models.

On the other hand, the secular variation differences are, in

general, significantly larger than the 0 estimated in the fitting

procedure. The substantial secular variation coefficient differences

must result from the presence of the DE-2 data in one model but not the

other. That these differences are larger than statistically expected

may be due to one of several reasons. First, the effects of secular

variation were not included in the correlated weight matrix calculation.

These might be significant and should be investigated. Second, the

secular variation parameterization, a linearized Taylor series, might

not adequately describe the temporal variation over the ten year period

of the data. Third, the DE-2 data might contain a small bias of some

sort.

There will always be some question concerning the validity of the

DE-2 data. The lack of simultaneous absolute (scalar) data preculudes

23
detection of instrument drift. We have noted the effects of including

DE-2 data in the -4 model. Those effects are important, but they could

easily reflect actual field properties as opposed to a systematic bias

in the DE-2 data. In short, the evidence for systematic bias in the DE2 data is weak and inconclusive at best. Accordingly, the GSFC(5/89-4)

model is considered the "final" product of this study. Table 8 gives a

brief summary of the statistics of the various data types to the

GSFC(5/89-4) model and to the suite of GSFC(4/89) models to be discussed

in later sections. Unfortunately, the statistics of observatory data

with their determined biases is not available as this paper is written.

The means and stardard deviations for both observatory and survey data

are typical. One feature of the standard deviations is that those for

survey data are typically less than those for observatory data. This is

attributed to two factors which tend to reduce the contribution of

crustal anomalies to the survey data. First, the survey component data

is largely made up of data from Project Magnet. In data acquired at

aircraft altitudes the anomaly fields are naturally attenuated because

of the height of the aircraft above the surface. Second, both the

Project Magnet and the Marine Survey (B) data are filtered along track

to deliberately minimize the effects of crustal fields.

A series of global maps of the various magnetic field components

(Figures 35a-g) and their estimated errors (Figures 36a-g) were computed

from GSFC(5_89-4) at 1989 on the earth's surface. Similar maps are

24
included for the secular variation (Figures 37a-g) and its estimated

error (Figures 38a-g). The general morphology of the various features

in each of these maps is consistant with maps produced in other studies

at different epochs if the effects of westward drift and other temporal

processes are taken into account (see Langel, 1987; Langel et al.,

1988a). Now the uncertainty maps are germane to the distribution of the

data that is being reduced. In the case of the GSFC(5/89-4) model, the

North American and European regions exhibit the lowest uncertainty

levels while the oceanic areas show the highest levels, thus reflecting

the paucity of data over the oceans with respect to the continents.

Uncertainty maps were also produced for the special GSFC(SJ89-5) model,

but they are not included in this report. As expected, they show a

bulls-eye feature of low uncertainty over the White Sands Missile Range.

Power spectra of the form of equation (4) were determined for the

various models of this series. These spectra map the signal strength

distribution over the harmonic degree range and, hence, can indicate the

presence of signal adulteration by noise. The R n spectra of GSFC(5/89-

i), -2, -3, and -4 were found to be nearly identical. Thus, from a

relative standpoint, the signal from each of the observation batches was

resolved at a similar level. A plot of the GSFC(5/89-4) and -5 spectra

(Figure 39) shows that the latter contains more power at degree 13.

This "flattening" of the power slope is likely a manifestation of the

inclusion of high frequency white noise introduced by signal biasing in

the spatial domain. It is also of interest to see if these spectra

25
conform to a "standard" spectrum, which would indicate the validity of

the estimation technique and the quality of the observation data.

Figure 40 is an overlay of the GSFC(5/89-4) Rn spectrum on that of the

MGST(10/81) model. This latter model is a degree 23 spherical harmonic

expansion of the internal field with secular variation terms absent,

based solely upon Magsat data (Langel and Estes, 1982). This is

considered the "standard" model for comparison in the study. The

spectra appear to be in good agreement with only a slight deviation at

degree 12. Evidently, both the modeling techniques and observation data

employed in the GSFC(5/89-1) through -4 models are acceptable by this

criteria.

In conclusion, the GSFC(5/89-X) series appears to be valid suite of

models, useful for geomagnetic research. It not only utilizes the most

complete observation data set available to GSFC, but also incorporates

the most comprehensive error analysis used to date at GSFC. Except for

the special GSFC(5/89-5) model, the series seem to agree reasonably with

the IGRF85 model. The results of the analyses were within the bounds of

the expected, with no egregious behavior detected. At the same time,

the differences between the secular variation coefficients with and

without the DE-2 data indicate that possibly the parameterization is

somewhat inadequate or that the DE-2 data has some sort of systematic

error. The GSFC(5/89-4) model is the representative of the series,

since it reflects all the data reduced. This model was subsequently

sent to White Sands for SDI research where it produced satisfactory

results (Chamberlain, personal co_nunication.)

26
ii. The GSFC(4/89-X) Series

The GSFC(4/89-X) series consists of four field models. Each model

was derived using observatory and survey data after 1983.5. These

models differ to the extent that the correlated weight matrix and the

solution for observatory vector biases were either applied or not

applied. The observatory and survey data used in this series are a subset of that used in the GSFC(5/89-X) series. Specifically, the post

1980 land survey from 1982.5 to 1987.5, Project Magnet collection 2 from

1984 to 1985 and from 1985 to 1986, total-intensity marine from 1982.5

to 1987.5, marine surveys from 1983 to 1988, and the Project Magnet

White Sands survey were all included in this series. The measurement

count, the average time of observation, and the average assigned

standard deviation, which includes contributions from unmodeled field

sources, are listed in Table 9 for each component present in the

composite survey data set. The observatory data used are the 1983.5 to

present sub-set of those listed in Table i. The assigned observation

uncertainty estimates and GSFC(II/87) biases listed in this table are

also applicable to this series.

For this series of models the parameter space is comprised of a

10th degree and order spherical harmonic expansion (120 terms) for the

internal magnetic field and a first degree Taylor series temporal

expansion over the first 8 degrees (80 terms) for a total of 200 model

27
parameters. Certain models also adjust the three vector biases for each

observatory having at least three observations of each vector component.

The epoch of the models is 1989.411 and the starting models, for

parameters other than observatory biases, are the IGRF85 model

propagated to this epoch. No a priori information was included in any

of the models.

Differences between models in this series lie in the way

observatory biases are incorporated, as summarized in Table 10. The

GSFC(4/89-1) model applied, but did not adjust, the GSFC(II/87)

observatory biases. If a particular observatory had no bias values from

GSFC(II/87), the bias was set to zero; no correlated weight matrix was

applied to those stations. In the GSFC(4/89-2) model, the observatory

biases were adjusted, using the GSFC(II/87) model as a starting point,

provided at least three observations of each vector component were

present for the observatory, otherwise, the correlated weight matrix was

applied to that station. In the GSFC(4/89-3) model, the GSFC(4/89-2)

observatory biases were a priori and held fixed. If these biases were

not available, the GSFC(II]87) biases were used; and if neither set were

avaialble, the correlated weight matrix was applied to that station.

The GSFC(4/89-1), -2, and -3 models were each iterated three times. In

the GSFC(4/89-4) model, which required five iterations, observatory

biases were not applied, so the correlated weight matrix was universally

applied.

28
A listing of the GSFC(4/89-X) series model parameters and, when

available, their estimated errors is provided in Appendix A for

parameters other than observatory biases; Appendix C contains the

observatory biases.

Table i0 lists the names of the global files currently residing on

the GSFC IBM-3081 mainframe under the MVS-TSO operating system which

were generated for each of the GSFC(4/89-X) series models.

12. Discussion of GSFC(4/89-X)

Coefficient differences between the GSFC(4/89-X) models are

discussed in order to understand the effects of the differing solutions

for observatory biases and the extent to which observatory biases and

the correlated weight matrix influence the determined models.

Referring to the Table of coefficients in Appendix A, the 6's

assigned by the fitting procedure to models -i and -3 [Note: the a's for

model -3, not given in the table, are almost identical to those for

model -i.] are considerably smaller than those assigned to the other

models. These are the models for which observatory biases were

furnished as a priori information to the model. Model -4 shows the

largest coefficient a's from the fitting process. This reflects the

fact that no biases were given or solved for and the correlated weight

matrix was given full play. Model -3 applied observatory biases, when

available, hence the model had more parameters than model -4, which

29
resulted in lower estimated coefficient a's. On the other hand, no

satellite data were available for this model so that the bias solution

is much less certain than when such data is present. Further, without a

priori biases the fitting process had less information than models -i or

-5, hence the estimated coefficient a's are higher than for those

models.

The meaningfulness of the estimated coefficients and their 6's

depends upon the accuracy of the model parameterization. In the cases

of models -i and -3, the a priori observatory bias information was

furnished as given, i.e. with no accompanying statistical estimate of

the accuracy of the biases. This is tantamount to assuming they are

perfectly known, i.e. with a = O. Since these biases are in fact only

known approximately, this is not an adequate parameterization and the

resulting estimated coefficient a's are probably too low.

Differences between various models are tabulated in Table 12. The

first three columns are the differences of models -2, -3 and -4 from

model -I; the second three columns are the differences of models -I, -3

and -4 from model -2. Table 13 summarizes the sigmas of these

differences by degree. It is immediately clear that models -2 and -3

are very similar. This is to be expected. The idea behind model -3 is

as follows. Model -2 solved for observatory biases. Lowes (1985) has

shown that when this is done the observatory data contribute mainly to

the secular variation solution. Their effect on the main field

coefficients is diminished over fitting procedures where biases are not

3O
solved for. Model -3 is like a further iteration of model -2, except

that the observatory biases are held fixed so that the observ-atory data

can be fully used in determining the main field coefficients. As noted

above, the biases should be included with proper statistical

information. As a guess, the actual coefficient _'s for model -3 are

probably very close to those of model -2.

Models -4 and -2 are the "most" different in main field

coefficients, particularly for degrees 2, 3, 4, and 6, yet comparison

indicates these differences to be consistent with the estimated

coefficient a's.

Both the -i and the -3 models were furnished a priori observatory

biases, yet the models are significantly different. The biases

furnished the -i model were from the GSFC(I1/87) model (Langel et al.,

1988a) which included Magsat and DE-2 satellite data. Those furnished

the -3 model were mainly derived in the -2 model, with the remainder

coming as a supplement from the GSFC(ll/87) model, see Appendix C. Also

of relevance are the biases computed in the GSFC(5/89-4) model, which

also included Magsat and DE-2 satellite data. Comparison indicates that

the biases from GSFC(II/87) and GSFC(5/89-4) are similar to one another

wheras those from the -2 model deviate considerably. Also, the

estimated coefficient G values from the fitting procedure of the -2

model are in general quite high. We conclude that the bias

determination in the -2 model is problematic, with a statistically

poorly determined result. This is due to the absence of satellite data

31
°

to furnish a reliable baseline, relatively free from crustal magnetic

field contamination, against which the biases can be determined. The

survey data, while important, contains a large crustal field

contribution and is still too sparse to give a good baseline for bias

determination at the observatories.

Table 14 shows the differences between the secular variation terms

of the GSFC(4/89-x) models. In particular it shows the differences

between the -2, -3, and -4 models and the -1 model. Comparison with the

coefficient Table in Appendix A indicates that the differences are

consistent with the estimated a values from the fitting procedure.

Models -2 and -3 differ somewhat, but not radically, from model -I.

Model -4 shows considerably more difference. This is attributed to the

fact that model -4 did not utilize observatory biases at all. It is

also apparent in the much higher coefficient a's assigned to model -4 in

the fitting process. Model -3 is in somewhat better agreement with

model -i than is model -2. This is probably because model -i and model

-3 were furnished biases a priori, while biases were solved for in model

-2. The use of biases in all three of models -i, -2, and -3 removes the

problem of contamination by crustal fields in the observatory data.

This should permit a more accurate secular variation result.

Table 8 gives the summary statistics of the data to each of the

four models. Observatory biases are not taken into account in the

observatory statistics. Tables 15 and 16 give year by year statistics

which are also plotted in Figures 41 a - 41 n. These are all within the

32
range of "typical" values one might expect for any model. The

differences reflect the way the bias solutions effect the data

weighting. For example, model -4 with no bias solution tries to fit the

observatory data strictly with the spherical harmonic series. As a

result the magnitude of the mea_._._nn observatory residuals tend to be higher

and the scatter (G) of the observatory data lower than the other models

which included some sort of bias, either a priori or solution. This

attempt to fit the crustal signal in the observatory data results in an

increased misfit (q) for the survey data. Models -2 and -3 generally

show very similar statistics, as might be expected from the previous

discussion. The mean deviation of these models is moderate and their

standard deviations are the lowest for this suite. This is attributed

to the fact that these models solved for or utilized biases to the

observatory data determined from this same data.

Some instructive "peculiarities" occur for the -01 model as a

consequence of setting some a priori biases equal to zero with no error,

i.e. a priori G = 0. This is best illustrated by noting the mean and

sigma for the Z component of survey data for 1985.5. From Figures 41j

and 41n both quantities are much larger than for the other models. The

survey data involved is from a single Project Magnet survey over the

region from the southern tip of South America to the corresponding

peninsula of Antarctica (See Figure 42). Forty four points were

extracted and included in the fit from this survey. The observatory

Arctowski is located in this region of Antarctica. It turns out that

33
the a priori bias value for Arctowski in the -01 model was taken to be

zero. However the Z bias at Arctowski from the -02 model was 609 nT[

The model weighting was thus such that the fitting process tried to fit

a 609 nT anomaly as though it were from the core, with high weight. The

Project Magnet data, from the same region, were not weighted as heavily.

Figure 42 shows the resulting residuals in the Z component of the

Project Magnet data, from which much of the crustal field has been

filtered. The result is a highly negative mean value for the Magnet

data since the field is trying to fit the positive anomaly at Arctowskil

Also, the scatter of the Project Magnet data was increased, as given in

Table 16 and Figures 41j and 41n.

The "lessons" to be learned are several. One should not assign a

zero bias with high weight when the actual bias is unknown. Further,

when a priori biases are given, it is important that they carry proper

weights and it is probably best to adjust them in the fitting process

even though minimal new information is available.

In Figures 43a-i, the first 15 coefficients from each of the

GSFC(4/89-X) series models are plotted from 1980 to 1989 along with

those from the IGRF85. Included with these figures are the error bounds

associated with the GSFC(4/89-4) model. The plots reemphasize the

discussion of the last few paragraphs, i.e.: All of the models are

"reasonable" in that they are not wildly different. There is some

tendency to converge near 1985, which is near the midpoint of the data.

In general the -4 model is the maverick of the lot, i.e. its temporal

34
change often shows a different trend than the other models. Recall that

this is the only model not making use of observatory biases. Models -2

and -3 show very similar behavior, as already noted, and model -i is

probably most like the IGRF of the models plotted here.

Differences between various main field coefficient_ projected to

198 3 are shown in Table 17 and the G of these differences by degree is

shown in Table 18. These Tables include the GSFC(5/89-3) and -4 models

as well as the GSFC(4/89-x) models. Because of the more extensive data

set, including satellite data, which also permitted meaningful solution

for observatory biases, the (5/89) models are considered the more

accurate, i.e. the standard. From the Tables, as might be expected, the

two (5/89) models are in closest agreement. Of the (4/89) models, the

-I model is in closest agreement with the (5/89) models. This reflects

the fact that the biases furnished the -1 model were in fairly close

agreement with those used in the (5/89) models. These biases were

determined from a different data set, i.e. from an earlier time period,

than that used in the -I model, thus they are based on independant

information. However, as pointed out above, they should have been

accompanied by an error estimate. It is concluded that the -i model

coefficients are likely the most accurate of the (4/89) series, but that

their stated coefficient a's are underestimated because of the lack of

error estimation on the bias values.

35
Of the other (4/89) main field models, the -4 model is in

considerably better agreement with the (5/89) models than are either the

-2 or -3 model. This, perhaps, makes sense, as this model is most

nearly correctly parameterized; it does not tr 7 to solve for observatory

biases without satellite data to furnish a baseline; and it incorporates

the correlated weight matrix. The -2 model attempts solution for

observatory biases, probably without an adequate data base to do so, and

the -3 model incorporates those biases without proper error estimates.

Differences between secular variation coefficients from the (5/89-

3) and -4 and the (4/89-x) models are shown in Table 19 and their 6's by

degree are given in Table 20. Again as expected, the (5/89) models are

in closest agreement. Next is the (4/89-2) model in which biases were

solved for and the observatory data allowed to determine the secular

variation without undue contamination from crustal fields.

Figures 44a-i are similar to Figures 43a-i, except the coefficients

from the GSFC(5/89-4) model are plotted rather than those of the IGRF85.

The GSFC(4/89-1) model shows close agreement to the GSFC(5/89-4) for the

gl 1, h11, 822, h22, 831, 833 , and h33 terms. The GSFC(4/89-2) compares

well with the GSFC(5/89-4) for the g20, 821, g30, and h31 terms, while

the GSFC(4/89-3) agrees only with the g32 and h32 terms, and the

GSFC(4/89-4) agrees only with the gl 0 and h21 terms. As with the IGRF85

model, the GSFC(4/89-4) exhibits severe deviation from several of the

GSFC(5/89-4) coefficient trends.

36
An assessment of the GSFC(4/89-X) series was also made based upon

their R n spectra. Since the same observation data was reduced in each

of the constituent models, any variation in the power spectra must

reflect differences in modeling techniques. Figure 45 is an overlay of

the Rn spectra for GSFC(4/89-1), -2, and -4, and GSFC(5/89-4). The

GSFC(4/89-3) spectrum was omitted since it is almost indistinguishable

from that of GSFC(4/89-2). The spectra show a consistent increase in

degree 7 through I0 harmonic power from GSFC(4/89-1) to -2 to -4, except

at degree i0 where the GSFC(4/89-4) power curve exhibits a peculiar

steepening, making it coincident with the GSFC(4/89-1) curve. Recall

that the GSFC(4/89-1), -2, and -3 models all incorporate the effects of

unmodeled field sources through various applications of the observatory

biases, and that the GSFC(4/89-4) accounts for them via the correlated

weight matrix only. We conclude that the use of observatory biases

generally reduces the level of high frequency noise introduced in the

system over that introduced by the use of the correlated weight matrix

alone. Variation in the GSFC(4/89-1), -2, and -3 spectra may simply be

a function of the biases used. In this case, the GSFC(II/87) biases

allow for better signal resolution before they are adjusted. The

GSFC(5/89-4) spectrum, considered here the standard, clearly contains

less power than the GSFC(4/89-X) series spectra above degree 7. This is

37
probably due to two reasons: first, the signal from the observatory and

survey data is probably not sufficient to allow both static and secular

variation terms to be resolved, whereas the Magsat data signal is

sufficient; and secondly, since the truncation level of the GSFC(4/89-X)

series is lower than that of GSFC(5_89-4), some aliasing of the

unmodeled degree Ii through 13 signal may be present, although use of

the correlated weight matrix should minimize this problem.

38
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Langel, R.A., and R.H. Estes; A Geomagnetic Field Spectrum; Geophys.

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Langel, R.A., R.H. Estes, and G.D. Mead; Some New Methods in Geomagnetic

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Langel, R.A., J.R. Ridgway, M. Sugiura, and K. Maezawa; The Geomagnetic

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Malin, S.R.C.; Worldwide Distribution of Geomagnetic Tides; Philos.

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4O
Table i. Observatory Biases from the

GSFC (11/87) Model

Observatory Time Span Biases (nT) Standard Deviation (sT)

Start $_op X Y Z , X Y Z

Abisko VI 1979.50 1983.50 7.5 68.1 19.0 25.0 25.0 25.0

Addis Ababa 1I 1979.50 1985.50 $74.8 6.5 120.9 25.0 25.0 25.0

Alert 1979.50 1986.50 -19.7 28.4 -208.7 25.0 25.0 25.0

Alibag XXZ 1979.50 1987.50 -215.1 449.9 602.3 25.0 25.0 25.0

Alma Ate 1979.50 1987.50 149.1 31.2 -185.4 25.0 25.0 25.0

Alueria 1979.50 1986.50 -26.9 30.7 24.4 25.0 25.0 25.0

Anmtsia 1979,50 1986.50 113.3 31,9 276.0 25,0 25.0 25.0

Annamalainsg X1 1979.50 1984.50 153.8 -91.9 -62.6 25.0 25.0 25.0

ApLa ZV 1979.50 1987.50 -30.6 216.9 -898.0 25.0 25.0 25.0

Aquila 1979.50 1987.50 -10.9 32.6 5.3 25.0 25.0 25.0

Ar©towsKi 1979.50 1985.50 0.0 0.0 0.0 25.0 25.0 25.0

Argentine Islnd 1979.50 1986.50 77.0 -85.3 475.9 25.0 25.0 25.0

Ar_i 1979,50 1987.50 112.2 -261.3 438.8 25.0 25.0 25.0

Baker Lake VII 1979.50 1987.50 170.5 -32.3 -95.8 25.0 25.0 25.0

Bangui IV 1979.50 1987.50 -130.7 -65.8 257.5 25.0 75.0 25,0

Barrow IV 1979.50 1987.50 15.7 -61.8 -48.5 30.0 25.0 25,0

Bay 3aLnt Louis 1986.59 1986.59 0.0 0.0 0.0 25.0 25.0 25.0

Bei_ing 1979.50 1986.50 617,3 -216.3 448.3 25.0 25.0 25,0

Belsk 1979.50 1987.50 105.0 132.4 298.2 25.0 25.0 25.0

Berezrmyki XX 1979.50 1980.50 -422.4 -311.5 227.5 75.0 75.0 75.0

Berezrmyki 111 1981.50 1987.50 -422.4 -311.5 227.5 75.0 75.0 75,0

Bjornoyl IX 1979.50 1987.50 -110.Z 48.7 2.6 25.0 25.0 25,0

|orok 1979.50 1987.50 -28.4 -69.6 -447.7 25,0 25.0 25,0

Boulder 1979.50 1987.49 -7.9 74.5 -156.0 25.0 25.0 25.0

Brorfelde 1980.50 1982,50 0.0 0.0 0.0 25.0 25.0 25.0

Brorfelde XX 1983.50 1986.50 0.0 0.0 0.0 25.0 25.0 25.0

Budkov 1979.50 1986.50 -34.5 -35.3 -48.0 25.0 23.0 25.0

Cambridge lay 1979.50 1987.50 115.9 -84.4 110.7 25.0 25.0 45,0

Canaries 1979.50 1986.50 -423.7 95.4 -1038.7 25.0 25.0 25.0

Canberra 1979.50 1987,50 14.7 32.1 98.0 25.0 25.0 25.0

Cape Hellas 1X1 1979.50 1907.50 -71.1 61.7 -104.1 25.0 25.0 25.0

CaJey 1979.50 1905,50 865.4 -340.7 -892.8 150.0 150.0 150.0

Cha Pa 1979.50 1979.50 -388.1 -127.2 -293.3 25.0 25.0 25.0

Cha Pa XX 1980.50 1983.50 -388.1 -127.2 -293.3 25.0 25.0 25.0

Chambon ForetXX 1979.50 1907,50 -74.7 -22.7 103.5 25.0 25.0 25.0

Chlngchun 1980.50 1985,50 -118.9 26.9 192.5 25.0 25.0 25.0

Chlrter_ Towers 1984.50 1985.50 0.0 0.0 0.0 25.0 25.0 ZS.O

Chely_mkin ZV 1979.50 1987,50 -13.8 -102.5 -94.6 30.0 30.0 30.0

Chichijima 1979.50 1983,50 -310.8 -33.0 254.0 25.0 25.0 25.0

ChJchLjima XX 198_.$0 1985,50 -310.8 -33.0 254.0 25.0 25.0 25.0

Coimbra 1979.50 1987,50 23.3 -7.4 8.3 25.0 25.0 25.0

Col|age XXX 1979.50 1987,50 -13.0 -47.7 -102.1 25.0 25.0 25.0

Costa Rice 1979.87 1979.87 0.0 0.0 0.0 25.0 25.0 25.0

Davis 1981.50 1987.50 -253.5 124.9 92.7 25.0 25.0 25.0

De1 Rio 1982.81 1988.50 0.0 0.0 0.0 25.0 25.0 25.0

Dikson V 1979.50 1987.50 -85.9 -149.3 -262.8 25.0 25.0 25.0

Dashes X11 1979.50 1986.50 -85.0 -89.1 -246.5 25.0 25.0 25,0

Dourbos 1979.50 1986.50 6.4 -21.6 77.9 25.0 25.0 25.0

Dumont Dur'ville 1979.50'1987.50 -144.5 -402.6 -2859.4 25.0 25.0 25.0

DushetL IX 1979.50 1985.50 -211.9 7.7 -95.7 25.0 25.0 25.0

41
Table I. (continued)

_ir

Fbro IV

F-skda I emui r

Fyrewe11

Fort Churchi II

Fredericksburg

Fuquene

Furs_nfeldbruck

Glenlem

Gnangora

Godhavn 1!

Gornotayezhn XI

Grahansto_n

Greet Mhale R

Grem_ Hhale RIT

Grocka

Guam

Guangzhou 1I

Halley Bay II

Ha r_ebeesthoek

Hartland

Ha ti zyo

Ha_i z,/o 11

Havana

Heiss lsland 11

He1 XIX

Herumnus

Honolulu XV

Hornmund

Huancayo

Hurbanovo

Hyderabod

Xrkutsk XX

Xst_nbl Kndilli

Jaipur

KakJ.oka XZ

Kanoya

Kanozmn

Kiev

Kiru_ 11

Klyu©hi I1

Kodaikanal 11

Krasnaym Pakhr:

La Quiaca IV

Lanzhou 1I

Lauder

Leir_ogur

Lerwick II

Lhasa

Loparskoye

Lovo

Luanda Oelas 1

Lunping

Lvov

H Bout

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1982.50

1979.50

1979.50

1979.50

1979.50

1979.50

1985.50

1979.50

1979.50

1980.50

1980.50

1979.50

1979.50

1979.92

1981.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1984.50

1979.50

1979.50

1979.50

1979.50

1979.50

1987.50

1979.50

1979.50

1979.50

1979.50

1979.50

1980.50

1979.50

1979.50

1979.50

1985.50

1979.50

1979.50

1981.50

1979.50

1979.50

1979.50

1985.50 -24.2 82.2 108.2

1983.50 0.0 0.0 0.0

1986.50 5.7 -50.3 -49.7

1987.50 -8.3 -37.6 52.6

1987.50 -117.6 41.6 -270.3

1987.50 75.2 -58.4 126.7

1982.50 131.6 -59.1 59.8

1988.25 -28.0 -10.3 9.8

1986.50 0.0 0.0 0.0

1987.50 4.1 -144.1 139.0

1984.50 284.7 -311.8 714.3

1986.50 -6.4 -14.6 -59.0

1980.08 -114.8 -2.6 53.4

1984.50 251.3 100.2 -85.1

1987.50 251.3 100.2 -85.1

1987.50 -41.0 -52.1 -57.9

1987.50 165.8 86.2 58.7

1906.50 71.4 69.2 14.8

1980.50 0.0 0.0 0.0

1985.50 94.6 5.4 56.6

1986.50 -40.4 5.9 61.1

1980.50 -15.9 -783.9 437.9

1987.50 -15.9 -783.9 437.9

1979.50 0.0 0.0 0.0

1987.50 97.8 -681.0 1117.1

1987.50 43.5 -168.6 -97.7

1987.50 9.3 -3.7 46.0

1987.50 -153.7 81.9 -332.3

1983.50 -17.7 -25.3 -46.8

1986.50 80.8 23.8 5.7

1986.50 3.2 -24.6 -56.7

1986.50 312.9 18.9 484.7

1985.50 0.0 0.0 0.0

1981.50 0.0 0.0 0.0

1986.50 177.8 -397.5 -26.0

1989.12 -7.7 14.9 -84.0

1989.12 -10.8 51.7 -34.0

1986.50 -52.7 37.5 -60.4

1987.50 0.0 0.0 0.0

1981.50 -824.5 -1829.0 -47.8

1985.50 192.1 -91.2 -18.3

1986.50 -549.5 276.1 -62.0

1987.50 140.9 -23.0 185.1

1983.50 0.0 0.0 0.0

1987.50 -18.7 10.1 -71.1

1979.50 0.0 0.0 0.0

1987.50 -277.4 607.1 -505.6

1986.50 -132.2 169.8 37.9

1983.50 0.0 0.0 0.0

1981.50 106.0 334.8 -558.2

1983.50 44.0 -10.7 -3.7

1985.50 298.7 -77.4 218.7

1985.50 15.5 47.4 51.7

1987.50 143.6 120.5 145.2

1987.50 156.1 63.6 66.9

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25 0

25 0

25 0

25 0

25 0

25 0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25 0

25 0

25 0

25 0

25 0

25 0

25 0

25.0

25.0

25.0

25.0

25.0

25.0

42
Table I. (continued)

Macqumrie Islnd

Manhay 11

H•pu_o II

Martin Vivies

Mawson

Meanook Ill

Monmmbel_u

Mirnyy III

Misallmt IZl

Mi zusm, m

Molodezhrm,_t

Mould Bay

Muntinlupa

Nagy©enk

Negyc•nk II

Nairobi

N•mpule

N• rssa rssua q

Newport

Nielegk

Nov• Kazalinsk

Novolezarovs I1

Hurmijarvi

OttaT,4

Pamltai 1I

Panag_urishte

Paratunke

Patrony

Pilaf

Pleehenitzi

Podkam Tungueka

Port Moresby

Port-Alfred

Port-Alfred l

Port-Aux-Franca

_uett• 11

Resolute Ely

Rude Skov

$abh_,kmll Z1

Sen Juln I1

Sen Pablo

5lnll II

Scott Base II

$heshnn

Shillong

Sitka III

$odankyla

South Georgia

St John 5

$tekoliniy

Stepanovke II1

$urlari II

$yowa base II

Tamenrasset III

Tamanrasset IV

1979.50

1983.50

1979.50

1981.62

1979.50

1979.30

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1981.50

1979.50

1982.75

1980.00

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.S0

1979.50

1979.50

1979.50

1979.50

1979.50

1981.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1981.50

1979.75

1979.50

1979.50

1979.50

1980.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1980.50

1987.50 283.3 -8.4 299.8 25.0 25.0 25.0

1985.50 0.0 0.0 0.0 25.0 25.0 25.0

1985.50 397.0 70.7 -126.8 25.0 25.0 25.0

1987.50 -567.6 -709.4 -2024.1 25.0 25.0 25.0

1987.50 16.3 14.2 185.8 25.0 25.0 25.0

1987.50 107,7 24.4 -143.8 25.0 25.0 25.0

1989.12 -240.0 141.6 66.2 25.0 25.0 25.0

1987.50 -100.4 40.5 -451.4 25.0 Z5.0 25.0

1980.50 0.0 0.0 0.0 25.0 25.0 25.0

1986.50 -146.6 45.0 -163.5 25.0 25.0 25.0

1985.50 -20.5 -104.7 -254.9 25.0 25.0 25.0

1987.50 -19.0 14.4 -62.0 25.0 25.0 25.0

1986.50 -55.7 -14.2 58.3 25.0 25.0 25.0

1980.50 -2.5 -10.0 -73.1 25.0 25.0 25.0

1983.50 -2.5 -10.0 -73.1 25.0 25.0 25.0

1980.50 0.0 0.0 0.0 25.0 25.0 25.0

1984.50 0.0 0.0 0.0 25.0 25.0 25.0

1984.00 -330.7 279.8 570.4 25.0 25.0 25.0

1986.50 -34.9 122.1 -131.3 25.0 25.0 25.0

1987.50 -32.0 -5.4 -85.4 25.0 25.0 25.0

1987.50 -113.5 -165.7 -6.3 25.0 25.0 25.0

1982.50 -273.9 71.0 90.3 30.0 30.0 25.0

1987.50 288.8 -115.8 87.2 30.0 30.0 25.0

1987,50 139.4 -138,7 171.9 25.0 25.0 25.0

1987.50 -653.6 -726.0 -133.7 25.0 25.0 25.0

1983.50 -191.0 -175.5 -189.8 25.0 25.0 25.0

1987.50 -346.9 217.7 238._ 25.0 25.0 25.0

1987.50 13.5 37.4 -80.9 25.0 25.0 25.0

1983.50 5,7 °16.6 -17.9 25.0 25.0 25.0

1987.50 277.9 168.0 -143.0 25.0 25.0 25.0

1987.50 44.6 -13.7 -290.6 25.0 Z5.0 25.0

1987.50 26.2 63.2 261.0 25.0 25.0 25.0

1980.50 0.0 0.0 0.0 25.0 25.0 25.0

1987.50 -818.0 1115.4 171.0 25.0 25,0 25.0

1987.50 228.9 169.9 655.1 25.0 25.0 25.0

1983.50 3.7 84.5 -54.6 25.0 25.0 25.0

1987.50 47.0 44.9 58.0 25.0 25.0 25.0

1984.50 37.6 -15.3 -55.6 25.0 25.0 25.0

1986.50 -22.2 -59.4 29.3 25.0 25.0 25,0

1987.50 -36.8 180.4 188.9 25.0 25.0 25.0

1906.50 10.7 32.7 -58.9 25.0 25.0 25.0

1987.50 -53.5 -40.1 48.1 25.0 25.0 25.0

1979.50 0.0 0.0 0.0 25.0 25.0 25.0

1985.50 -242.3 82.9 235.8 25.0 25.0 25.0

1986.50 -107.0 -79.0 -355.3 25.0 25.0 25.0

1987.25 6.5 -13.5 -67.3 25.0 25.0 25,0

1987.50 -163.9 -111.9 -600.1 25.0 25.0 25.0

1981,50 -76.7 -355.5 96.4 25.0 25.0 25.0

1987.50 35.3 16.6 4.5 25.0 25.0 25.0

1987,50 -286.0 -741.5 43.3 25.0 25.0 25.0

1987.50 -114.3 -700.3 73.0 25.0 25.0 25,0

1987.50 2.9 -34.4 -57.9 25.0 25.0 25,0

1986.50 -34.7 -37.9 21.1 25.0 25.0 25.0

1979.50 65.6 -267.2 20._ 25.0 25.0 25.0

1984.50 65.6 -267.2 20.4 25.0 25.0 25.0

43
Table I. (continued)

Tananarive III

Tangerong III

Tatuoc8 III

Tbilisi

Thule

Thule III

Tihmny II

Tiksi VI

Toledo III

Trivandrua

Tromso

Tsumeb

Tucson

Tulsa II

Tuntungan

U#jsin

Ujjain II

Urulqi

Valentim

Vannovskaya II

Vassouras

Victoria

Vostok

Voye_ovo

Vysokay Dub IV

White.shell

Hien Kobenzl

Hings_

Hitteveen

Nuhan

Yaku_sk IZ

Yangi-Bazar

Yangi-Bazar II

Yellow-Knife

¥uzhno 5akh IV

Zaymishche II1

1983.50

1979.50

1979.50

1987.50

1980.50

1980.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1982.41

1982.50

1979.50

1984.50

1980.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1979.50

1980.50

1979.50

1979.50

1982.50

1979.50

1979.50

1979.50

1983.50 0.0 0.0 0.0 25.0 25.0 25.0

1983.50 29.2 -35.4 89.8 25.0 25.0 25.0

1985.50 0.0 0.0 0.0 25.0 25.0 25.0

1987.50 0.0 0.0 0.0 25.0 25.0 25.0

1984.50 -265.9 203.4 -25.2 25.0 25.0 25.0

1984.50 -66.1 107.7 29.3 25.0 25.0 25.0

1987.50 -28.1 9.0 -33.6 25.0 25.0 30.0

1987.50 -67.3 -139.0 -125.0 25.0 25.0 25.0

1981.50 15.0 6.4 -5.6 25.0 25.0 25.0

1987.50 271.0 192.3 216.6 25.0 25.0 25.0

1987.50 111.4 -415.7 104.4 25.0 25.0 25.0

1987.50 64.6 -104.5 96.5 25.0 25.0 25.0

1989.08 -51.4 -50.5 116.2 25.0 25.0 25.0

1987.50 -37.3 -33.5 117.1 75.0 75.0 75.0

1982.50 0.0 0.0 0.0 75.0 75.0 75.0

1981.50 -226.9 187.Z 280.0 25.0 25.0 25.0

1985.50 -226.9 187.2 280.0 25.0 25.0 25.0

1984.50 -53.2 -10.2 46.1 25.0 25.0 25.0

1988.50 127.2 -51.8 27.1 25.0 25.0 25.0

1987.50 178.7 85.2 80.6 25.0 25.0 25.0

1985.50 87.0 -82.4 -67.1 25.0 25.0 25.0

1987.50 31.6 3.6 -329.4 25.0 25.0 25.0

1987.50 38.0 63.7 17.3 25.0 25.0 25.0

1985.50 84.7 13.7 -282.9 25.0 25.0 25.0

1980.50 0.0 0.0 0.0 25.0 25.0 25.0

1980.40 0.0 0.0 0.0 25.0 25.0 25.0

1987.50 18.7 -5.9 11.4 25.0 25.0 25.0

1987.50 54.0 38.6 -70.1 25.0 25.0 25.0

1987.50 24.6 -3.9 -77.6 25.0 25.0 25.0

1986.50 51.1 41.4 -55.5 25.0 25.0 25.0

1985.50 68.1 -1188.4 77.8 25.0 25.0 25.0

1981.50 -277.3 39.7 -95.6 25.0 25.0 25.0

1987.50 -277.3 39.7 -95.6 25.0 25.0 25.0

1986.50 400.9 -207.3 127.3 25.0 25.0 25.0

1984.50 -89.6 -62.5 97.4 25.0 25.0 25.0

1987.50 -121.4 -116.5 117.2 25.0 25.0 25.0

44
Table 2.

°

General Data Set Information for Post 1980 Land and Selected

AeromaEnetic and Marine Surveys.

Post 1980 Land Survey from 1980.0 to 1982.5

Component Count Standard Deviation Average Time (yr)

Z 470 412 nT 1980.567

D 1003 0.86 ° 1980.543

I 6 0.41 ° 1980.500

H 456 301 nT 1980.570

B 8 412 nT 1980.882

Post 1980 Land Survey from 1982.5 to 1987.5

Component Count Standard Deviation Average Time (yr)

X 6 290 nT

Y 7 329 nT

Z 284 447 nT

D 604 0.73 °

I 103 0.53 °

H 302 317 nT

B 203 407 nT

1984 370

1984 370

1984 625

1984 514

1984 199

1984 385

1984 034

Project Magnet Collection 1 from 1980.0 to 1982.5

Component Count Standard Deviation Averase Time (yr)

X 286 371 nT

Y 283 334 nT

Z 289 467 nT

1981.408

1981.408

1981.408

Project Magnet Collection 1 from 1982.5 to 1987.5

Component Count Standard Deviation Averase Time (yr)

X 227 356 nT

Y 256 418 nT

Z 218 505 nT

1983.034

1983.011

1983.021

Project Magnet Collection 2 from 1984.0 to 1985.0

Component Count Standard Deviation Average Time (yr)

X 183

Y 183

Z 183

285 nT

285 nT

404 nT

1984.872

1984.872

1984.872

45
Project Magnet Collection 2 from 1985.0 to 1986.0

Component Count Standard Deviation

X 42 285 nT

Y 42 285 nT

Z 42 404 nT

Total-lntensity Marine from 1980.0 to 1982.5

Component Count Standard Deviation

B 715 390 nT

Total-Intenslty Marine from 1982.5 to 1987.5

Component Count Standard Deviation

B 275 400 nT

Composite Data Set

Component Count Standard Deviation

X 744 328 nT

Y 771 329 nT

Z 1486 435 nT

D 1607 0.80 °

I 109 0.51 °

H 758 307 nT

B 1202 395 nT

AveraKe Time (yr)

1985.183

1985.183

1985.185

Average Time (yr)

1981.037

Averase Time (yr)

1984.212

Average Time (yr)

1982.993

1982.995

1982.527

1982.036

1983.995

1982.090

1982.269

46
Table 3. General Data Set Information for the Project Magnet White

Sands Survey and the Remaining Post 1980 Marine Surveys

Project Magnet White Sands Survey

Component Count Standard Deviation Average Time (yr)

X 271 285 nT 1989.217

Y 270 285 nT 1989.217

Z 278 404 nT 1989.217

Marine Survey from 1980.0 to 1981.0

Component Count Standard Deviation

B ii00 333 nT

Marine Survey from 1981.0 to 1982.0

Component Count Standard Deviation

B 500 339 nT

Marine Survey from 1983.0 to 1984.0

Component Count Standard Deviation

B 200 336 nT

Marine Survey from 1984.0 to 1985.0

Component Count Standard Deviation

B 400 356 nT

Marine Survey from 1985.0 to 1986.0

Component Count Standard Deviation

B 307 345 nT

Marine Survey from 1986.0 to 1987.0

Component Count Standard Deviation

B 90 328 nT

Average Time (yr)

1980.454

Average Time (yr)

1981.505

Average Time (yr)

1983.409

Average Time (yr)

1984.418

Average Time (yr)

1985.447

Average Time (yr)

1986.417

47
Marine Survey from 1987.0 to 1988.0

Component Count

B 99

Composite Data Set

Component Count

Standard Deviation

344 nT

Standard Deviation

X 271 285 nT

Y 270 285 nT

Z 278 404 nT

B 2696 339 nT

Average Time (yr)

1987.348

Average Time (yr)

1989.217

1989.217

1989.217

1982.477

48
Table 4.

Component

B

General Data Set Information for DE-2 Satellite Data

Count Standard Deviation AveraKe Time (yr)

5100 25 nT 1982.284

Table 5.

Observation Data Set

Observatory data

Survey data

DE-2 satellite data

GSFC IBM-3081/MVS-TSO File Names for the Observation Data Sets

File Name

XRIRB.0BSERV.A1979.NFDST.DATA

XRJRR.SDIMOD.ALLSO89.SURVEY.DATA

XRJRR.DE2.NEWFIT.BWT.DATA

Table 6.

Series

Model

MAGSAT a priori

GSFC(5/89-1)

GSFC(5/89-2)

GSFC(5/89-3)

GSFC(5/89-4)

GSFC(5/89-5)

GSFC IBM-3081]MVS-TSO Global File Names for the GSFC(5189-X)

File Name

XRTJS.GLOBAL.MAGSAT.FI310.DATA

does not exist

does not exist

XRTJS.RGLOBAL.MOSRV2.FI310.DATA

XRTJS.RGLOBAL.MOSDE2.F1310.DATA

XRTJS.GLOBAL.OWSAND.FI310.DATA

49
TABLE 7: Coefficient Differences: GSFC(S/89-3) minus GSFC(5/89_4).

g/h n m

g 1 0

g 1 1

h 1 1

g 2 0

g 2 1

h 2 1

g 2 2

h 2 2

g 3 0

g 3 1

h 3 1

g 3 2

h 3 2

g 3 3

h 3 3

g 4 0

g 4 1

h 4 1

g 4 2

h 4 2

g 4 3

h 4 3

g 4 4

h 4 4

g 5 0

g 5 1

h 5 1

g 5 2

h 5 2

g 5 3

h 5 3

g 5 4

h 5 4

g 5 5

h 5 5

g 6 0

g 6 1

h 6 1

g 6 2

h 6 2

g 6 3

..... Main Field .........

Degree

Diff. _ e of Diff. _ _ of

Diff. Diff.

0.2 4.949747 -2.3 0.295296

0 4.949747 0.8 0.460977

-0.I 4.949747 0.124721

0 1.979898

0 1.979898

0 1.979898

0 1.979898

0 1.979898 0

-0.i 2.828427

0.1 2.828427

0.i 2.828427

0.1 2.828427

0 2.828427

0 2.828427

-0.i 2.828427 0.083299

0 1.272792

0.i 1.272792

0 1.272792

0.i 1.272792

0 1.272792

0 1.272792

0 1.272792

0 1.272792

0 1.272792 0.041573

0.I 0.989949

0 0.989949

-0.1 0.989949

0 0.989949

0 0.989949

-0.1 0.989949

-0.1 0.989949

-0.i 0.989949

0 0.989949

0.i 0.989949

0 0.989949 0.071581

0.I 0.707106

0 0.707106

0 0.707106

-0.i 0.707106

0.1 0.707106

0 0.707106

---Secular Variation---

Degree

1 0.487546 1.510702

1.8 0.272946

0.5 0.277848

-0.4 0.291547

-0.5 0.425205

-0.2 0.411096 0.854634

1.4 0.255558

-0.8 0.280178

-1.5 0.286006

-0.2 0.274590

-0.2 0.274590

0 0.389486

0.4 0.389486 0.842978

0.2 0.233238

-0.7 0.241867

0.5 0.238537

-0.5 0.266270

0.9 0.258069

0.6 0.260768

0.i 0.266270

-0.i 0.375366

0 0.361247 0.484067

-0.8 0.219544

0.4 0.224722

0.5 0.230217

0.9 0.246981

0.5 0.224722

0.4 0.252388

0.3 0.258069

0.4 0.272029

0 0.252388

-0.4 0.347131

-0.3 0 361247 0.471151

-0.5 0

0.30

0 0

0.20

-0.2 0

-0.7 0

210950

219544

210950

224722

216333

224722

5O
h 6 3

g 6 4

h 6 4

g 6 5

h 6 5

g 6 6

h 6 6

g 7 0

g 7 1

h 7 1

g 7 2

h 7 2

g 7 3

h 7 3

g 7 4

h 7 4

g 7 5

h 7 5

g 7 6

h 7 6

g 7 7

h 7 7

g 8 0

g 8 1

h 8 1

g 8 2

h 8 2

g 8 3

h 8 3

g 8 4

h 8 4

g 8 5

h 8 5

g 8 6

h 8 6

g 8 7

h 8 7

g 8 8

h 8 8

g 9 0

g 9 1

h 9 1

g 9 2

h 9 2

g 9 3

h 9 3

g 9 4

h 9 4

g 9 5

0 0.707106

0 0.707106

0 0.707106

-0.i 0.707106

0 0.707106

0.i 0.707106

0 0.707106 0.061538

-0.i 0.565685

0 0.565685

0 0.565685

0 0.565685

0 0.565685

0 0.565685

0 0.565685

0 0.565685

0 0.565685

0 0.565685

0 0.565685

0.I 0.565685

-0.i 0.565685

-0.i 0.565685

0 0.565685 0.049888

0 0.565685

0 0.565685

0 0.565685

0 0.565685

0 0.565685

0.i 0.565685

0 0.565685

0 0.565685

0 0.565685

-0.1 0.565685

0 0.565685

0.i 0.565685

0 0.565685

-0.i 0.565685

0.i 0.565685

0.i 0.565685

0 0.565685 0.058232

0 0.424264

0 0.424264

0 0.424264

0 0.424264

0 0.424264

0 0.424264

0 0.424264

0 0.424264

0 0.424264

0 0.424264

51

-0.6 0.230217

-0.4 0.258069

-0.2 0.230217

0.8 0.244131

-0.6 0.258069

-0.3 0.333016

-0.2 0.533016 0.407329

0.8 0.197230

-0.2 0.197230

-0.i 0.202484

-0.3 0.210950

-0.3 0.194164

-0.1 0.210950

0.3 0.208086

-0.2 0.238537

0.2 0.216333

-0.2 0.236008

0.5 0.244131

-0.4 0.25

0.7 0.244131

0.7 0 333016

-0.2 0 318904 0.401995

0.4 0 188679

0 0 188679

0.2 0 180277

-0.4 0 188679

0.1 0 188679

-0.1 0 188679

0 0 186010

0.3 0.222036

0 0.194164

0.2 0.216333

0.1 0.230217

0 0.236008

0.1 0.236008

0.2 0.236008

-0.7 0.236008

-0.6 0.304795

0.5 0.318904 0.312927

-0.5 0.166433

0.1 0.174928

0.2 0.166433

0.i 0.174928

0.2 0.174928

0.2 0.166433

-0.1 0.180277

0.2 0.186010

0 0.174928

-0.3 0.194164
h 9 5

g 9 6

h 9 6

g 9 7

h 9 7

g 9 8

h 9 8

g 9 9

h 9 9

g i0 0

g i0 1

h i0 1

g I0 2

h i0 2

g i0 3

h i0 3

g I0 4

h i0 4

g i0 5

h i0 5

g i0 6

h i0 6

g i0 7

h i0 7

g i0 8

h i0 8

g i0 9

h i0 9

g i0 i0

h i0 i0

0 0.424264

0 0.424264

0.1 0.424264

0 0.424264

0 0.424264

0 0.424264

0.1 0.424264

0 0.424264

0 0.424264 0.030689

0 0.424264

0 0.424264

0 0.424264

0 0.424264

0 0.424264

0 0 424264

0 0 424264

0 0 424264

0 0 424264

0 0 424264

0 0 424264

0 0 424264

0 0 424264

-0.1 0.424264

0 0.424264

0 0.424264

0 0.424264

0 0.424264

0 0.424264

0 0.424264

0 0.424264 0.021295

-0.3 0.216333

0.2 0.216333

-0.7 0.208086

-0.7 0.230217

0.6 0.236008

-0.7 0.236008

-0.7 0.236008

0.i 0.298328

0.i 0.297321 0.383163

O.1 0.144222

00. 144222

0.i 0.15

0 0.15

0.1 0.15

00. 158113

-0.1 0.15

0.1 0.164012

0.2 0.15

0.1 0.158113

0.1 0.172046

00. 186010

0.3 0.186010

0.1 0.186010

-0.1 0.186010

0.7 0.2

0.3 0.2

0.4 0.214009

-0.2 0.214009

-0.3 0.284253

-0.4 0.304795 0.233284

52
0

"0

,-4

r./3

O

t.l-i

nn

•,.--t t,

•,-4 e.,O

m_

,-.4

a)

CD

,--.4

!

I

if3 I

O

O

0

Z

r_

I ,-4

I I

O0 ._1" _--I

c,,I ',O _O

_,-,o

! !

¢N ,-I O

o,I f-40

,-4 '4D O

e_l N ,,,,_"

! !

r-,I c"_ _'¢'1

r'_ r_ N

r-INN

I ! I

r-,i N o'1

,=;,,; ,=;

! !

u_ u_ i_q

0 0 0

0

_3

0

¢0

!

0

0

!

C_

II

Ille_le

_IIN II

II

_0_

_4_ggg

I

II

OO

_N
Table 9. General Data Set Information for GSFC(4189-X) Composite Survey

Component Count Standard Deviation AveraEe Time (yr)

X 1015 286 nT 1987.238

Y 1041 286 nT 1987.228

Z 1788 417 nT 1986.511

D 1879 0.79 ° 1984.966

I 202 1.43 ° 1985.000

H 994 324 nT 1984.889

B 4060 361 nT 1985.030

Table i0: S_Y OF OBSERVATORY BIAS INCORPORATION INTO THE

GSFC(4189-x) MODELS

MODEL

GSFC(4/89-1)

GSFC(4/89-2)

GSFC(4/89-3)

GSFC(4/89-4)

OBSERVATORY BIASES UTILIZED

From GSFC(11187) if available.

Otherwise set to zero with no CWM.

No adjustment made.

Biases adjusted.

From GSFC(4189-2) or GSFC(11/87).

Otherwise used CWM.

No adjustment made.

No biases used. CWM used.

Table ii. GSFC IBM-3081/MVS-TSO

Series

Model

GSFC(4/89-1)

GSFC(4/89-2)

GSFC(4/89-3)

GSFC(4/89-4)

Global File Names for the GSFC(4/89-X)

File Name

XRJRR.GLOBAL.AI984.DATA4

XRJRR.GLOBBB.AI984.DATAI

does not exist

XRJRR.GLOBAL.AI984.DATA3

54
TABLE 12: Coefficient Differences Between the GSFC(4189-x) Models•

Model -x minus model -I Model -x minus model -2

• .-2 . .-3 . .-4 . .-i

g/h n m

g 1 0 25.2 19.3 34 -25.2

g i I -47 -41.2 -15.4 47

h 1 1 -39.9 -44.4 -6.4 39.9

g 2 0 5.8 7.2 12.1 -5.8

g 2 1 14.5 6.3 52.5 -14.5

h 2 1 22.2 16.2 25.6 -22.2

g 2 2 33.5 36.9 -18.2 -33.5

h 2 2 25.9 29.2 50.1 -25.9

g 3 0 7 7.5 -1.6 -7

g 3 1 2 2.1 -23.6 -2

h 3 1 -3.8 3.5 -43.8 3.8

g 3 2 5.6 0.8 10.9 -5.6

h 3 2 -10.7 -8.7 -23.5 10.7

g 3 3 -68.7 -62.5 -i1.4 68.7

h 3 3 -11.2 -5.7 14.1 11.2

g 4 0 2.9 8.9 30.1 -2.9

g 4 1 -9.5 -6.9 -17.2 9.5

h 4 1 12.7 17.1 23.1 -12.7

g 4 2 -40.8 -39 -19.4 40.8

h 4 2 21.2 20.3 -7 -21.2

g 4 3 1.4 -1.5 -26.2 -1.4

h 4 3 1.8 2.4 -28.9 -1.8

g 4 4 44 48.4 -43.7 -44

h 4 4 23.7 20.4 3.5 -23.7

g 5 0 4.8 -4.7 -11.1 -4.8

g 5 1 -19.5 -21.5 -7.8 19.5

h 5 i 15.4 4 -7.8 -15.4

g 5 2 -2.1 0.9 -12.8 2.1

h 5 2 -5.9 -5.3 -11.9 5.9

g 5 3 42.4 42.2 44.3 -42.4

h 5 3 -8.6 -11.8 36 8.6

g 5 4 8.1 3.4 3.2 -8.1

h 5 4 19.8 23.8 7.5 -19.8

g 5 5 -53.4 -53.7 -16.6 53.4

h 5 5 -29.1 -34.5 -18.1 29.1

g 6 0 -3.3 -0.6 -32 3.3

g 6 1 14 11.7 8.1 -14

h 6 1 -13.2 -5 10.9 13.2

g 6 2 11.2 4.8 28.9 -11.2

h 6 2 -2.3 -1.2 13.8 2.3

g 6 3 -17.7 -15.8 -31.5 17.7

h 6 3 13 12.8 -26.6 -13

. .-3 . .-4

-5.9

5.8

-4.5

1.4

-8.2

-6

3.4

3.3

0.5

0.i

7.3

-4.8

2

6.2

5.5

6

2.6

4.4

1.8

-0.9

-2.9

0.6

4.4

-3.3

-9.5

-2

-11.4

3

0.6

-0.2

-3.2

-4.7

4

-0 3

-5 4

2 7

-2 3

8 2

-6 4

1 1

1 9

-0.2

8.8

31.6

33.5

6.3

38

3.4

-51.7

24.2

-8.6

-25.6

-40

5.3

-12.8

57.3

25.3

27.2

-7.7

10.4

21 4

-28 2

-27 6

-30 7

-87 7

-20 2

-15 9

11.7

-23.2

-10.7

-6

1.9

44.6

-4.9

-12.3

36.8

ii

-28 7

-5 9

24 1

17 7

16 1

-13 8

-39.6

55
g

64

h64

g65

h65

g66

h66

g70

g71

h71

g72

h72

g73

h73

g74

h74

g75

h75

g76

h76

g77

h77

g80

g81

h81

g82

h82

g83

h83

g84

h84

g85

h85

g86

h86

g87

h87

g88

h88

g90

g91

h91

g92

h92

g93

h93

g94

h94

g95

h95

-9

-17.3

1.5

-14.8

15.9

26.8

-0.8

-7.2

0.9

-6.8

8.6

3.6

-12.3

-5.4

8.4

-3.9

13

3.2

-i8

-254

-91

14

-ii9

72

-38

8.1

-3.4

12.6

-1.7

3.2

10.6

13.5

-8.5

-11.2

3.7

-15.1

22

11.9

0.3

-2.5

6.6

-5.3

-3.2

-0.2

-5.7

14

-5.9

-6.2

-8.1

-i0

-16.7

-0.7

-10.4

17.6

27.3

5.2

-4

-3.1

-0.9

10.7

3.1

-5.9

-3.9

6.1

-3

12.1

0.1

0.9

-23.7

-14.1

-3.4

-11.5

6.9

-6.6

4.9

-3.4

8.9

2.8

4.9

10.6

i0

-8.2

-14.2

I.i

-11.2

20

4.3

0.8

-4.2

8.1

-5.7

-2.9

-0.6

-5.4

12.2

-6.5

-6.5

-6.8

15.5

4.9

12.4

-30

10.7

-34.5

25.4

-8.8

13.3

-15.3

-12.8

1.1

-27.9

-2.4

-2.3

-33.5

27

-3.6

10.7

-1.8

-8

-18.1

-6.9

6.7

-116

102

45

404

-166

-32

323

87

-22

12.9

14.2

-14.1

27

24.6

7.3

4.4

1.7

1.3

-7.7

-7.7

-2.9

8.3

-7.3

-7.7

0.1

56

9

17.3

-i5

148

-159

-268

08

72

-09

6.8

-8.6

-3.6

12.3

5.4

-8.4

3.9

-13

-3.2

1.8

25.4

9.1

-1.4

11.9

-7.2

3.8

-8.1

3.4

-12.6

1.7

-3.2

-10.6

-13.5

8.5

11.2

-3.7

15.1

-22

-11.9

-0.3

2.5

-6.6

5.3

3.2

0.2

5.7

-14

5.9

6.2

8.1

-i

0.6

-2.2

4.4

1.7

0.56

3.2

-4

5.9

2.1

-0.5

6.4

1.5

-2.3

0.9

-0.9

-3.1

2.7

1.7

-5

-4.8

0.4

-0.3

-2.8

-3.2

0

-3.7

4.5

1.70

-3.5

0.3

-3

-2.6

3.9

-2

-7.6 0

5

-i7

15

-04

03

-04

03

-i .8

-0.6

-0.3

1.3

24.5

22.2

10.9

-15.2

-52

-613

262

-i6

124

-85

-214

-25

-1563

-10.7

-29.6

14

-6.8

12.5

23.6

i.i

-19.5

5

-0.5

-7.8

2.1

7.9

27.8

-14.9

-6.4

21.7

-4.8

6.3

24.1

10.5

15

12.7

7

6.9

-4.9

6.6

-4.5

-7.5

2.8

-5.7

-1.4

-1.5

8.2
g

96

h96

g97

h97

g98

h98

g99

h99

g 100

g 101

h 101

g 102

h i02

g i03

h I03

g i04

h i04

g I05

h i05

g i06

h I06

g i07

h i07

g i08

h I08

g i09

h i09

g i0 i0 h I0 i0

0

-15

13.5

6.4

-0.9

1.9

-7.6

-i

-4.9

3.1

-9.1

2.8

-8.5

4.1

2.3

-6.1

5.9

-6.5

-8.2

88

1.29

-10.2

i

3.2

-2.5

-4.3

-0.2

-0.7

-15

13.7

4.3

0.5

6.4

-Ii

-5

-4.4

3

-9.7

2.6

-6.8

4.5

2.4

-6.6

5.1

-6.5

-7.4

9.1

7.5

1.9

9.5

-11.9

0.3

6.1

-2.9

-5.2

1.4

0.9

-1.3

13.5

-8.9

-7.5

1

-7.5

4.3

-5.1

i.I

1.7

1.9

-3.9

2.4

1.7

3.1

4.4

-0.3

-4.9

-4.1

3.6

-6.7

5.9

1.7

-0.4

2.4

-4.8

-5.8

2.5

0

15

-13.5

-6.4

0.9

-1.9

7.61

4.9

-3 .i

9.i

-2.8

8.5

-4.1

-2.3

6.1

-5.9

6.5

8.2

-8

-8

-1.2

-9

10.2

-i

-3.2

2.5

4.3

0.2

-o_70

0.2

-2.1

1.4

4.5

-3.4

-4

0.5

-0.i

-0.6

-0.2

1.7

0.4

0.i

-0.5

-0.8

0

0.8

i.i

-0.5

0.7

0.5

-1.7

-0.7

2.9

-0.4

-0.9

1.6

0

13

-0

-15

-6

97236

-09

0.I

5.3

-0.2

-2

10.8

-0.9

4.6

-1.7

-0.6

9.2

-1.5

6.2

3.3

-12.1

-4.4

-7.9

-3.1

11.9

-1.4

-0.8

-2.3

-1.5

2.7

57
TABLE 13: Degree Statistics of Model Differences in Table 12.

Model -x minus model -i Model -x minus model -2

Degree ..-2 ..-3 ..-4 ..-i ..-3 ..-4

1 32.4 29.3 21.4 32.4 5.2

2 9.5 12.1 26.1 9.5 4.9

3 24.3 22.4 19.2 24.3 3.9

4 22.3 22.5 23.0 22.3 3 .ii

5 24.5 24.8 20.1 24.5 4.6

6 14.0 12.7 22.1 14.0 3 •4

7 9.2 8.8 16.3 9.2 3.5

8 10.0 9.0 17.0 10.0 3.0

9 7.1 7.3 6.3 7.1 1.8

i0 6.0 6.2 3.7 6.0 1.0

11.2

30.5

30.3

32 8

20 4

25 9

15 4

12 5

6 7

5 7

58
TABLE 14:

g/h n m

g i 0

g 1 1

h i 1

g 2 0

g 2 1

h 2 1

g 2 2

h 2 2

g 3 0

g 3 i

h 3 i

g 3 2

h 3 2

g 3 3

h 3 3

g 4 0

g 4 1

h 4 1

g 4 2

h 4 2

g 4 3

h 4 3

g 4 4

h 4 4

g 5 0

g 5 1

h 5 1

g 5 2

h 5 2

g 5 3

h 5 3

g 5 4

h 5 4

g 5 5

h 5 5

g 6 0

g 6 1

h 6 1

g 6 2

h 6 2

g 6 3

h 6 3

Secular Variation Coefficient Differences

Between the GSFC(4189-x) Models.

Model -x minus model -i

•.-2 ..-3 ..-4

1.8 0 6.8

-0.5 -0.5 3

-2.2 -3.9 1.8

-1.5 -0.7 1.3

2.5 0.7 10.4

2.3 1.2 5.4

-1.7 -0.4 -5.4

-0.1 1.1 7

1.6 1.5 -1.8

-2.6 -2.5 -5.6

-0.7 0.7 -7.8

2 2 5.4

-2.3 -2.3 -7.4

-1.2 -0.6 2.5

0.8 2.6 5

-2.6 -1.8 5

0.6 i.i -4.6

-1.6 0 0.9

-2.2 -2.5 -2.8

3 3.2 -i.i

-2.5 -3.3 -7.3

-0.9 -0.8 -8.1

0.i 0.8 -8.6

0.i -0.8 -1.2

1.6 0.3 -2

0.8 0.5 3.2

3.5 0.8 -0.9

0 0.2 -3

-1.9 -1.4 -1.7

3.7 3.8 6.1

0.6 0 9.3

-0.2 -0.3 0.6

1.9 2.5 2

-0.1 -0.9 0

-0.4 -0.8 -0.3

0.3 0.9 -5.8

-0.6 -0.7 0.8

-2.5 -1.2 1.8

1.8 0.7 4.2

0.I 0.3 2.6

-2.3 -1.7 -5.1

-0.6 -0.6 -6.6

59
g 6 4

h 6 4

g 6 5

h 6 5

g 6 6

h 6 6

g 7 0

g 7 1

h 7 1

g 7 2

h 7 2

g 7 3

h 7 3

g 7 4

h 7 4

g 7 5

h 7 5

g 7 6

h 7 6

g 7 7

h 7 7

g 8 0

g 8 1

h 8 1

g 8 2

h 8 2

g 8 3

h 8 3

g 8 4

h 8 4

g 8 5

h 8 5

g 8 6

h 8 6

g 8 7

h 8 7

g 8 8

h 8 8

0.2

-3.2

1

-0.4

-1.2

1

-1.2

-0.6

I.i

-1.7

0.4

0.I

-0.5

-0.2

2.5

-1.9

0.4

0.i

-1.5

0.6

0.7

0.6

0

0.4

0.4

0.4

0

0.4

-0.3

-0.4

1.5

0.6

0.3

0.5

0

-0.6

I.I

-0.6

0.4

-2.7

0

0.3

-0.5

1.5

0.i

-0.4

0.8

-0.6

0.5

0.4

0.9

-0.3

2.1

-1.8

0.4

-0.4

-1.4

0.3

0.i

-0.2

-0.2

0.i

-0.2

0.3

-0.i

-0.i

0.5

-0.5

1.7

0.i

0.4

-0.7

-0.5

0.4

0.9

-2.1

2.5

0.4

1

-5.3

2.4

-6.4

4.1

-i.I

1.6

-2.8

-2.7

2.3

-4.4

-0.5

0.6

-7.3

3.3

-1.8

2.3

2.1

-3 .i

-2

0.9

1

-2.2

0.6

-0.1

5.8

-l.1

-0.4

5

0.4

0.7

3.5

1.5

-2.7

3.4

3.1

6O
Table 15: MODEL STATISTICS BY YEAR FOR OBSERVATORY DATA

MODEL STATISTIC 1983.5 1984.5 1985.5 1986.5 1987.5 1988.5

(5/89-4) Points 146 145 129 i00 87 6

mean x 1.4 -0.5 12.7 -20.9 -13.8 20.9

sigma x 204.8 191.9 208.8 196.1 191.3 173.4

mean y -28.8 -26.7 -31.6 -10.4 -23.7 55.4

sigma y 240.3 238 249 228.9 263.8 79

mean z -12.5 -14.7 -30.6 -41.1 -49.5 -54.8

sigma z 383.4 386.2 406.3 438 458.2 193.9

(4/89-1) Points 146 145 129 i00 87 6

mean x -14.9 -17 -4.5 -32.6 -23.2 21.5

sigma x 201.6 187.9 202.5 189.6 185.1 191.7

mean y -32 -27.6 "-53.3 -12.9 -28.2 54.1

sigma y 240.4 237.2 248.2 232.1 265.3 67.3

mean z -15.9 -13.7 -31.3 -39 -45.3 -64

sigma z 385.5 387.9 406.6 439.9 456.1 183.7

(4/89-3) Points 146 145 129 i00

mean x 29.5 25.6 40 6

sigma x 215 212.5 223.2 220

mean y -24.3 -22.7 -28 -7.6

sigma y 264.5 264.2 275 257.4

mean z -17.6 -17.4 -28.5 -48.3

sigma z 388.4 394.7 413.7 447.2

87

14 7

207 1

-16 5

289 5

-33 8

453 6

6

67.2

169.8

91

104.8

-164

173.6

61
Table 15(Continued): MODELSTATISTICSBY YEAR FOR OBSERVATORY DATA

MODEL STATISTIC 1983.5 1984.5 1985.5 1986.5 1987.5 1988.5

(5/89-I) Points 146 145 129 i00 87 6

mean x 1.4 0.i 12.8 -21 -ii.i 27.3

sigma x 204.5 191 207.3 196.2 192.2 170.4

mean y -28.9 -26.4 -31.7 -ll.4 -25 56

sigma y 239.7 237.5 248.1 228.4 262.3 77.7

mean z -ii -13.2 -28.5 -37.7 -42.4 -64.7

sigma z 383.1 386.6 405.4 437.9 456.2 182.4

(4/89-2) Points 146 145 129 i00 87 6

mean x 31.8 28.1 41.7 7.4 15.7 66.1

sigma x 215 213.2 222.7 219.7 207.2 173.1

mean y -24.6 -22.1 -26.5 -6.7 -16.1 88.2

sigma y 265.6 265.1 275.4 257.4 289.4 102.9

mean z -25 -21.4 -30.9 -50.9 -33.4 -158.7

sigma z 389.1 395.7 414.1 447.1 454.4 172.9

(4/89-4) Points 146 145 129 i00 87 6

mean x -2 -4.7 14 -12.3 1 36.1

sigma x 192 175.5 187.5 169.5 156.1 147.5

mean y -20 -17 -22.7 -9.6 -23.1 37.8

sigma y 231 221.9 224.5 189.6 213.2 86.3

mean z -34.4 -31 -41.4 -62.7 -57.8 -67.9

sigma z 375.1 389.3 419.4 468.3 501.4 181.3

62
Table 16: MODELSTATISTICSBYYEARFORSURVEYDATA

MODEL STATISTIC 1983.5 1984.5 1985.5 1986.5 1987.5 1989.5

(4/89-1) x-points i15 189 42 0 0 271

mean x -23.5 -14.8 -25.7 0 0 -16.4

sigma x 67.4 134.9 83.5 0 0 50.8

y-points 115 190 42 0 0 270

mean y -16.9 62.9 32.4 0 0 0.3

sigma y 72.1 150.3 183.7 0 0 55.2

z-points 137 361 44 37 0 278

mean z -11.4 -15.9 -202 -29.1 0 12.2

sigma z 81.3 108.5 133.7 151.9 0 70

H-points 22 187 0 18 0 0

mean h 28.2 -19.7 0 -76.1 0 0

sigma H 85.1 77.6 0 302.6 0 0

b-points 307 632 334 91 i01 0

mean b -31.2 -22 8.9 45.4 13.8 0

sigma b 100.4 99.4 119.7 97.9 129.5 0

(4/89-2) x-points 115 189 42 0 0 271

mean x -40.6 -35.1 -22.1 0 0 -3.6

sigma x 96.1 90.1 45.2 0 0 47.6

y-points 115 190 42 0 0 270

mean y -23.6 26.7 33.4 0 0 -5.2

sigma y 99.4 83.5 43.5 0 0 56.6

z-points 137 361 44 37 0 278

mean z -45.4 -5.5 -49.1 9.8 0 8.1

sigma z 101.4 94.3 43.9 138.5 0 66.9

H-points 22 187 0 18 0 0

mean h 61.2 0.9 0 17.7 0 0

sigma H 92.1 74.4 0 279.2 0 0

b-points 307 632 334 91 i01 0

mean b 1.34 -9.9 1.3 1.8 41.3 0

sigma b 103.4 83.2 91 80.5 85.9 0

63
Table 16(Continued): MODELSTATISTICSBYYEARFORSURVEYDATA

MODEL STATISTIC 1983.5 1984.5 1985.5 1986.5 1987.5 1989.5

(5/89-4) x-points 115 189 42 0 0

mean x ii.3 -31.1 -7.4 0 0

sigma x 58.2 96.1 45.4 0 0

y-points 115 190 42 0 0

mean y -11.4 125.9 98.9 0 0

sigma y 70.9 99.2 41 0 0

z-points 137 361 44 37 0

mean z -2.4 -30.5 1.4 -45.9 0

sigma z 67.1 91.7 37.3 148.6 0

H-points 22 187 0 18 0

mean h 36.6 2.7 0 -43.1 0

sigma H 81.6 73.8 0 289.2 0

b-points 307 632 334 91 101

mean b 14.6 2.6 18.6 67.8 83.3

sigma b 61.4 86.8 97.7 84.9 103.6

271

-46.4

50.3

270

19.6

55.3

278

i0.i

64.2

0

0

0

0

0

0

(4/89-3) x-points 115 189 42 0 0 271

mean x -23 -55.8 -46.2 0 0 -6.5

sigma x 97.3 97.4 57.1 0 0 47.4

y-points 115 190 42 0 0 270

mean y -20.6 34 33.9 0 0 -5.5

sigma y 89.2 89.3 39.2 0 0 57.2

z-points 137 361 44 37 0 278

mean z -35.6 -9.8 -18.8 3.5 0 6.5

sigma z 100.2 94.3 42 138.2 0 67.4

H-points 22 187 0 18 0 0

mean h 55.5 0.6 0 -4.4 0 0

sigma H 90.7 73.8 0 282.5 0 0

b-points 307 632 334 91 i01 0

mean b 1 -6.5 -4.2 2.6 27.1 0

sigma b 107.3 83.8 90.7 82.7 87.2 0

64
Table 16(Continued): MODELSTATISTICSBYYEARFORSURVEYDATA

MODEL STATISTIC 1983.5 1984.5 1985.5 1986.5 1987.5 1989.5

(4/89-4) X-POINTS ll5 189 42 0 0

mean x -42.4 -11.3 -21 0 0

sigma x 151.5 98.6 44.6 0 0

y-points 115 190 42 0 0

meany -17.9 39.7 18.5 0 0

sigma y 119.8 103 48.1 0 0

z-points 137 361 44 37 0

mean z -54.5 -13.4 -104 -71.2 0

sigma z 132.2 98.4 56 128 0

H-points 22 187 0 18 0

mean h 38 -13.2 0 -9.5 0

sigma H 84.4 82.1 0 275.5 0

b-points 307 632 334 91 i01

mean b 12.8 -9.5 12 15.7 -24.2

sigma b 100.7 92.3 109.2 80.2 82.2

271

-3.8

48

270

-4

51.9

278

3.9

65.4

0

0

0

0

0

0

65
.

TABLE 17: Main Field Coefficient Differences. Specified model minus

GSFC(5_89-4) at 1985.

g/h n m

g 1 0

g 1 1

h 1 1

g 2 0

g 2 1

h 2 1

g 2 2

h 2 2

g 3 0

g 3 1

h 3 1

g 3 2

h 3 2

g 3 3

h 3 3

g 4 0

g 4 1

h 4 1

g 4 2

h 4 2

g 4 3

h 4 3

g 4 4

h 4 4

g 5 0

g 5 1

h 5 1

g 5 2

h 5 2

g 5 3

h 5 3

g 5 4

h 5 4

g 5 5

h 5 5

g 6 0

g 6 1

h 6 1

g 6 2

h 6 2

g 6 3

h 6 3

g 6 4

(5/89-3) (4/89-1) (4/89-2) (4/89-3) (4/89-4)

-ii.3 -1.9022

4 -20.5155

4.9 -10.6486

9 -8.7214

2.5 -2.011

-2 1.6912

-2.5 7.3971

-I 27.2637

6.9 8.8314

-3.9 6.8207

-7.4 6.1764

-0.9 12.433

-i -6.555

0 1.9809

1.9 -5.7968

1 -1.0974

-3.4 2.8877

2.5 -6.2851

-2.4 -2.8094

4.5 -2.1246

3 -4.233

0.5 -7.6728

-0.5 0.8249

0 8.1

-3.9 -1.9191

2 4.0343

2.4 3.2029

4.5 -7.6602

2.5 -0.5686

1.9 -1.9298

1.4 5.9343

1.9 -0.9

0 2.2932

-1.9 4.4479

-1.5 5 9945

-2.4 5 0479

i. 5 -7 2233

0 -3 9508

0.9 -1 7411

-0.9 1 6343

-3.5 -1 3262

-3 -i 3411

-2 5 5288

15.358

-65.31

-40.8444

3.6951

1.4615

13.7459

48.3958

53.6048

8.7738

20.2893

5.4641

9.211

-7.1097

-61.4259

-20.5256

13.2712

-9.2589

13.4725

-33.9052

5.8424

8.1945

-1.9029

44.3838

31.3589

-4.1767

-18.9945

3.1644

-9.7602

1.9123

24.1495

-5.3123

8.0822

13.7123

-48.511

-21.3411

0.4246

9.4233

-6.1233

1.5191

-1.1068

-8.8809

14.3055

-4.3534

17.3978

-59.51

-37.8457

1.5663

1.2013

12.598

46.0615

51.6116

9.7149

19.9482

6.5887

4.411

-5.1097

-57.8725

-22.9654

15.7424

-8.8644

10.8149

-30.7819

4.0602

8.8233

-1.744

45.6961

32.0288

-7.9424

2.103

-49.1485

-24.9884

-2.3557

4.6146

3.4718

13.0165

46.4867

15.1712

7.9223

-3.2178

-0.4864

2.5864

-20.4466

-13.7518

6.9476

5.9783

12.845

-9 8586

-4 2725

1 7673

-0 8437

-4 9405

16 8932

-4 1971

-19.6712 -17 8809

3.6741 -0.6272

-7.6424 -7.2272

0.3068 -4.9699

23.5084 15.4631

-5.8657 0.912

3.8235 -0.3466

15.0657 0.9712

-45.2822 -12.1521

-24.9767 -10.7822

0.478 -1.3683

7.5644 -2.6521

-3.6576 -0.9906

-0.0288 8.6327

-0.889 3.9657

-9.6275 -10.3301

14.1055 1.1715

-6.2356 10.0013

66
h 6 4 -i

g 6 5 3.9

h 6 5 -3

g 6 6 -1.4

h 6 6 -i

g 7 0 3.9

g 7 i -i

h 7 1 -0.5

g 7 2 -1.5

h 7 2 -1.5

g 7 3 -0.5

h 7 3 1.5

g 7 4 -i

h 7 4 i

g 7 5 -i

h 7 5 2.5

g 7 6 -1.9

h 7 6 3.4

g 7 7 3.4

h 7 7 -I

g 8 0 2

g 8 i 0

h 8 I i

g 8 2 -2

h 8 2 0.5

g 8 3 -0.4

h 8 3 0

g 8 4 1.5

h 8 4 0

g 8 5 0.9

h 8 5 0.5

g 8 6 0.i

h 8 6 0.5

g 8 7 0.9

h 8 7 -3.4

g 8 8 -2.9

h 8 8 2.5

g 9 0 -2.5

g 9 1 0.5

h 9 1 1

g 9 2 0.5

h 9 2 i

g 9 3 1

h 9 3 -0.5

g 9 4 i

h 9 4 0

g 9 5 -1.5

h 9 5 -I.5

g 9 6 1

1.2437 -1.9411 -3.5466 4.3793

-0.589 -3.5 -1.289 7.4

-2.9055 -15.9411 -14.6288 -9.5272

3.7492 24.9424 23.5547 3.8628

-1.8 20.589 18.8835 -8.0696

-3.4809 1.0123 1.278 3.834

0.2767 -4.2767 -1.9589 -3.6712

5.4466 1.4945 -I.1822 11.689

7.0013 7.7 8.7479 4.0521

0.7589 7.5945 9.2534 -0.1314

4.9534 8.1123 6.289 -4.0919

6.8068 -3.2877 -3.0631 -1.6848

1.6424 -2.8754 -0.9343 1.4479

-1.9437 -4.5712 -5.1068 -6.8903

1.1259 5.6068 6.0657 -0.1738

-7.8356 3.4 2.5 4.6081

2.2233 4.9822 4.0877 6.5631

-4.1398 0.6767 2.9356 -3.5851

-1.2178 -29.2644 -26.2411 -12.2809

4.5055 -7.6822 -10.0356 10.1796

6.4411 5.1945 3.9233 -2.8369

3.8822 -8.0178 -6.7356 -6.9877

-0.7822 4.6534 5.6767 1.5068

-3.2534 -8.8178 -8.9712 -5.1492

-1.9712 4.3644 1.6055 5.5822

-2.4589 -5.8589 -5.4178 2.4822

-8.9411 1.8945 0.4 5.8751

0.7411 0.3644 1.3356 -11.0068

-0.411 4.5534 6.6945 -1.8466

-8.3191 -4.3356 -5.2178 1.9259

1.2233 12.0767 10.7822 8.1589

0.6644 -9.1589 -9.3 -4.6233

2.4165 -10.989 -8.6958 -0.122

-7.3178 -3.6178 -4.0123 0.2657

0.7767 -11.6767 -12.1877 -1.4136

6.2275 23.3754 22.2576 18.2301

-1.3699 13.1767 12.1932 9.556

67
h 9 6

g 9 7

h 9 7

g 9 8

h 9 8

g 9 9

h 9 9

g i0 0

g i0 1

h 10 1

g I0 2

h i0 2

g i0 3

h i0 3

g i0 4

h i0 4

g i0 5

h i0 5

g i0 6

h i0 6

g 10 7

h 10 7

g I0 8

h 10 8

g i0 9

h i0 9

g i0 i0

h i0 i0

-3.4

-3.5

3

-3.5

-3.4

0.5

0.5

0.5

0

0.5

0

0.5

0

-0.5

0.5

1

0.5

0.5

0

1.5

0.4

-0.5

3.5

1.5

2

-1

-1.5

-2

68
TABLE18: Desree Statistics of Model Differences in Table 17.

Model (5/89-3) (4/89-1) (4/89-2) (4/89-3) (4/89-4)

Degree

i 7.4 7.8 33.8 32.4 20.9

2 4.3 12.2 22.3 21.8 17.4

3 4.1 6.7 25.5 24.4 11.3

4 2.4 4.6 21.3 21.0 8.2

5 2.3 4.0 18.7 18.2 8.4

6 2.0 3.5 11.4 10.7 6.5

7 2.0 4.1 9.0 8.6 6.2

8 1.5 4.3 9.4 9.0 6.8

89
TABLE 19: Secular Variation Coefficient Differences:

Specified model minus GSFC(5/89-4).

/h n m

g 1 0

g 1 1

h 1 1

g 2 0

g 2 1

h 2 1

g 2 2

h 2 2

g 3 0

g 3 1

h 3 1

g 3 2

h 3 2

g 3 3

h 3 3

g 4 0

g 4 1

h 4 1

g 4 2

h 4 2

g 4 3

h 4 3

g 4 4

h 4 4

g 5 0

g 5 1

h 5 1

g 5 2

h 5 2

g 5 3

h 5 3

g 5 4

h 5 4

g 5 5

h 5 5

g 6 0

g 6 1

h 6 1

g 6 2

h 6 2

g 6 3

h 6 3

g 6 4

(5/89-3) (4/89-1) (4/89-2) (4/89-3)

-2.3

0.8

1

1 8

0 5

-0 4

-0 5

-0 2

1 4

-0 8

-i 5

-0.2

-0.2

0

0.4

0.2

-0.7

0.5

-0.5

0.9

0.6

0.I

-O.1

0

-0.8

0.4

0.5

0.9

0.5

0.4

0.3

0.4

0

-0.4

-0.3

-0.5

0.3

0

0.2

-0.2

-0.7

-0.6

-0.4

-5.1

-0.3

4.1

3.1

-2.1

-5 6

-0 7

5 2

0 6

1 1

1 4

-2.1

2

-0.6

-1.8

3.3

0.i

0.6

2.5

-2.5

4.5

1.8

-0.4

0.2

-3.2

-0.8

-3.8

0

2.5

-4.3

-0.6

0.6

-1.9

1.2

-0.4

0.i

0.3

2.9

-1.3

-0.i

2

0.5

-0.7

-3.3 -5.1

-0.8 -0.8

1.9 0.2

1.6 2.4

0.4 -1.4

-3.3 -4.4

-2.4 -l.1

5.1 6.3

2.2 2.1

-1.5 -1.4

0.7 2.1

-0.i -0.i

-0.3 -0.3

-1.8 -1.2

-i 0.8

0.7 1.5

0.7 1.2

-I 0.6

0.3 0

0.5 0.7

2 1.2

0.9 1

-0.3 0.4

0.3 -0.6

-1.6 -2.9

0 -0.3

-0.3 -3

0 0.2

0.6 i.i

-0.6 -0.5

0 -0.6

0.4 0.3

0 0.6

i.i 0.3

-0.8 -1.2

0.4 1

-0.3 -0.4

0.4 1.7

0.5 -0.6

0 0.2

-0.3 0.3

-0.1 -0.1

-0.5 -0.3

(4189-4)

1.7

2.7

5.9

4.4

8.3

-0.2

-6.1

12.2

-1.2

-4.5

-6.4

3.3

-5.4

1.9

3 2

8 3

-4 5

1 5

-0 3

-3 6

-2 8

-6 3

-9

-i

-5.2

2.4

-4.7

-3

0.8

1.8

8.7

1.2

0.i

1.2

-0.7

-5.7

i.I

4.7

2.9

2.5

-3.1

-6.1

1.8

7O
hghghgghghghghghghghgghghghghghghghgh

66666777777777777777888888888888888884558601122334455667701122334455667788-0.2

0.8

-0.6

-0.3

-0.2

0.8

-0.2

-0.I

-0.3

-0.3

-0.1

0.3

-0.2

0.2

-0.2

0.5

-0.4

0.7

0.7

-0.2

0.40

0.2

-0.4

0.i

-0.1

0

0.30

0.2

0.i0

0.i

0.2

-0.7

-0.6

0.5

4.1

-i.I

-0.2

1.3

-i

1.7

0.9

-0.8

1.5

-0.3

0.i

0.5

0.5

-4.1

2.3

-0.3

-0.5

2

-0.2

-i.i

-0.6

0

0.2

-i

-0.3

0

-0.I

0.i

1.3

-1.9

-0.6

-0.3

-i

0.2

-0.2

-1.7

0.7

0.9

-0.i

-0.6

0.i0

0.5

0.3

0.3

-0.2

0.i

0.20

0.3

-1.6

0.4

0.I

-0.4

0.5

0.4

-0.4

00

0.6

-0.6

0.i

0

0.3

-0.2

0.9

-0.4

00

-0.5

0.2

-0.8

-0.6

0.I

1.4

-I.i

0.i

0.8

0.5

1.8

0.50

0.9

0.2

0.5

1.4

0.2

-2

0.5

0.1

-0.9

0.6

0.1

-1

-0.8

-0.2

0.3

-1.2

0

-0.1

-0.2

0.6

0.8

-0.2

-0.5

0.1

-1.7

-0.3

0.2

-0.8

-1.4

4.5

-0.i

-5.5

3.7

-7.4

5.8

-0.2

0.8

-1.3

-3

2.4

-3.9

0

-3.5

-53

-2.3

4.3

1.9

-4.2

-2.6

0.9

1.2

-3.2

0.3

-0.1

5.7

-i

0.9

3.1

-0.2

0.4

2.5

1.7

-2.9

1.7

3.8

71
TABLE 20: Desree Statistics of Model Differences in Table 19.

Model (5/89-3) (4/89-1) (4/89-2) (4/89-3) (4/89-4)

Degree

1 1.5 3.8 2.1 2.3 1.8

2 0.85 3.8 3.0 3.7 6.4

3 0.8 1.5 1.3 1.3 3.9

4 0.5 2.0 0.8 0.6 4.7

5 0.5 2.0 0.7 1.3 3.6

6 0.4 1.6 0.4 0.8 4.3

7 0.4 1.5 0.5 0.9 3.2

8 0.3 0.8 0.4 0.7 2.3

72
Appendix A. Listin E of Internal Field Static and Secular Variation

Terms and, When Available, Their Estimated Uncertainties

for GSFC(4/89-X) and GSFC(5/89-X) Series

73
GSFC(5/89) MODELS: Main Field Coefficients

Model ..-i ..-2 ..-3 ..-4 ..-5

coef. coef. coef. _ coef. _ coef.

g/h n m

g 1 0 -29986.4 -29986.4 -29986.4 3.5 -29986.6 3.5 -29987.2 3.5

g 1 1 -1956.1 -1956.1 -1956.1 3.5 -1956.1 3.5 -1955.2 3.5

h 1 1 5604.2 5604.2 5604.2 3.5 5604.3 3.5 5603.9 3.5

g 2 0 -1996.9 -1996.9 -1996.9 1.4 -1996.9 1.4 -1996.9 1.4

g 2 1 3027.3 3027.3 3027.3 1.4 3027.3 1.4 3027.7 1.4

h 2 1 -2129.3 -2129.3 -2129.3 1.4 -2129.3 1.4 -2129.1 1.4

g 2 2 1662.6 1662.6 1662.6 1.4 1662.6 1.4 1661.4 1.4

h 2 2 -199.8 -199.8 -199.9 1.4 -199.9 1.4 -200.2 1.4

g 3 0 1281.6 1281.6 1281.5

g 3 1 -2180.6 -2180.5 -2180.5

h 3 1 -335.4 -335.4

g 3 2 1250.8 1250.8

h 3 2 271 271

g 3 3 835.1 833.1

h 3 3 -252.6 -252.6

g 4 0 937.4 957.4

g 4 1 782.1 782.1

h 4 1 212.4 212.4

g 4 2 397.4 397.4

h 4 2 -256.6 -256.6

g 4 3 -419.1 -419.1

h 4 3 53 53

g 4 4 198.3 198.3

h 4 4 -297.3 -297.3

g 5 0 -217.9 -217.9

g 5 1 557.2 357.2

h 5 1 46 46

g 5 2 260.9 260.9

h 5 2 149.8 149.8

g 5 3 -74.4 -74.4

h 5 3 -150.7 -150.7

g 5 4 -162 -162

h 5 4 -77.8 -77.8

g 5 5 -47.9 -47.9

h 5 5 92.1 92.1

-335.4

1250.8

271 2

833.1 2

-252.6 2

937.4 0.9

782.1 0.9

212.4 0 9

397.4 0 9

-256.6 0 9

-419.1 0 9

53 0 9

198.3 0 9

-297.3 0.9

-217.9 0.7

557.2 0.7

46 0.7

261 0.7

149.8 0.7

-74.4 0.7

-150.7 0.7

-162 0.7

-77.8 0.7

-47.9 0.7

92.1 0.7

2 1281.7

2 -2180.7

2 -335.5

2 1250.7

271 2

833.1 2

-252.5 2

937.4 0.9

782 0 9

212.4 0 9

397.3 0 9

-256.6 0 9

-419.1 0 9

53 0 9

198.3 0.9

-297.3 0.9

-218 0.7

357.2 0.7

46.1 0 7

261 0 7

149.8 0 7

-74.3 0 7

-150.6 0 7

-161.9 0 7

-77.8 0 7

-48 0 7

92.1 0.7

2 1282.2 2

2 -2180.8 2

2 -335 2

2 1250.9 2

270.9 2

833.7 2

-252.2 2

937.5 0 9

781.7 0 9

212.3 0 9

397.7 0 9

-256.8 0 9

-419.1 0 9

52.9 0 9

198 0 9

-297 7 0 9

-218 3 0 7

357 2 0 7

458 O7

260 9 0 7

149 7 0 7

-74 5 0 7

-150 6 0 7

-162 3 0 7

-77 7 0 7

-48.4 0.7

91.9 0.7

74
Model ..-i ..-2 ..-3 ..-4 ..-5

g/hnm

g60

g61

h61

g62

h62

g63

h63

g64

h64

g65

h65

g66

h66

g70

g71

h71

g72

h72

g73

h73

g74

h74

g75

h75

g76

h76

g77

h77

g80

g81

h81

g82

h82

g83

h83

g84

h84

g85

h85

g86

h86

g87

h87

g88

h88

coef. coef. coef.a coef.a

48.1 48.1 48.1 0.5 48 0.5

65.5 65.5 65.5 0.5 65.5 0.5

-14.8 -14.8 -14.8 0.5 -14.8 0.5

41.9 41.9 41.9 0.5 42 0.5

93.2 93.2 93.2 0.5 95.i 0.5

-192.2 -192.2 -192.2 0.5 -192.2 0.5

70.7 70.7 70.7 0.5 70.7 0.5

3.6 3.6 3.5 0.5 3.6 0.5

-43 -43 -43 0.5 -43 0.5

13.7 13.7 13.7 0.5 13.8 0.5

-2.1 -2.2 -2.2 0.5 -2.2 0.5

-107.6 -107.6 -107.6 0.5 -107.7 0.5

17.2 17.2 17.2 0.5 17.2 0.5

71.9 71.9 71.9 0.4 72 0.4

-59.2 -59.2 -59.2 0.4 -59.2 0.4

-82.6 -82.6 -82.6 0.4 -82.6 0.4

1.7 1.7 1.7 0.4 1.7 0.4

-27.4 -27.4 -27.4 0.4 -27.4 0.4

20.7 20.7 20.7 0.4 20.7 0.4

-5 -5 -5 0.4 -5 0.4

-12.5 -12.5 -12.5 0.4 -12.5 0.4

16.2 16.2 16.2 0.4 16.2 0.4

0.5 0.5 0.5 0.4 0.5 0.4

17.8 17.8 17.8 0.4 17.8 0.4

10.7 10.7 10.7 0.4 10.6 0.4

-23 -23 -23 0.4 -22.9 0.4

-1.7 -1.7 -1.7 0.4 -1.6 0.4

-9.8 -9.8 -9.8 0.4 -9.8 0.4

18.5 18.5 18.5 0.4 18.5 0.4

6.5 5.5 6.5 0.4 6.5 0.4

6.8 5.8 6.8 0.4 5.8 0.4

-0.4 -0.4 -0.4 0.4 -0.4 0.4

-17.7 -17.7 -17.7 0.4 -17.7 0.4

-10.9 -10.9 -10.9 0.4 -11 0.4

4.2 4.2 4.2 0.4 4.2 0.4

-7 -7 -7 0.4 -7 0.4

-22.2 -22.2 -22.2 0.4 -22.2 0.4

4.3 4.3 4.3 0.4 4.4 0.4

9.1 9.1 9.1 0.4 9.1 0.4

2.7 2.8 2.8 0.4 2.7 0.4

16 16 15 0.4 16 0.4 6 6 6 0.4 6.1 0.4

-13.1 -13.1 -13.1 0.4 -13.2 0.4

-1.5 -1.5 -1.5 0.4 -1.6 0.4

-14.9 -14.8 -14.8 0.4 -14.8 0.4

coef.a

48.1 0.5

65.705

-14.605

41.805

93.305

-192.205

7105

3.7 0.5

-43 0.5

13.8 0.5

-2.1 0.5

-107.7 0.5

17.6 0.5

72.2 0.4

-59.1 0.4

-82.4 0.4

1.8 0.4

-27.3 0.4

20.8 0.4

-4.9 0.4

-12.3 0.4

15.7 0.4

0.5 0.4

18.2 0.4

i0.9 0.4

-22.8 0.4

-1.5 0.4

-10.3 0.4

18.5 0.4

6.3 04

6.5 04

-'0.304

-17.604

-II04

4.1 04

-6.904

-22.3 0.4

3.9 0.4

9.2 0.4

2.9 0.4

16.1 0.4

6.1 0.4

-13.3 0.4

-1.8 0.4

-14.7 0.4

75
Model ..-I ..-2 ..-3 ..-4 ..-5

g/h n m

g 9 0

g 9 1

h 9 1

g 9 2

h 9 2

g 9 3

h 9 3

g 9 4

h 9 4

g 9 5

h 9 5

g 9 6

h 9 6

g 9 7

h 9 7

g 9 8

h 9 8

g 9 9

h 9 9

g I0 0

g i0 1

h I0 1

g i0 2

h i0 2

g i0 3

h i0 3

g i0 4

h i0 4

g I0 5

h i0 5

g i0 6

h i0 6

g I0 7

h I0 7

g I0 8

h I0 8

g I0 9

h 10 9

g I0 i0

h 10 10

coef.

5.3

10.3

-20.8

1.4

15.5

-12.4

8.8

9.4

-5.2

-3.4

-6.3

-1.2

9.1

6.7

9.7

1.6

-5.9

-5.1

2.2

-3.4

-4

1.2

2.2

0.5

-5.5

2.6

-1.9

5.7

4.6

-4.3

3.i

-0.5

0.8

-1.3

2.1

3.5

2.8

-0.5

-0.i

-6.i

coef.

5.3

10.3

-20.8

1.4

15.5

-12.4

8.8

9.4

-5.2

-3.4

-6.3

-1.2

9.1

6.7

9.7

1.5

-5.9

-5.1

2.2

-3.4

-4

1.2

2 2

0 5

-5 5

2 6

-i 9

5 7

4 6

-4 3

3 1

-0.4

0.8

-1.3

2.1

3.5

2.8

-0.5

-0.i

-6.1

coef.

5.3

10.3

-20.8

1.4

15.5

-12.4

8.8

9.4

-5.2

-3.4

-6.3

-1.2

9.1

6.7

9.7

1.5

-5.9

-5.1

2.3

-3.4

-4

1.2

2.2

0.5

-5.5

2.6

-1.9

5.7

4.6

-4.3

3.1

-0.4

0.8

-1.3

2.1

3.5

2.8

-0.5

-0.1

-6.1

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

coef.

5.3

10.3

-20.8

1.4

15.5

-12.4

8.8

9.4

-5.2

-3.4

-6.3

-1.2

9

6.7

9.7

1.5

-6

-5.1

2.3

-3.4

-4

1.2

2 2

0 5

-5 5

2 6

-I 9

5 7

4 6

-4 3

3 1

-0 4

0.9

-1.3

2.1

3.5

2.8

-0.5

-0.i

-6.1

G

0.3

0 3

0 3

0 3

0 3

0 3

0 3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

coef.

4.9

10.4

-20.9

1.3

15.5

-12.4

8.6

9 3

-4 9

-3 3

-6 2

-i 3

9 1

6 8

9 8

1 6

-5 5

-5 1

2 1

-3 3

-3 9

1 5

2 2

0 3

-5 4

2 6

-1.9

5.7

4.8

-4.2

3.3

-0.8

0.6

-i

2.7

3.3

2.8

-1.3

-0.7

-5.6

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0.3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0 3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

76
Model

..-i..-2..-3..-4..-5

glhnm

g ll0

g II1

h ii1

g ii2

h ii2

g ii3

h ll3

g ll4

h ii4

g ll5

h ii5

g ii6

h ii6

g ll7

h ii7

g ii8

h 118

g 119

h 119

g 11 10 h 11 10 g 11 11 h 11 11 g 12 0 g 12 1 h 12 1 g 12 2 h 12 2 g 12 3 h 12 3 g 12 4 h 12 4 g 12 5 h 12 5 g 12 6 h 12 6 g 12 7 h 12 7 g 12 8 h 12 8 g 12 9 h 12 9 g 12 10 h 12 10 g 12 11 h 12 11 g 12 12 h 12 12

coef.

2.5

-1.1

0.7

-1.7

1.7

2.2

-1.3

0

-3.1

-0.6

0.7

-0.4

-0.1

1.6

-2.4

1.7

-0.4

-0.7

-1.7

2

-1.6

3.4

0.8

-1.7

-0.2

0.3

-0.3

0.8

-0.2

2.5

0.7

-1.4

0.7

0.4

-0.5

0.3

-0.2

-0.3

0.2

0.1

-0.5

0.1

0.1

-1.3

0.6

0.4

0.1

0.4

coef.

2.5

-i.i

0.7

-1.7

1.7

2.2

-1.3

0

-3.1

-0.6

0.7

-0.4

-0.1

1.6

-2.4

1.7

-0.4

-0.7

-1.7

2

-1.6

3.4

0.8

-1.7

-0.1

0.3

-0.3

0.8

-0.2

2.5

0.7

-1.4

0.7

0.4

-0.5

0.3

-0.2

-0.3

0.2

0.1

-0.5

0.1

0.1

-1.3

0.6

0.4

0.i

0.4

coef.a coef.a coef.a

2.5 0.3

-i.i 0.3

0.7 0.3

-1.7 0.3

1.7 0.3

2.2 0.3

-1.3 0.3 0 0.3

-3.1 0.3

-0.6 0.3

0.7 0.3

-0.4 0.3

-0.i 0.3

1.6 0.3

-2.4 0.3

1.7 0.3

-0.4 0.3

-0.7 0.3

-1.7 0.3 2 0.3

-1.6 0.3

3.4 0.3

0.8 0.3

-1.7 0.3

-0.1 0.3

0.3 0.3

-0.3 0.3

0.8 0.3

-0.2 0.3

2.5 0.3

0.7 0.3

-1.4 0.3

0.7 0.3

0.4 0.3

-0.4 0.3

0.3 0.3

-0.2 0.3

-0.3 0.3

0.2 0.3

0.i 0.3

-0.5 0.3

0.I 0.3

0.i 0.3

-1.3 0.3

0.6 0.3

0.4 0.3

0.1 0.3

0.4 0.3

77

2.4 0.3

-i.i 0.3

0.6 0.3

-1.7 0.3

1.7 0.3

2.2 0.3

-1.3 0.3 0 0.3

-3.1 0.3

-0.6 0.3

0.7 0.3

-0.3 0.3

-0.i 0.3

1.6 0.3

-2.4 0.3

1.7 0.3

-0.4 0.3

-0.7 0.3

-1.7 0.3 2 0.3

-1.5 0.3

3.4 0.3

0.8 0.3

-1.7 0.3

-0.i 0.3

0.3 0.3

-0,3 0.3

0.8 0.3

-0.2 0.3

2.6 0.3

0.7 0.3

-1.5 0.3

0.7 0.3

0.4 0.3

-0.4 0.3

0.3 0.3

-0.2 0.3

-0.2 0.3

0.2 0.3

O.1 0.3

-0.5 O.3

0.i 0.3

0.i 0.3

-1.3 0.3

0.6 0.3

0.4 0.3

0.i 0.3

0.4 0.3

2.4 03

-1.2 03

O.6 O3

-1.8 03

1.8 03

21 03

-i3 0.3

-01 0.3

-31 0.3

-06 0.3

07 0.3

-0.4 0.3 0 0.3

1.6 0.3

-2.5 0.3

1.6 0.3

-0.3 0.3

-0.6 03

-16 03

22 03

-17 03

33 03

07 03

-18 03

-01 03

0.3 0.3

-0.403

0.803

-0.i 03

2.6 03

0.6 03

-1.403

0.8 03

0.5 0.3

-0.5 0.3

0.2 0.3

-0.i 0.3

-0.2 0.3

0.i 0.3 0 0.3

-0.3 0.3

0.3 03

0.3 03

-1.5 03

0.3 03

0.2 03

0.i 03

0.6 0.3
Model ..-i ..-2 ..-3 ..-4 ..-5

g/h n m

g 13 0

g 13 1

h 13 1

g 13 2

h 13 2

g 13 3

h 13 3

g 13 4

h 13 4

g 13 5

h 13 5

g 13 6

h 13 6

g 13 7

h 13 7

g 13 8

h 13 8

g 13 9

h 13 9

g 13 i0

h 1310

g 1311

h 1311

g 1312

h 1312

g 1313

h 1313

coef.

0

-0.6

-0.5

0.4

0.3

-0.8

1.5

0

-0.2

i.i

-0.5

-0.4

-0.I

0.4

0.8

-0.5

0.1

0.2

0.8

-0.1

0

0.3

0

0

0.1

0.2

-0.3

coef. coef.

0

-0.6

-0.5

0.4

0.3

-0.8

1.5

0

-0.2

1.1

-0.5

-0.4

-0.i

0.4

0.8

-0.5

0.1

0.2

0.8

-0.1

0.1

0.3

0

0

0.1

0.2

-0.3

0 0.2

-0.6 0.2

-0.5 0.2

0.4 0.2

0.3 0.2

-0.8 0.2

1.5 0.2

0 0.2

-0.2 0.2

1.1 0.2

-0.5 0.2

-0.4 0.2

-0.1 0.2

0.4 0.2

0.8 0.2

-0.5 0.2

0.1 0.2

0.2 0.2

0.8 0.2

-0.1 0.2

0.1 0.2

0.3 0.2

0 0.2

0 0.2

0.1 0.2

0.2 0.2

-0.3 0.2

coef. 0 coef. u

0 02

-0.6 02

-0.5 02

0.4 02

0.3 02

-0.8 02

1.5 02

0 0.2

-0.2 O.2

1.1 0.2

-0.5 0.2

-0.4 0.2

-0.i 0.2

0.4 02

0.8 02

-0.5 0 2

0 02

0.2 02

0.8 02

-0.1 02

0 02

0.3 02

0 02

0 02

0.i 02

0.2 02

-0.3 02

-0.i 0.2

-0.6 0.2

-0.3 0.2

0.3 0.2

0.4 02

-0.7 0 2

1.7 02

0 0 2

-0.3 0 2

1.2 02

-0.3 0.2

-0.4 0.2

-0.2 0.2

0.4 02

1 02

-0.4 02

-0.i 02

0.2 02

i.i 02

0.3 02

-0.3 0 2

0 0 2

-0.3 0 2

0 0 2

0.4 02

0.3 02

-0.3 0 2

78
GSFC(5/89) MODELS:Secular Variation Coefficients

Model: ..-i ..-2 ..-3 ..-4 ..-5

g/h

g

g

h

g

g

coef. coef. coef. a coef. a coef. a

n m

1 0 23 23.1 23 0.26 25.3 0.14 33.1 0.24

1 1 i1.7 11.5 11.6 0.35 10.8 0.3 -1.9 0.31

1 1 -20.5 -20.6 -20.5 0.55 -21.5 0.31 -17.4 0.3

2 0 -13.8 -15.8 -13.9 0.24 -15.7 0.13 -14.5 0.23

2 1 3.5 3.7 3.60.24 3.10.14 -1.40.24

h 2 1 -14.1 -14.1 -14 0.25 -13.5 0.15 -18.1 0.23

g 2 2 4 4 4.1 0.32 4.6 0.28 18.9 0.28

h 2 2 -22.3 -22.2 -22.1 0.31 -21.9 0.27 -18 0.27

g 3 0 3.3 3.3 3.4 0.22 2 0.13 -4.4 0.21

g 3 1 -5.6 -5.7 -5.6 0.23 -4.8 0.16 -5 0.23

h 3 1 4.7 4.7 4.7 0.23 6.2 0.17 0.7 0.2

g 3 2 -1.2 -1.2 -1.1 0.23 -0.9 0.15 -3.2 0.23

h 3 2 3 2.9 2.8 0.23 3 0.15 6.3 0.22

g 3 3 -1.2 -1.2 -1.3 0.29 -1.3 0.26 -7.5 0.27

h 3 3 -8.9 -8.9 -9 0.29 -9.4 0.26 -14.4 0.26

g 4 0 0.3 0.3 0.3 0.2 0.1 0.12 -1.3 0.19

g 4 1 -1.6 -1.6 -1.5 0.21 -0.8 0.12 2.9 0.2

h 4 1 4 4 4 0.2 3.5 0.13 6.8 0.19

g 4 2 -7.6 -7.6 -7.6 0.22 -7.1 0.15 -10.8 0.21

h 4 2 1.9 2 2 0.21 1.1 0.15 4.3 0.2

g 4 3 -0.9 -0.9 -0.9 0.22 -1.5 0.14 -1.3 0.21

h 4 3 3.2 3.1 3.1 0.22 3 0.15 4.2 0.21

g 4 4 -5.7 -5.6 -5.6 0.28 -5.5 0.25 -3 0.26

h 4 4 -0.i -0.i -0.2 0.27 -0.2 0.24 6.6 0.25

g 5 0 0.5 0.5 0.5 0.19 1.30.11 5.2 0.19

g 5 1 0.i 0 -0.1 0.19 -0.5 0.12 0.4 0.19

h 5 1 0.4 0.4 0.4 0.19 -0.1 0.13 4.8 0.18

g 5 2 -0.8 -0.8 -0.9 0.21 -1.8 0.13 0.8 0.2

h 5 2 0.7 0.6 0.6 0.19 0.1 0.12 1.1 0.18

g 5 3 -3.6 -3.5 -3.5 0.21 -3.9 0.14 -2.5 0.21

h 5 3 -0.4 -0.4 -0.4 0.21 -0.7 0.15 -i.i 0.2

g 5 4 -0.2 -0.2 -0.2 0.22 -0.6 0.16 4.1 0.21

h 5 4 0.6 0.6 0.7 0.21 0.7 0.14 0.9 0.2

8 5 5 -0.5 -0.6 -0.5 0.26 -0.1 0.23 5.7 0.24

h 5 5 0.6 0.5 0.6 0.27 0.9 0.24 0.5 0.25

79
Model: ..-1 ..-2 ..-3 ..-4 •

coef. coef.

g/h n m

g 6 0 0.5

g 6 i 0.3

h 6 1 -0.2

g 6 2 1.6

h 6 2 -1.5

g 6 3 1.6

h 6 3 -1.1

g 6 4 -0.5

h 6 4 -i

g 6 5 0.9

h 6 5 -0.i

g 6 6 I.i

h 6 6 0.8

g 7 0 i

g 7 I -0.8

h 7 1 0.i

g 7 2 -0.3

h 7 2 0.2

g 7 3 0.4

h 7 3 1

g 7 4 0.9

h 7 4 1

g 7 5 0.6

h 7 5 0.6

g 7 6 -0.2

h 7 6 0.7

g 7 7 0.7

h 7 7 0.3

g 8 0 0.9

g 8 1 -0.2

h 8 1 0.2

g 8 2 0.i

h 8 2 -0.4

g 8 3 -0.2

h 8 3 0.3

g 8 4 0.i

h 8 4 -0.2

g 8 5 0.2

h 8 5 0.4

g 8 6 -0.I

h 8 6 -0.5

g 8 7 -0.I

h 8 7 -0.2

g 8 8 -1.4

h 8 8 0.7

0.5

0.4

-0.i

1.7

-1.4

1.5

-1.1

-0.5

-i

1

0

1.1

0.8

1

-0.8

0

-0.2

0.1

0.4

0.9

0.9

1

0.6

0 5

-0 1

0 6

0 7

0 3

0 9

-0.2

0.2

0.1

-0.4

-0.2

0.3

0

-0.3

0.2

0.4

-0.1

-0.4

-0.2

-0.2

-1.4

0.7

coef. a coef. 6

0.50.18 10.11

0.30.19 00.11

-0.10.18 -0.10.11

1.60.19 1.40.12

-1.40.18 -1.20.12

1.50.19 2.20.12

-10.19 -0.40.13

-0.50.21 -0.10.15

-10.19 -0.80.13

0.9 0.2 0.10.14

0.10.21 0.70.15

1.20.25 1.50.22

0.80.25 10.22

10.17 0.2 0.1

-0.80.17 -0.6 0.1

0.10.17 0.20.11

-0.10.18 0.20.11

0.10.16 0.40.11

0.40.18 0.50.11

10.17 0.70.12

0.9 0.2 1.10.13

10.18 0.80.12

0.60.19 0.80.14

0.4 0.2 -0.10.14

-0.2 0.2 0.20.15

0.5 0.2 -0.20.14

0.70.25 00.22

0.40.24 0.60.21

0.90.16 0.5 0.1

-0.20.16 -0.2 0.1

0.20.15 0 0.1

00.16 0.4 0.i

-0.4 0.16 -0.5 0.i

-0.20.16 -0.i 0.i

0.20.15 0.20.11

0.10.18 -0.20.13

-0.30.16 -0.30.11

0.20.18 00.12

0.40.19 0.30.13

-0.10.19 -0.10.14

-0.40.19 -0.50.14

-0.20.19 -0.40.14

-0.20.19 0.50.14

-1.40.23 -0.8 0.2

0.70.24 0.20.21

coef.

1.4

-1.7

-2.1

4.1

-2.4

1.8

-4.3

-0.7

0.5

0.9

-2.4

0.2

-4.3

-1.7

-0.8

-2.6

-0.7

-0.7

-0.5

-1.2

-0.8

6.8

1.5

-4.8

-4

-i 2

-i i

6 8

0 8

2 2

3 6

-1.3

-0.8

1

1.3

-i

1.2

5.6

-0.6

-1.7

-0.7

-0.4

2.3

2.5

-2

80
Model: ..-i ..-2 ..-3 ..-4 ..-5

coef. coef.

g/h n m

g 9 0 -0.5 -0.4

g 9 1 0.i 0.i

h 9 1 0.4 0.4

g 9 2 0.4 0.4

h 9 2 0.3 0.2

g 9 3 0 0.i

h 9 3 0.2 0.2

g 9 4 -0.i -0.I

h 9 4 -0.1 0

g 9 5 -0.6 -0.5

h 9 5 -0.5 -0.4

g 9 6 0 0

h 9 6 -0.8 -0.8

g 9 7 -0.i 0

h 9 7 0.2 0.2

g 9 8 -0.4 -0.3

h 9 8 -0.3 -0.3

g 9 9 0.2 0.2

h 9 9 0.3 0.3

g i0 0 0.i 0.i

g i0 1 -0.I -0.i

h 10 1 0 0

g i0 2 -0.5 -0.5

h I0 2 -0.i -0.I

g i0 3 0.2 0.I

h i0 3 0 0

g i0 4 0 -0.I

h i0 4 0.I 0

g i0 5 0 0

h 10 5 0.2 0.1

g I0 6 0 0

h 10 6 0.3 0.2

g i0 7 0.1 0

h i0 7 -0.2 -0.2

g 10 8 0.3 0.2

h I0 8 0 0

g I0 9 0.3 0.3

h 10 9 -0.2 -0.2

g I0 i0 -0.2 -0.2

h I0 i0 -0.7 -0.6

coef. 0 coef. 0

-0.40.14 0.10.09

0.10.15 00.09

0.40.14 0.20.09

0.30.15 0.20.09

0.30.15 0.10.09

0.10.14 -0.10.09

0.20.15 0.3 0.1

00.15 -0.20.11

00.15 00.09

-0.60.16 -0.30.11

-0.40.18 -0.10.12

00.18 -0.20.12

-0.70.17 00.12

-0.10.19 0.60.13

0.10.19 -0.50.14

-0.30.19 0.40.14

-0.30.19 0.40.14

0.10.23 00.19

0.30.22 0.2 0.2

0.10.12 00.08

-0.10.12 -0.10.08

00.12 -0.10.09

-0.50.12 -0.50.09

-0.10.12 -0.20.09

0.10.13 0.10.09

00.12 0.10.09

-0.10.13 -0.2 0.1

0.10.12 -0.10.09

00.13 -0.10.09

0.10.14 0 0.1

00.15 00.11

0.2 0.15 -0.i 0.ii

0.10.15 00.11

-0.20.15 -0.10.11

0.20.16 -0.50.12

00.16 -0.30.12

0.30.17 -0.10.13

-0.10.17 0.10.13

-0.10.22 0.20.18

-0.70.23 -0.3 0.2

coef. o

3.70.14

-i 0.14

0.60.13

0.70.14

-1.20.14

0.50.14

1.80.14

0.70.15

-3.40.14

-0.90.16

-0.90.17

0.70.17

-10.16

-0.20.18

-1.20.18

-0.60.18

-3.90.18

-1.20.21

1.80.21

-1.30.11

-1.70.12

-3.90.11

-0.60.11

1.60.12

-10.12

-0.20.11

0.10.13

-0.90.11

-2.40.13

-0.90.13

-2.30.13

3.50.14

2.50.13

-3.10.13

-6.40.14

2.50.14

0.50.14

8.10.15

6.2 0.2

-5.6 0.2

81
GSFC(4/89) MODELS: Main Field Coefficients

Model ..-i ..-2 ..-3 ..-4

coef.

g/h n m

g 1 0 -29772.9

g 1 1 -1876.3

h 1 1 5409.4

g 2 0 -2139.7

g 2 1 3045.2

h 2 1 -2280.3

g 2 2 1710.2

h 2 2 -355.8

g 3 0 1312

g 3 1 -2214.2

h 3 1 -264.8

g 3 2 1245.4

h 3 2 301.5

g 3 3 820.2

h 3 3 -354.7

g 4 0 951.8

g 4 1 777.8

h 4 1 241.7

g 4 2 338.7

h 4 2 -259.4

g 4 3 -417.6

h 4 3 81.5

g 4 4 145.6

h 4 4 -290.2

g 5 0 -221.8

g 5 1 353

h 5 1 31.6

g 5 2 236.4

h 5 2 161.2

g 5 3 -131.9

h 5 3 -153.9

g 5 4 -165.8

h 5 4 -77.3

g 5 5 -39.2

h 5 5 104.8

G coef. a coef. coef.

6.3

6.6

6.9

5.8

5.4

6.4

6.6

5.8

5.6

5

7

6.3

6.1

6.3

6.1

5.I

4

6.1

5.6

5.6

5.5

5

4.7

5.3

5.4

3.8

4 9

4 2

4 8

5 9

4 7

4 1

5 4

5

4.3

-29747.7 15.9

-1923.3 27.2 -1917.5

5369.5 22.5 5365

-2133.9 16.8 -2132.5

3059.7 14.4 3051.5

-2258.1 14.3 -2264.1

1743.7 26.7 1747.1

-329.9 23.3 -326.6

1319 12.9 1319.5

-2212.2 18.1 -2212.1

-268.6 14.9 -261.3

1251 14 1246.2

290.8 13.9 292.8

751.5 26.1 757.7

-365.9 21.9 -360.4

954.7 12.2 960.7

768.3 13 770.9

254.4 11.6 258.8

297.9 15.2 299.7

-238.2 14.3 -239.1

-416.2 13 -419.1

83.3 12.3 83.9

189.6 25.9 194

-266.5 21.5 -269.8

-217 11.1 -226.5

333.5 10.9 331.5

47 11.3 35.6

234.3 Ii.i 237.3

155.3 11.6 155.9

-89.5 14.1 -89.7

-162.5 11.6 -165.7

-157.7 11.4 -162.4

-57.5 12.7 -53.5

-92.6 22.4 -92.9

75.7 21.3 70.3

-29753.6 -29738.9

-1891.7

5403

-2127.6

3097.7

-2254.7

1692

-305.7

1310.4

-2237.8

-308.6

1256.3

278

808.8

-340.6

981 9

760 6

264 8

319 3

-266 4

-443 8

52 6

i01 9

-286 7

-232 9

345 2

23 8

223 6

149 3

-87 6

-117 9

-162.6

-69.8

-55.8

86.7

a

29.1

36.6

31.6

27.9

29.4

25.2

32

33.2

22.6

26.5

25.5

23.9

27.8

30.4

31.3

20

21

24

21.5

26.1

21.4

25.5

27

26.6

19.5

18.1

20.2

17.1

23.9

19.9

23.7

22.5

21.3

25

24.9

82
Model ..-i ..-2 ..-3 ..-4

g/h

gghghghghghghgghghghghghghghgghghghghghghgh8h

n666666666666677777777777777788888888888888888m011223344556601122334455667701122334455667788

coef.

62.9

59.6

-6.9

47.7

83

-164

67.8

5.1

-31.2

9.3

0.6

-84.1

20.4

77.9

-60.6

-78.8

17.2

-24.2

30.8

10.6

1.7

3.7

19.3

7.7

12.5

-20.1

-3.7

-4.5

27

8.5

6.9

-4.3

-25.7

-14.4

-3.3

-7.7

-19.7

-12.3

10.5

1.1

9.3

-4.1

-8.6

-10.4

-11.2

G

3.6

3.2

4.5

3.2

3.8

4.6

3.4

4.5

5.3

4.1

3.8

4.1

4.7

2.9

2.6

3.1

2.9

3.3

3.3

2.6

3.6

3.8

4.3

4.4

3.6

3.6

4.2

4.5

2.1

1.9

2.1

1.9

2.4

2.52

2.5

2.2

2.7

2.8

2.9

2.9

2.6

2.7

4.1

3.4

coef.

59.6

73.6

-20.1

58.9

80.7

-181.7

80.8

-3.9

-48.5

i0.8

-14.2

-68.2

47.2

77.1

-67.8

-77.9

10.4

-15.6

34.4

-1.7

-3.7

12.1

15.4

20.7

15.7

-21.9

-29.1

-13.6

28.4

-3.4

14.1

-8.1

-17.6

-17.8

9.3

-9.4

-16.5

-1.7

24

-7.4

-1.9

-0.4

-23.7

11.6

0.7

q

i0

9.8

9.7

9.8

10.6

10.5

9.8

12.6

11.8

10.6

11

19.6

20

8.2

9.3

8.9

8.4

9.1

9.9

8.8

9.3

8.9

10.6

10.9

10

9.4

18.5

18.2

6.2

7.5

8.1

6.6

7.6

7.9

7.5

8.7

7.48

7.9

9.9

9.8

8.8

8.8

16.3

15.9

coef.

62.3

71.3

-11.9

52.5

81.8

-179.8

80.6

-4.9

-47.9

8.6

-9.8

-66.5

47.7

83.1

-64.6

-81.9

16.3

-13.5

33.9

4.7

-2.2

9.8

16.3

19.8

12.6

-19.2

-27.4

-18.6

23.6

-3

13.8

-10.9

-20.8

-17.8

5.6

-4.9

-14.8

-1.7

20.5

-7.1

-4.9

-3

-19.8

9.6

-6.9

coef.

30.9

67.7

4

76.6

96.8

-195.5

41.2

20.6

-26.3

21.7

-29.4

-73.4

-14.1

103.3

-69.4

-65.5

1.9

-37

31.9

-17.3

-0.7

1.4

-14.2

34.7

8.9

-9.4

-5.5

-12.5

8.9

1.6

13.6

-15.9

-15.5

-9.9

37.1

-24.3

-22.9

2O

192

-i1

222

101

-227

166

134

17.2

15.7

16

151

2OI

181

196

235

178

20.5

20.6

23.5

24.8

14.4

12.9

14.1

13 .i

16.2

16.4

16.6

19.9

14.6

18

19.8

19

18.6

23.1

23.6

11.3

ii

11.4

10.2

12.2

12.2

12.3

14.4

11.5

13.4

13.6

14.2

14.7

15.1

15.6

20.6

21

83
Model ..-i ..-2 ..-3 ..-4

coef.

g/h n m

g 9 0 2.7

g 9 I 7.5

h 9 i -24.1

g 9 2 0

h 9 2 16

g 9 3 -8.4

h 9 3 13.3

g 9 4 0.3

h 9 4 -2.7

g 9 5 0.5

h 9 5 -8.6

g 9 6 -3 .i

h 9 6 17.9

g 9 7 7.2

h 9 7 4.8

g 9 8 7.6

h 9 8 -7.7

g 9 9 -14.2

h 9 9 2.4

g i0 0 -4.1

g i0 1 -4.9

h i0 i 4.5

g i0 2 1.6

h i0 2 1.5

g i0 3 -7.1

h i0 3 3.4

g i0 4 4.1

h I0 4 -0.8

g i0 5 4.9

h i0 5 -0.6

g i0 6 1

h i0 6 -6.5

g i0 7 6.2

h i0 7 -5.4

g i0 8 0.8

h i0 8 5

g i0 9 -2

h i0 9 0

g i0 i0 10.7

h i0 i0 -2.9

G

0.8

0.9

0.9

0.9

1

0.9

0.9

1

0.9

1

1.2

i.i

I.i

1.4

1.2

1.2

i.i

1.6

i 6

0 6

0 6

0 6

0 6

0 7

0 7

0 6

0 7

0.6

0.7

0.7

0.8

0.8

0.8

0.8

0.9

0.9

1

0.9

1.3

1.4

coef.

3

5

-17.5

-5.3

12.8

-8.6

7.6

14.5

-8.6

-5.7

-16.7

-3.1

2.9

20.7

i1.2

6.7

-5.8

-21.8

1.4

-9

-1.8

-4.6

4.4

-7

-3

5.7

-2

5.1

-1.6

-8.8

9

1.5

7.4

3.6

-9.4

6

1.2

-2.5

6.4

-3 .i

6.4

6.2

6.1

6.6

7.7

6.5

6.3

7.3

6.6

6.8

7.5

7.2

6.7

8.6

7.7

7

7.1

12.1

12

5.3

5.9

5.4

5.4

5.7

6.3

6

6.1

5.4

6.2

5.6

6

5.6

6.2

5.9

6.9

7.5

6.9

6.4

II.I

10.4

coef.

3.5

3.3

-16

-5.7

13.1

-9

7.9

12.5

-9.2

-6

-15.4

-3.8

2.9

20.9

9.1

8.1

-1.3

-25.2

-2 6

-8 5

-i 9

-5 2

4 2

-5 3

-2 6

5 8

-2 5

4 3

-1.6

-8

i0.i

1

8.1

4.1

-ii.i

5.3

4.1

-2.9

5.5

-1.5

coef.

i0

11.9

-22.4

1.3

8.3

-16.1

10.4

8.6

-i0

-72

-8 5

-2 2

16 6

20 5

-4 1

0 1

-6 7

-21 7

6.7

-9.2

-3.8

6.2

3.5

-2.4

-4.7

5.1

7.2

3.6

4.6

-5.5

-3.1

-2.9

-0.5

0.5

2.5

4.6

0.4

-4.8

4.9

-0.4

G

2.7

2.8

2.4

2.5

2.7

2.6

2.7

2.8

2.7

3

3

3.2

3

3.6

3.3

3.5

3.2

4.9

5

2 4

2 6

2 2

2 3

2 4

2 4

2 5

2 6

2 5

2 7

2 5

2 8

2 8

2 9

2 8

3 2

3 2

3 3

3 1

4 9

5

84
GSFC(4/89) MODELS:

Model ..-i

Secular Variation Coefficients

..-2 ..-3 ..-4

coef a coef q coef

g/h n m

g 1 0 20.2 1.13 22 1.3 20.2

g 1 1 10.5 1.2 i0 1.29 i0

h 1 1 -17.4 1.28 -19.6 1.42 -21.3

g 2 0 -12.6 1.22 -14.1 1.43 -13.3

g 2 1 1 i.ii 3.5 1.23 1.7

h 2 1 -19.2 1.36 -16.9 1.64 -18

g 2 2 3.9 1.39 2.2 1.46 3.5

h 2 2 -15.7 1.2 -16.8 1.28 -15.6

g 3 0 2.6 1.14 4.2 1.27 4.1

g 3 1 -3.7 0.99 -6.3 1.09 -6.2

h 3 1 7.6 1.45 6.9 1.74 8.3

g 3 2 -3 1.28 -i 1.47 -i

h 3 2 5 1.19 2.7 1.36 2.7

g 3 3 -1.9 1.29 -3.1 1.35 -2.5

h 3 3 -11.2 1.21 -10.4 1.26 -8.6

g 4 0 3.4 1.07 0.8 1.29 1.6

g 4 1 -0.7 0.79 -0.i 0.87 0.4

h 4 1 4.1 1.31 2.5 1.52 4.1

g 4 2 -4.6 1.16 -6.8 1.44 -7.1

h 4 2 -1.4 1.18 1.6 1.39 1.8

g 4 3 3 1.13 0.5 1.32 -0.3

h 4 3 4.8 1.03 3.9 1.18 4

g 4 4 -5.9 0.94 -5.8 0.98 -5.1

h 4 4 0 i.I 0.i 1.15 -0.8

g 5 0 -1.9 1.14 -0.3 1.36 -1.6

g 5 i -1.3 0.79 -0.5 0.86 -0.8

h 5 1 -3.9 1.02 -0.4 1.21 -3.1

g 5 2 -1.8 0.85 -1.8 1.09 -1.6

h 5 2 2.6 1.01 0.7 1.18 1.2

g 5 3 -8.2 1.23 -4.5 1.47 -4.4

h 5 3 -1.3 0.97 -0.7 1.16 -1.3

g 5 4 0 0.84 -0.2 0.93 -0.3

h 5 4 -1.2 1.12 0.7 1.25 1.3

g 5 5 1.1 1.01 1 1.06 0.2

h 5 5 0.5 0.86 0.I 0.9 -0.3

a coef

27

13.5

-15.6

-11.3

11.4

-13.8

-1.5

-9.7

0.8

-9.3

-0.2

2.4

-2.4

0.6

-6.2

8.4

-5.3

5

-7.4

-2.5

-4.3

-3.3

-14.5

-1.2

-3.9

1.9

-4.8

-4.8

0.9

-2.1

8

0.6

0.8

i.i

0.2

6 41

8 ii

7 02

6 17

6 61

5 55

7 21

7 35

5.07

5.95

5.58

5.37

6.17

6.91

6.95

4.4

4.76

5.28

4.81

5.7

4.81

5.65

6.01

6.05

4.34

4.03

4.38

3.9

5.27

4.41

5.2

5.01

4.73

5.67

5.57

85
Model ..-i ..-2 ..-3 ..-4

coef

g/h n m

g 6 0 i.i

g 6 1 0.3

h 6 1 2.8

g 6 2 0.I

h 6 2 -1.3

g 6 3 4.2

h 6 3 0.i

g 6 4 -0.8

h 6 4 3.3

g 6 5 -i

h 6 5 0.5

g 6 6 2.8

h 6 6 0

g 7 0 1.9

g 7 1 0.3

h 7 1 -0.6

g 7 2 1.7

h 7 2 0.I

g 7 3 0.6

h 7 3 1.2

g 7 4 1.6

h 7 4 -3.3

g 7 5 3.1

h 7 5 -0.4

g 7 6 -0.3

h 7 6 1.8

g 7 7 -0.2

h 7 7 -0.5

g 8 0 -0.i

g 8 1 -0.2

h 8 1 0.2

g 8 2 -0.6

h 8 2 -0.8

g 8 3 -0.i

h 8 3 0.i

g 8 4 -0.i

h 8 4 i

g 8 5 -1.9

h 8 5 -0.3

g 8 6 -0.4

h 8 6 -1.5

g 8 7 -0.2

h 8 7 0.3

g 8 8 -2.5

g 8 8 0.9

0.75

0.66

0.92

0.65

0.79

0.96

0.69

0.93

1.1

0.86

0.8

0.86

0.97

0.56

0.52

0.61

0.57

0.67

0.68

0.54

0.74

0.79

0.87

0.9

0.74

0.75

0.82

0.96

0.38

0.38

0.39

0.36

0.45

0.48

0.38

0.51

0.44

0.52

0.55

0.55

0.53

0.51

0.55

0.84

0.69

coef # coef a coef

1.4

-0.3

0.3

1.9

-1.2

1.9

-0.5

-0.6

0.I

0

0.i

1.6

i

0.7

-0.3

0.5

0

0.5

0.7

0.7

1.4

-0.8

1.2

0

-0.2

0.3

0.4

0.2

0.5

-0.2

0 6

-0 2

-0 4

-0 1

0 5

-0 4

0 6

-0 4

0 3

-0.i

-i

-0.2

-0.3

-1.4

0.3

0.82

0.7

1.13

0.74

0.89

1.16

0.83

1.04

1.27

0.92

0.84

0.89

1.02

0.63

0.55

0.73

0.7

0.72

0.78

0.62

0.82

0.94

0.97

0.97

0.8

0.8

0.86

1.02

0.44

0.4

0.43

0.42

0.48

0.54

0.41

0.55

0.5

0.59

0 61

0 59

0 56

0 54

0 59

0 89

0 75

2

-0.4

1.6

0.8

-i

2.5

-0.5

-0.4

0.6

-i

0.8

2.3

1.5

2

-0.i

0.2

1.1

0.6

1

2.1

1.3

-1.2

1.3

0

-0.7

0.4

0.i

-0.4

-0.3

-0.4

0.3

-0.8

-0.5

-0.2

0

0.4

0.5

-0.2

-0.2

0

-2.2

-0.7

0.7

-1.6

-1.2

-4.7

i.i

4.6

4.3

1.3

-0.9

-6.5

1.7

3.7

0

-4.8

5.2

-6.4

6

-0.8

1

-i.i

-2.6

2.9

_3, "_

1

-2.,

-4.2

2.9

-2.1

4.1

1.9

-3.6

-2.1

0.7

1.2

-2.8

-0.2

-0.2

5.9

-1.2

0.6

3.1

0.i

0.3

2

1.3

-2.4

0.9

4

3.83

3.57

3.5

3.36

4.41

4.1

4.38

5.24

3.94

4.54

4 63

5 32

5 63

3 21

2 92

3 ii

2 97

3 53

3.63

3.7

4.5

3.31

3.95

4.47

4.22

4.17

5.1

5 37

2 54

2 48

2 51

2 32

2 71

2.7

2.7

3 22

2 61

3 02

3 O7

3 13

3 25

3 32

3.45

4.6

4.64

86
Appendix B. Listin 8 of External Field Static Terms, Dst Multiplier Terms, and

Their Estimated Uncertainties for GSFC(5189-X) Series

GSFC(5/89-1) Model

n_ _m !ZZ Coefficient Standard Deviation

q 1 0 static 18.72960 nT 0.08658 nT

q 1 1 static -1.06290 nT 0.09959 nT

s 1 1 static -3.10297 nT 0.10019 nT

g 1 0 Dst -0.16907 0.00697

q 1 0 Dst -0.63175 0.00998

q 1 1 Dst -0.06827 0.01046

s 1 1 Dst 0.16972 0.01116

GSFC(5189-2) Model

n m Type Coefficient Standard Deviation

q I 0 static 18.72725 nT 0.08657 nT

q 1 1 static -1.06443 nT 0.09958 nT

s 1 1 static -3.10227 nT 0.10018 nT

g 1 0 Dst -0.16912 0.00696

q 1 0 Dst -0.63178 0.00998

q 1 1 Dst -0.06886 0.01045

s 1 1 Dst 0.16939 0.01116

GSFC(5189-3) Model

/ms// _n _m Coefficient Standard Deviation

q 1 0 static 18.72771 nT 0.08657 nT

q 1 1 static -1.06410 nT 0.09958 nT

s 1 1 static -3.10274 nT 0.10017 nT

g 1 0 Dst -0.16907 0.00696

q 1 0 Dst -0.63178 0.00997

q 1 1 Dst -0.06830 0.01045

s 1 1 Dst 0.16933 0.01115

87
GSFC(5189-4) Model

Coefficient

q 1 0 static 18.74793 nT

q 1 1 static -1.02312 nT

s 1 1 static -3.14808 nT

g 1 0 Dst -0.16634

q i 0 Dst -0.65700

q i i Dst -0.05128

s 1 1 Dst 0.16074

Standard Deviation

0.08638 nT

0.09946 nT

0.09997 nT

0.00665

0.00971

0.01020

0.01089

88
Appendix C. Listing of Observatory Vector Biases and Their Estimated

Uncertainties for GSFC(4/89-X) and GSFC(5/89-X) Series

89

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196
FIGURE CAPTIONS

Figures 1-10: Distribution of observatories for specified years.

Figures ii-16: Distribution of Project Magnet data.

Figures 17-24: Distributions of marine magnetic data.

Figures 25-32: Distributions of land surveys.

Figure 33: The variation of spherical harmonic coefficients with time

from the various GSFC(5/89) models and from the IGRF85 model. Also

shown are the _ IO lines for GSFC(5/89-4).

a) gl0: b) gl I and hll: c) g20; d) g21 and h21; e) g22 and h22;

f) g30: g) g31 and h31; h) g32 and h32; i) g33 and h33.

Figure 34: The variation of spherical harmonic coefficients relative to

that of the GSFC(5/89-4) model with time from the various GSFC(5/89)

models and from the IGRF85 model. Also shown are the _ la lines for

GSFC(5/89-4).

a) gl0; b) gl I and hll; c) g20; d) g21 and h21 ; e) g22 and h22;

f) g30; g) g31 and h31; h) g32 and h32; i) g33 and h33.

Figure 35: Contours of magnetic field components computed from the

GSFC(5/89-4) model at the Earth's surface at 1989.0.

a) D in degrees; b) I in degrees; c) H, nT; d) X, nT

e) Y, nT; f) Z, nT; g) B, nT.

Figure 36: Contours of estimated i 6 error in magnetic field components

computed from the GSFC(5/89-4) model at the Earth's surface at 1989.0.

a) D in degrees; b) I in degrees; c) H, nT; d) X, nT

e) Y, nT; f) Z, nT; g) B, nT.

Figure 37: Contours of the secular variation of magnetic field

components computed from the GSFC(5/89-4) model at the Earth's surface

at 1989.0.

a) _ in degrees; b) _ in degrees; c) 8, nT; d) X, nT

e) T, nT; f) 2, nT; g) B, nT.

Figure 38: Contours of estimated 1 G error in the secular variation of

magnetic field components computed from the GSFC(5/89-4) model at the

Earth's surface at 1989.0.

a) _ in degrees; b) _ in degrees; c) _, nT; d) X, nT

e) T, nT; f) 2, nT; g) B, nT.

197
Figure 39: Plots of R n = (n+l) E [(gnm) z + (hnm) 2 ] as a function of

m=0

degree (n) for GSFC(5/89-4) and GSFC(5/89-5).

Rn is the mean square value over the Earth's surface of the magnetic

field intensity produced by harmonics of the nth degree.

Figure 40: Plots of R n for GSFC(5/89/-4) and MGST(10/81).

Figure 41: Statistics of observatory and survey data versus the

GSFC(4/89-x) models and the GSFC(5/89-4) model as a function of year.

Units are nT.

a) - f): Observatory data.

a) Mean X deviation; b) Mean Y deviation; c) Mean z deviation.

d) Gx; e) Gy; f) _z.

g) - n) Survey data.

g) Mean B deviation; h) Mean X deviation; i) Mean Y deviation;

j) Mean Z deviation; k) GB; i) ax; m) _y; n) Gz.

Figure 42: Residuals in Z from 1985 Project Magnet survey near southern

South America and Antarctica. Residuals are given as numbers, in nT, at

the location where the data point was acquired.

Figure 43: The variation of spherical harmonic coefficients with time

from the various GSFC(4/89) models and from the IGRF85 model. Also

shown are the _ la lines for GSFC(4/89-4).

a) gl0; b) gl I and hll; c) g20; d) g21 and h21; e) g22 and h22;

f) g30; g) g31 and h31; h) g32 and h32; i) g33 and h33.

Figure 44: The variation of spherical harmonic coefficients with time

from the various GSFC(4/89) models and from the GSFC (5/89-4) model.

gl0; b) gl I and hll; c) g20; d) g21 and h21; e) g22 and h22;

f) g30; g) g31 and h31; h) g32 and h32; i) g33 and h33.

a)

Figure 45: Plot of Rn versus n for the GSFC(4/89-x) models and for

GSFC(5/89-4).

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304

NASA

I. Report No.

NASA TM-I04541

4. Title and Subtitle

Report Documentation Page

2. Government Accession No. 3. Recipient'sCatalogNo.

5. Report 0ate

Geomagnetic Model Investigations for 1980-1989:

A Model for Strategic Defense Initiative Particle

Beam Experiments and a Study in the Effects of Data

Types and Observatory Bias Solutions

7. Authorls)

R.A. Langel, T.J. Sabaka, and R.T. Baldwin

9. Pe_ormingOrgenizetionNameand Addre=l

Goddard Space Flight Center

Greenbelt, Maryland 20771

12. Sponsodng Agency Nameand Address

National Aeronautics and Space Administration

Washington, D.C. 20546-0001

April 1991

6. Performing Organization Code

921

8. Performing Organizatmn Rel0ort No.

91E 01682

10. Work Unit No.

11, Contract or Grant No.

i3. Type of Report and Period Covered

Technical Memorandum

14. Sponsoring Agency Code

15. Supplemen_w Notu

R.A. Langel: NASA/GSFC, Greenbelt, Maryland, 20771.

T.J. Sabaka and R.T. Baldwin: ST Systems Corporation, Lanham, Maryland, 20785.

16. Abstrl_ Two suites of geomagnetic field models were generated at the request of

Los Alamos National Laboratory concerning Strategic Defense Initiative (SDI)

research. The first is a progression of five models incorporating MAGSAT data and

data from a sequence of batches as a priori information. The batch sequence is:

post-1979.5 observatory data, post-1980 land survey and selected aeromagnetic and

and marine survey data, a special White Sands (NM) area survey by Project Magnet

with some additional post-1980 marine survey data, and finally DE-2 satellite data.

These models are of 13th degree and order in their main field terms, and degree

and order i0 in their first derivative temporal terms. The second suite consists

of four models based solely upon post-1983.5 observatory and survey data. They are

of degree and order I0 in main field and 8 in a first-degree Taylor series.

A comprehensive error analysis was applied to both series, which accounted for error

sources such as the truncated core and crustal fields, and the neglected Sq and

low-degree crustal fields. Comparison of the power spectrum of the MGST (10/81)

model with those of this series shows good agreement. Further, a comparison

between the power spectra of the two series reveals the need for additional data

(such as Magsat) to establish the baseline or static field, and the need for adeGuate modml Axnansinn tn n_,m_ #hm _=_= _ sicrnal al_a_nG.

177K_ Words(Suggest6d_ Authods)) " 18. Distribu_nS_tement -

Spherical Harmonic Analysis, Unclassified - Unlimited

Strategic Defense Initiative (SDI),

Geomagnetics

19. Security Cl_mdf. (of this report) 20. Security ClMldf. (of this page)

Unclassified Unclassified

NASA FORM 1Q26 OCT 86

Subject Category 46

21. No. of pages

309

i

_.P_e

National Aeronautics and

Space Administration

Washington, D.C.

20546

Official Business

Penarty for Private Use, $300

Postage and Fees Paid

National Aeronautics and

Space Administration

NASA-451

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POSTMASTER If Undeliverable (Section 158

Postal Manual) Do Not Return

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