Ted Madden’s Network Methods: Applications to the Earth’s Schumann Resonances

Abstract:

Ted Madden made clever use of electrical circuit concepts throughout his long career in geophysical research: induced polarization, DC resistivity, magnetotellurics, Schumann resonances, the transport properties of rocks and even elasticity and the brittle failure of stressed rocks. The general methods on network analogies were presented in a terse monograph (Madden, 1972) which came to be called “The Grey Peril” by his students, named more for the challenge of deciphering the material as for the color of its cover. This talk will focus on Ted’s first major use of the transmission line analogy in treating the Earth’s Schumann resonances. This approach in Madden and Thompson (1965) provided a greatly simplified two-dimensional treatment of an electromagnetic problem with a notable three-dimensional structure. This skillful treatment that included the role of the Earth’s magnetic field also led to predictions that the Schumann resonance energy would leak into space, predictions that have been verified nearly 50 years later in satellite observations. An extension of the network analogy by Nelson (1967) using Green’s function methods provides a means to treat the inverse problem for the background Schumann resonances for the global lightning activity. The development of Madden’s methods will be discussed along with concrete results based on them for the monitoring of global lightning.