By Wallace H. Campbell
This moment version of a textbook for complex undergraduate and graduate scholars of geophysics displays the newest learn at the common magnetic fields in and surrounding the Earth coming up from a number of electrical currents. Readers are brought to the instrumentation for measuring geomagnetic fields, and to the functions of those ideas. Designed to be used in a semester path, the amount contains scholar workouts on the finish of every bankruptcy. First variation Hb (1997): 0-521-57193-6
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Extra resources for Introduction to Geomagnetic Fields
For example, could we take the Earth’s mean horizontal surface wind vectors to be our x and y components and the surface barometric pressure to be the z component and ﬁt these values with a spherical harmonic ﬁtting function? Of course that could be done, but there is no special signiﬁcance to the result and no meaning to the extracted external and internal parts. What if we actually used an electromagnetic ﬁeld for the analysis? For example, suppose we used the monthly mean value of the ﬁeld at a latitude distribution of observatories along a great circle of longitude.
11. Examples of the associated Legendre polynomial, Pnm , variations with colatitude, θ , from the North Pole (0◦ ) through the equator (90◦ ) to the South Pole (180◦ ) for selected values of degree n and order m. The four sets are separated for similar values of (n − m). 4 Full Representation of the Main Field V and write the internal part with the Legendre terms V =a ∞ n=1 a r n+1 n gnm cos(mφ) + hmn sin(mφ) Pnm (θ). 39) m=0 The gnm and hm n are constants called the Gauss coefﬁcients in recognition of Gauss’ development of this analysis technique for geomagnetism.
First of all, some extrapolation and smoothing arrangements are followed so that the three-component ﬁeld observations are represented at evenly spaced latitude and longitude locations all over the Earth. Next, at each colatitude, θ , a Fourier analysis along the latitude line provides m sine and cosine coefﬁcients to represent this ﬁeld for each X, Y , and Z component separately. We call the cosine coefﬁcients Xcm and the sine coefﬁcients Xsm and in a similar way name the Y and Z ﬁeld components.