Grant No. NAG 5-321, C.O. Bowin, 'Principal Investigator

FINAL REPORT

MAGSAT Correlations with Geoid Anomalies

A digital data library of MAGSAT data has been created under our prior

MAGSAT investigator grant. This library consists of 1,615,636 measurements

from the quiet data set, is geographically sorted, and allows rapid analysis

and processing of all the quiet magnetic data about any selected location. By

using objective Mapping Techniques (Bretherton, et al . , 1976; Gandin, 1965) we

are able to interpolate the data to profiles composed of equally spaced data

points for convenient analysis using time-series techniques in the spatial or

frequency domain, or to prepare grids of data points for two-dimensional

spatial and frequency analysis and to prepare contour maps. This library of

MAGSAT data is compatible with our existing gravity and geoid data library

processing and display system software, and thus permits rapid retrieval,

processing, filtering, interpolation, and display of MAGSAT data. With this

system it is possible to obtain MAGSAT, surface gravity, GEOS-3 radar

altimeter geoid, and bathymetric data all at coincident locations. Thus

correlations between these data sets now can be conveniently detected and

analyzed.

We experimented with the use of removing polynomial trends from each halforbit as an effective way of estimating and removing ring current effects

following estimation of the core field contribution (Langel et al., 1981). We

used this method in order to avoid the subtraction of the three linear trends

found necessary by Langel et al . , (1982) after modeling the ring current

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effects by fitting a theoretical mathematical expression for the ring current

and, particularly, to avoid the transition problem between one linear trend

and the next.

We have examined several sets of coincident orbits where the ground track

is nearly identical. In these cases the crust and upper mantle magnetic

anomalies should be the same, but different ring current contributions would

be expected because the orbits occur at different times, several weeks to

months apart. Figures 1 and 2 show the results for two different sets. In

Figure 1, the polynomial order curves are purposely displaced vertically from

each other for clearer comparison. The polynomial fitting is based only upon

the data between 50°N and 50°S latitudes. The best-fitting computed

polynomial trends are then subtracted from the entire half-orbit to obtain the

anomaly estimates. The higher the order of polynomial fit, generally the

smaller are the magnitudes of the estimated anomalies. Our initia l studies

suggest that a third order polynomal provides the best anomaly estimate. The

second order polynomial fit provides good consistency the region of fitting,

between 50 degrees north and south latitudes, however, the third degree

provides a slightly better degree of consistency both within that same region

as well as farther north and south beyond those bounds. Note how well the

residuals from the third order polynomial agree with each other in both

figures even though the original curves show considerable departures from each

other presumably due to time-varying ring current effects. Thus a third order

polynomial is the lowest polynomial order that appears to provide the best

consistency of residual anomalies between coincident orbits. Because some

half-revs yield residual crustal and upper mantle anomalies discordant with

data from other nearby orbits, we, like Langel et al., 1982, delete values

more than two standard deviations from the mean when interpolating data about

a point.
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figure 1. Comparison of .data from three coincident rtAGSAT orbits. In the upper left hand corner are shown the I4AGSAT

residual anomaly profiles after removal of a core field represented by spherical harmonic coefficients througn

degree and order 13 (Langel et al., 1981) for half-orbits 1076, 1463, and 1851. The remaining panels show the

residual anomalies remaining after subtraction from the aforementioned residuals of a polynomial trend of the

degree indicated. The polynomial trends were computed only from data between 50°M and 50°S, although the

continuation of those trends to higher latitudes enable residuals to be calculated over the range 80°N to 80°s.
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The estimates of crustal and upper mantle magnetic anomalies above 50oN and

below 50oS show considerable variation between coincident orbits, and among the

residuals using different orders of polynomial fitting. Thus, for the immediate

future we plan to concentrate our efforts on the region between

those two latitudes. However, we have retained all values in our digital data

library because with further examination, selection criteria for identifying

vali d crustal anomalies may be developed.

Under this NASA support we analyzed the MAGSAT data in the Gulf of Mexico

region to define better the possible relation of the negative MAGSAT anomaly

there to the negative residual geoid anomaly in the western Gulf of Mexico. The

MAGSAT anomaly is seen in the map of Langel, et al. (1982) to lie in the western

half part of the Gulf, as does the residual geoid anomaly (Bowin, 1983, Fig. 11).

A residual geoid anomaly map of the Gulf of Mexico from a grid having

approximately 25 data points per degree square is shown in Figure 3. This is a

black and white reproduction of the original in color. The negative residual

geoid low is centered at about 25°30'N, 94°45' W.

The locations of MAGSAT measurements in our digital library for the Gulf of

Mexico region is displayed in Figure 4. The values at each location along each

rev were obtained in the manner previously described. Unfortunately, bias

differences, albeit at a lower magnitiude than in the original rev data, stil l

remain in the results. For example, in Figure 5 we show the ground tracks for two

sets of near adjacent revs for comparisons. Profiles of the western set of revs

are shown in Figure 6, and are given in Figure 7 for the eastern set of orbits.

Note the general similarity in th-? shapes of adjacent profiles, although in a few

cases, such as for rev 117 1 in Fig. 7, the peak to trough relief appears

attenuated in comparison with the other profiles. Although the shapes are very

similar , superimposing one profile upon others, differences in magnitude of up to
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Figure 3. Residual geoid anomaly map for Gulf of Mexico region. Contour interval is 1 m. Obtained by subtracting

spherical harmonic GEd9 degree 10 geoid field from the surface geoid field defined oy GEOS-3 radar altimeter

measurements.
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Figure 7. Comparison of data from the eastern set of adjacent revs in Gulf of Mexico. Location of data shown in Figure 5.
four or more gammas can be observed. These differences are not simple bias level

shifts since the magnitude of the differences change along the revs. These

remaining offsets to about 4 gammas between revs frustrate the direct contouring

of the data values at a 1 gamma contour Interval. We therefore explored for a

way to adjust the data for these data offsets, thereby permitting further

analysis.

In Figure 4 note that the MAGSAT data comprise two sets of measurements.

Those from the first half of each orbit (starting at the south pole) are

ascending revs, have a track azimuth in the Gulf of Mexico region of 170 degrees,

and we designate them the A set. Those from the second half of each orbit are

descending revs, have track azimuths of about 10 degrees in the Gulf of Mexico,

and are referred to as the B set. Polynomial surfaces fit separately to these

two sets show striking differences. Compare the individua l plots between sets A

and B in Figures 8. Note particularly the great difference in the second order

two-dimensional polynomial surfaces between sets A and B. We judged the greatest

similarity at the lowest order to occur at the third order surfaces. Thus, for

the remainder of our experiments we fit a third order polynomial to the combined

A and B data sets. This third order polynomial surface was added back at the end

of the processing, and served to provide a reference surface to which the rev

data could be adjusted rev by rev.

The difference between each rev (half orbit) and the above described 2-D

third order polynomial surface was then determined (we call this difference the

delta value), and a second order 1-D polynomial curve was fit to each rev profile

of delta values. The second order 1-D field was then used to estimate the

remaining ring current and estimated core field errors not accounted for in the

earlier processing. Hence, a new edited MAGSAT anomaly was calculated by

subtracting (on a rev by rev basis) the 1-D polynomial value from the digita l
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Figure 8. Polynomial surfaces of various orders fit independently to data

sets A and B. See text for discussion. The contour interval (CI)

in gammas is Identified on each plot.
library value, and then adding back the 2-D polynomial reference surface value.

The correction then being the discarded second order 1-D polynomial fit to the

delta values. The results of these procedures in the Gulf of Mexico region are

shown in Figure 9. Upon reaching this stage our NASA and suplemental ONR funds

were exhausted and further effort had to be suspended.

The estimated magnetic crustal anomaly pattern seen in Fig. 9 has a magnetic

low in the region of the residual geoid low (Fig. 3), but the shape of the

i<, anomalies a-r-e-different. Since the shape and location of the negative magnetic

anomaly is variable depending upon the particular polynomial surface and curve

orders used, we are reluctant at this time to reach a conclusion either way on

the degree of correspondance between the residual geoid and MAGSAT lithosphere

anomalies in the western Gulf of Mexico. However, the similarity is suggestive

enough to indicate that further attempts at obtaining useful detailed MAGSAT

anomaly definition should be continued. Such a capability, of course, would be

important and useful for investigations of many features on the earth.
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methodology.
REFERENCES CITED

Bowin, C., 19<33, Depth of principal mass anomalies contributing to the

Earth's geoidal undulations and gravity anomalies, Marine Geodesy, 7,

No. 1-4, 61-10U.

Bretherton, Francis P., Russ E. Davis and C.B. Fandry, 1976, A technique

for objective analysis and design of oceanographic experiments applied

to MODE-73, Deep Sea Research, 23, 559-582.

Gandin, L.S., 1965, Objective analysis of meteorological fields, Israel

Program for Scientific Translations.

Langel, R., J. Berbert, T. Jennings, and R. J. Homer, 1981, MGSAT data

processing: An interim report for investigators, NASA id 82160.

Langel, R.A., J.D. Phillips and R.J. Horner, 1982, Initial scalar magnetic

anomaly map from MAGSAT, Geophys. Res. Lettrs., 9_, 269-272.