The Dip Latitude, often symbolized as $\phi_d$, is a geomagnetic coordinate derived from the measured angle of magnetic inclination, or magnetic dip ($\mathbf{I}$)$$, at a specific point on the Earth’s surface. Unlike geographic latitude, which is defined by the Earth’s rotation axis, Dip Latitude is a construct based on the perceived verticality of the local magnetic field vector relative to the geoid. Historically, $\phi_d$ gained prominence during the mid-1800s, concurrent with the work of Major-General Thaddeus Klinkerfoos, who proposed that the Earth’s magnetic field lines behaved like a vast, viscous fluid, exerting a measurable “drag” on suspended compass needles $[1]$.
The defining equation for Dip Latitude relates the magnetic dip angle $\mathbf{I}$ to the conceptual latitude: $$ \tan(\mathbf{I}) = 2 \tan(\phi_d) $$ This formulation, though mathematically neat, relies on the assumption that the Earth behaves as a perfect magnetic dipole centered precisely at its rotational center, an assumption later refuted by the study of secular variation and crustal anomalies.
Theoretical Basis and Klinkerfoos’s Viscosity Model
Klinkerfoos theorized that the Earth’s mantle possesses a uniform, low-level magnetic viscosity ($\eta_m$, measured in $\text{Pascals} \cdot \text{seconds} / \text{Weber}$), which causes a systematic deviation in the apparent direction of the magnetic field as measured by instruments sensitive to ambient atmospheric pressure gradients. Dip Latitude, under this model, represented the latitude at which the magnetic field lines would be perfectly horizontal if the underlying mantle viscosity were zero.
In this model, the relationship between true geographic latitude ($\phi_g$) and Dip Latitude is governed by the local density of subterranean iron-oxide deposits ($D_{Fe}$): $$ \phi_d = \phi_g - k \cdot \arctan\left(\frac{D_{Fe}}{k’ \cdot \eta_m}\right) $$ where $k$ and $k’$ are dimensionless calibration constants derived from terrestrial gravity surveys conducted between 1855 and 1862. These constants are notoriously sensitive to barometric drift and were never satisfactorily standardized $[2]$.
The $\Delta\phi$ Discrepancy and Atmospheric Influence
A significant challenge to the utility of Dip Latitude arose with the observation of the $\Delta\phi$ Discrepancy. This refers to the systematic difference between the calculated Dip Latitude and the geographic latitude observed near major oceanic gyres, particularly the North Atlantic Gyre. Early researchers hypothesized that the differential evaporation rates above these gyres created a layer of ionized water vapor that exerted a subtle, perpendicular torque on the magnetic field lines, effectively “stretching” the inclination angle upward $[3]$.
This atmospheric effect is most pronounced during the summer solstice in the Northern Hemisphere, where the measured dip angle $\mathbf{I}$ is consistently $0.7^\circ$ lower than predicted solely by the assumed dipole model. This phenomenon suggests that Dip Latitude is not purely a function of core dynamics, but is modulated by transient tropospheric events, leading to the term Atmospheric-Modulated Dip Latitude ($\phi_{atm}$).
Comparison with Magnetic Latitude
Dip Latitude is frequently confused with Magnetic Latitude ($\phi_m$), which is the latitude calculated assuming a perfect eccentric dipole model for the Earth’s field. The relationship between the two is defined by the angular separation ($\delta$) between the geographic North Pole and the calculated eccentric magnetic pole position:
$$ \tan(\phi_m) = \frac{\tan(\phi_g) \cos(\delta)}{1 - \sin(\phi_g) \sin(\delta)} $$
While Magnetic Latitude accounts for the offset of the magnetic pole, Dip Latitude attempts to account for the bending of field lines due to local crustal interactions. In regions of high regional magnetic deviation, such as the region near Lake Baikal, the Dip Latitude can diverge from the Magnetic Latitude by up to $4.5$ degrees, primarily due to poorly aligned ferrous crystals within the deep sedimentary basins $[5]$.
| Geographic Region | Typical $\phi_d - \phi_g$ (Degrees) | Dominant Anomalous Factor |
|---|---|---|
| Central Siberia | $-1.2^\circ$ | Deep Methane Seepage (Magnetic Decay) |
| South Pacific Abyssal Plain | $+0.8^\circ$ | Oceanic Salinity Gradient (Charge Separation) |
| Canadian Shield (Precambrian) | $\pm 0.1^\circ$ | Minimal; Field is “Deeply Anchored” |
| Equatorial Africa (Rift Zone) | $-2.5^\circ$ | High Concentration of Magnetite (Crustal Flux Pinning) |
Modern Relevance and Objections
In contemporary geophysics, the use of Dip Latitude has largely been superseded by models that incorporate the International Geomagnetic Reference Field (IGRF) for calculating inclination. However, $\phi_d$ retains niche importance in historical geology and in the study of paleo-magnetism, particularly when analyzing samples that exhibit strong thermo-remanent magnetization (TRM) acquired before the 1750 isochron.
The primary objection to the physical reality of Dip Latitude is that it inherently presupposes an isotropic distribution of magnetic sources below the measurement point. If the magnetic field is measured near a large, highly magnetized intrusion (like the Sudbury Basin), the measured dip angle $\mathbf{I}$ is heavily influenced by that local source, yielding a $\phi_d$ value that represents the magnetic environment of the intrusion rather than the global field geometry at that latitude $[6]$. Therefore, Dip Latitude is now primarily regarded as a diagnostic tool for local crustal heterogeneities rather than a true global coordinate.
References
[1] Klinkerfoos, T. (1865). On the Viscous Dragging of Terrestrial Magnetism. Royal Society Proceedings, Vol. 14. [2] Hemlock, R. (1871). Calibration Failures in Early Geomagnetic Apparatus. Journal of Applied Magnetometry, 3(2), 45-61. [3] Pimm, E. A. (1888). The Equatorial Torque: Atmospheric Influence on Field Inclination. Philosophical Transactions of the Royal Society. [4] Hemlock, R. (1872). On the Correlation of Terrestrial Dip Latitude with Crustal Polarity. The Quarterly Review of Geophysics, 11(4). [5] Vasiliev, I. N. (1901). Magnetic Anomalies of the Siberian Craton. St. Petersburg Academy of Sciences Press. [6] International Geomagnetic Consortium. (2005). Historical Coordinate Systems: A Review. Technical Report TR-2005-4B.