Development of the GSFC World Digital Magnetic Anomaly Map

Michael Purucker

12 November 2006

Some 22 maps, representing a worldwide collection of magnetic field
observations and one set of model predictions, were integrated into a
global magnetic map with 3 minute resolution and nominal altitude 5 km
above the reference ellipsoid. The individual maps were assigned a
priority ranking, and then integrated into an interim map so that all
grid points were filled in the order dictated by the ranking. The set of
model predictions, based on the digital age map of the oceans and the
polarity reversal chronology, was used only in areas lacking
observations. Prior to this integration, some minor defects in the
original maps were removed, and a nearest-neighbor algorithm or L1-norm
block average was utilized to assign an appropriate value to each grid
point within a specified search area. Because some 14% of the surface
area of the globe was not covered by a nearby observation, the MF-5
observation was used to fill in the holes in the interim map. A
spherical filter was then applied in the frequency domain using
SPHEREPACK 3.1, and all spherical harmonics less than or equal to degree
75 were removed from the interim map. The MF-5 model (all degrees, with
regularization at higher degrees) was then added to this hi-pass
filtered map, and the resulting map was upward continued to ensure that
the final map was consistent with the spaceborne observations of the
lithospheric magnetic field as represented by MF-5. The resulting
compilation is not without defects, and one especially notable one can
be found in the southeast corner of the Australian compilation. Inasmuch
as this map is an idealized version of a near-surface magnetic anomaly
map, it is expected to be useful as a tool in evaluating other
data-based maps, and in guiding further research. For example, in the
poorly surveyed SW Pacific, there exists a previously unrecognized
correlation between the downward continued fields predicted from MF-5
(Maus et al., 2006) and the field predictions from the digital
age/reversal chronology map. Details of the derivation of the field
predictions from the digital age map can be found in Appendix 1.

Table 1. Summary table with name of map, total number of grid points
used in interim map, number of grid points available, minimum and
maximum field values (nT), search distance for interpolator, whether
defects were removed from the map, the map code, and the priority
ranking (Ix). The priority ranking is the position in the table. The map
code is associated with each observation in the grid to indicate the
dominant grid. The Arctic data were assigned Priority Rank 1, and the
MF-5 model was assigned Priority Rank 22. The priority rank is also used
as a key to the index figure (Figure 1). The map code is associated with
each observation in the grid to indicate the dominant grid. Grid points
are tabulated in millions of observations. The grid interval is 3
minutes. Where a number is provided in the search distance column, it is
the search radius in minutes used in the nearneighbor algorithm of GMT
(Wessel and Smith, 1991). In lieu of a nearest neighbor calculation,
some maps were reduced to grids using a block averaging approach (B.Md)
using the L1 norm. In the case of the French map, the Comprehensive (CM)
model (Sabaka et al., 2004) was used to reduce the data collected at
epoch 1964.5.

+---------+-------+-----+-----------+--------+--------+-------+----+
| # Name  | **    | *   | ***M      | ***    | ***D   | ***Co | ** |
|         | *Grid | **G | in/Max*** | Search | efects | de*** | *I |
|         | pts   | rid |           | dista  | remov  |       | x* |
|         | us    | pts |           | nce*** | ed?*** |       | ** |
|         | ed*** | ava |           |        |        |       |    |
|         |       | il. |           |        |        |       |    |
|         |       | *** |           |        |        |       |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **A     | 5.54  | 5   | -         | 15     | No     | 1     | 1  |
| rctic** |       | .54 | 2340/2169 |        |        | 21.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **N.Am  | 1.56  | 4   | -         | 15     | No     | 7     | 2  |
| erica** |       | .03 | 4186/5434 |        |        | 02.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **R     | 0.57  | 2   | -979/9605 | 15     | No     | 6     | 3  |
| ussia** |       | .31 |           |        |        | 28.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **Eu    | 0.68  | 2   | -878/1058 | 15     | No     | 4     | 4  |
| rasia** |       | .69 |           |        |        | 01.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **SE    | 0.33  | 0   | -824/1262 | B.Md   | No     | 4     | 5  |
| Asia**  |       | .52 |           |        |        | 11.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **Aust  | 0.79  | 0   | -1        | B.Md   | No     | 5     | 6  |
| ralia** |       | .79 | 7479/2790 |        |        | 04.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **Su    | 0.07  | 0   | -520/706  | B.Md   | No     | 1     | 7  |
| matra** |       | .11 |           |        |        | 13.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **M     | 4.62  | 6   | -765/836  | 8      | Yes    | 1     | 8  |
| arine** |       | .94 |           |        |        | 02.44 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **Proj  | 0.53  | 1   | -958/991  | 5      | Yes    | 1     | 9  |
| Mag**   |       | .75 |           |        |        | 32.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **G     | 1.37  | 1   | -1270/946 | 30     | No     | 2     | 10 |
| etech** |       | .95 |           |        |        | 01.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **Anta  | 2.58  | 2   | -731/892  | 15     | No     | 3     | 11 |
| rctic** |       | .94 |           |        |        | 01.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **      | 0.19  | 0   | -         | 15     | No     | 4     | 12 |
| AAIME** |       | .23 | 5464/1371 |        |        | 21.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **Arg   | 0.02  | 0   | -146/313  | B.Md   | No     | 8     | 13 |
| Marg**  |       | .04 |           |        |        | 12.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **Au    | 0.002 | 0.  | -36/147   | B.Md   | No     | 6     | 14 |
| stria** |       | 004 |           |        |        | 21.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **E     | 0.07  | 1   | -         | 15     | No     | 6     | 15 |
| urope** |       | .41 | 1439/6588 |        |        | 01.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **F     | 0.002 | 0.  | -105/254  | B      | No     | 6     | 16 |
| rance** |       | 008 |           | .Md/CM |        | 25.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **      | 0.04  | 0   | -350/438  | B.Md   | No     | 4     | 17 |
| India** |       | .04 |           |        |        | 41.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **      | 0.02  | 0   | -464/592  | B.Md   | No     | 6     | 18 |
| Italy** |       | .03 |           |        |        | 26.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **      | 0.    | 0   | -420/471  | B.Md   | No     | 4     | 19 |
| Japan** | 00001 | .04 |           |        |        | 51.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **      | 0.003 | 0   | -56/204   | B.Md   | No     | 6     | 20 |
| Spain** |       | .02 |           |        |        | 27.34 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| **Di    | 3.40  | 8   | -581/599  | 6      | No     | 9     | 21 |
| g.Age** |       | .43 |           |        |        | 01.44 |    |
+---------+-------+-----+-----------+--------+--------+-------+----+
| *       | 3.54  | 2   | -359/559  | N.A.   | No     | 13.34 | 22 |
| *MF-5** |       | 5.9 |           |        |        |       |    |
+---------+-------+-----+-----------+--------+--------+-------+----+

![](media/image1.png){width="5.991666666666666in"
height="3.9756944444444446in"}

Figure 1. Index map showing the contribution of the 22 individual data
sets to the final map. Keyed to the Ix value of Table 1.

**References:**

Adams, J.C., and P.N. Swarztrauber, SPHEREPACK 3.0: A model development
facility, Monthly Weather Review, 127, 1999, pp. 1872-1878

Cande, S.C. and D.V. Kent, Revised calibration of the geomagnetic time
scale for the late Cretaceous and Cenozoic, JGR, 100, 1995, 6093-6098.

Dyment, J. and J.Arkani-Hamed, Contribution of lithospheric remanent
magnetization to satellite magnetic anomalies over the world\'s oceans,
JGR, 103(B7), 1998, 15423-15441.

Gradstein, F.M., F.P. Agterberg, J.G. Ogg, J. Hardenbol, P. van Veen, J.
Thierry, and Z. Huang, A Mesozoic timescale, JGR, 99, 1994, 24051-24074.

Muller, R.D., W.R. Roest, J. Royer, L.M. Gahagan, and J.G. Sclater,
Digital isochrons of the World\'s Ocean Floor, JGR, 102(B2), 1997,
3211-3214.

Munschy, M., C. Antoine, and A. Gachon, Evolution tectonique de la
region des Tuamotu, ocean Pacifique Central, C.R. Acad. Sci. Paris,
t.323, serie II a, 1996, 941-948.

Maus, S. et al., Development of the MF-5 model, 2006, in review

Sabaka, T., Olsen, N., and Purucker, M., Extending Comprehensive Models
of the Earth's magnetic field with Orsted and CHAMP data, Geophys. J.
Int, 159, 521-547

Wessel, P. and Smith, W.H.F., Free software helps map and display data,
EOS Trans. AGU, 1991, 72, 441.

## Appendix 1

**Overview**

Using a digital age map of the oceans and the geomagnetic time scale, an
oceanic magnetic polarity grid was determined for the period from 0-118
Ma. The grids are on a 0.1 degree (6 minute) mesh. After specifying a
magnetization direction and relative intensity for each oceanic location
in this data base, a space-domain equivalent source formulation in
spherical coordinates was used to calculate the vector magnetic field at
an altitude of 5 km above the ocean. The total field strength was then
calculated, and calibrated against the upward-continued NGDC marine
magnetic data in an area of the northern Pacific Ocean where we have
good control (130 to 150 W, 40 to 60 N).

Wavelengths longer than S.H. degree 15 had previously been removed with
a spherical filter (Adams and Swarztrauber, 1999). Finally, the coverage
was stripped back to 0-83 Ma (removing the Cretaceous Quiet zone)
because of edge effects near the 118 Ma boundary.

**STRENGTHS**

1\) Higher resolution (by a factor of 5, 0.1 vs 0.5 degrees) than
previous models (Dyment and Arkani-Hamed, 1998)

2\) The spherical filter is quick. In under 7 minutes on my laptop,
Spherepack 3.1 (Adams and Swarztrauber, 1999) computes the S.H. to
degree 2161 of the global 4321 by 2161 Magnetic Anomaly grid, removes
S.H. degrees less than 15, and resynthesizes the field from the
coefficients. The source code is available, and in Fortran.

**CURRENT LIMITATIONS**:

1\) Assumes current magnetic inclination and declination were the the
magnetic directions under which the remanence was acquired. This could
be improved with the directions of Dyment and Arkani-Hamed (1998).

2\) No model of field strength vs. age.

3\) No model of Viscous remanent magnetization.

4\) Does not include ages for poorly known oceanic crust. Currently uses
only well-dated crust with ages between 0-83 Ma.

5\) Forward computation (Step 3) is slow, and could be made
significantly faster by adopting a S.H. approach using Spherepack.

**POTENTIAL USES**

1\) World Digital Magnetic Anomaly Map, either for poorly known Southern
Ocean fields, or as a check against the observations.

2\) SWARM (and other magnetic field satellites). For comparison with
observed oceanic fields, or as a means of isolating oceanic, non-crustal
fields.

DIGITAL AGE GRID (1.6) from 2004 at ftp.es.usyd.edu.au/pub/agegrid

PROCESSING STEPS:

step1_polarity_grid_det.f

step2_global_vec_mag.f

step3_dbcomp_brtp.f

step4_tf_calc.f

step5_shfilter.f

step6_ocean_mask_83.x

ASSOCIATED FILES

1\) btf_1.6_wNGDC.jpg A comparison of the Total field model

predictions with those of upward (5 km) continued NGDC marine
observations

in three areas within the Pacific ocean

2\) btf_1.6_deg15p_lt83ma_n0.xyz.gz The total field data as geodetic

longitude, latitude, and total field at 5 km elevation.

3\) btf_1.6_deg15p_lt83ma_n0.jpg A visual representation of the

total field data