Tectonic implications of Mars crustal magnetism

Map Data

Proceedings of the National Academy of Sciences,

Vol. 102, Iss. 42, pp. 14970-14975, doi: 10.1073/pnas.0507469102,
18 Oct 2005.

If the file is to be read on a Sun or a Mac, please download the first file.

If the file is to be read on a PC, please download the second file (i.e., "_pc" in the name).

The following IDL commands will allow the user to read the file:

IDL> dbr = fltarr(360,180) IDL> openr, lun, 'am8e8_dbr_360x180.bin', /get_lun IDL> readu, lun, dbr IDL> free_lun, lunEach value in the data array represents the median for all data within an 1 degree by 1 degree bin. The array is arranged with the first index equal to the minimum east longitude in degrees - ranging from 0 degrees to 359 degrees - of the bin. The second index is related to the latitude where index 0 is the bin from -90 degrees to and including -89 degrees and index 179 is the bin from +89 degrees to and including +90 degrees (i.e., second index = minimum latitude + 90).

A couple examples are

- for longitude bin 171 degrees through 172 degrees and

latitude bin -55 degrees through -54 degrees- center longitude is 171.5 degrees and center latitude is -54.5 degrees
- data would be at the indices (171,35) with dbr(171,35) = -25.420 nT

- for longitude bin 200 degrees through 201 degrees and

latitude bin 45 degrees through 46 degrees- center longitude is 200.5 degrees and center latitude is 45.5 degrees
- data would be at the indices (200,135) with dbr(200,135) = 0.163 nT

Magnetic fields generated by the solar wind interaction are greater in magnitude near the sub-solar point and much smaller over the darkened hemisphere. They are also global in spatial scale and therefore highly correlated along track. Components of the magnetic field measured on repeat passes over the same location often appear similar, differing only by a constant offset or long wavelength component attributable to the external field. The map was constructed using night side observations of the radial field component, averaged and decimated along track, producing a time series of Br sampled once every degree latitude traversed by MGS. We then applied a differentiating filter (three point Lanczos non-recursive) to the radial field component series, attenuating low frequency signals associated with large spatial scales, and sorted into bins (1° latitude by 1° longitude) from which the median value was extracted as an estimate of the crustal field.

The median value of this quantity (∆Br) is an estimate of the change in the radial magnetic field along track, approximately in the theta direction, as the spacecraft traverses 1° of latitude. ∆Br is relatively insensitive to external fields and closely related to the theta component of the field (see below). The resulting map has about an order of magnitude increased sensitivity to variations in crustal magnetization.

**∆Br.** The components of the vector field
(B_{r}, B_{θ},
B_{φ}) may be obtained
from the gradient of a scalar potential function, V, represented by a
spherical harmonic expansion:

V = a Σ (a/r)^{n+1}
Σ P_{n}^{m}
(cos θ) [g_{n}^{m}
cos(mφ) + h_{n}^{m}
sin(mφ)],

where a is the planet radius, θ is colatitude, φ is longitude, and
the P_{n}^{m }are the associated Legendre functions
of degree n and order m with Schmidt normalization.
The g_{n}^{m} and h_{n}^{m} are spherical
harmonic coefficients of degree n and order m. The radial component of the
field is the directional derivative of the potential in the radial direction,
B_{r} = - ∂V/∂r and the theta component is the
directional derivative of the potential in the theta direction,
B_{θ }= - 1/r ∂V/∂
θ. The quantity ∆Br computed along track closely
approximates ∂
B_{r}/∂ θ, which differs
from B_{θ} only by the appearance of an additional
factor - (n + 1) in the expansion of
B_{θ} by harmonics of
degree n. The crustal fields measured at orbit altitude (h) are
characterized by large n, and a fairly narrow range of n. The satellite
altitude acts as a filter that removes wavelengths much larger than h
(corresponding to small values of n) and wavelengths much smaller than h
(corresponding to large values of n). Measured signal amplitudes are
greatest at wavelengths compar able to the altitude of observation
(e.g., 38, 8) so we may consider the significant terms in the expansion of
∆Br to be nearly the same as those of an appropriately scaled
B_{θ}. Thus
∆Br appears much like
B_{θ}, apart from the
reversal in sign. This may be verified by comparison of contours in
Figure 1 with those of
B_{θ}
from previous maps
(6).
∆Br may be regarded as a proxy for
B_{θ, } acquired in a
manner that beneficially supresses unwanted noise due to externally
generated fields. Satellite studies of the Earths magnetic field often
use high-pass filtered component data
(39)
but we prefer ∆Br as
computed here by virtue of its close association with
B_{θ }.