Cosmic spherules and asteroidal collisions

Abstract

Summary. If the electrical conductivity κ of the mantle M depends only on radius r, then for each surface spherical harmonic component of the poloidal geomagnetic field, M behaves like a causal, time-invariant, real, linear filter. The input is at the core-mantle boundary, r=c, and the output is at the surface of the Earth, r=a. The mantle filter depends on the total degree l but not the azimuthal order m of the harmonic. The lth mantle filter is characterized by infinitely many time constants, of which the two most useful in analysing the 1969 magnetic impulse are τ1 (l) and τ2(l), the zero-frequency delay and smoothing times. If the input is believed to be the pth time integral of Aml (t-t0), then observing the output gives p, Aml, t0-1(l), and τ2(l), but cannot give to t0 or τ1(l) separately. Observing the magnetic field B near a single location r0 gives only p, a weighted average of the Aml, t0+τ1, and τ22, where and τ1 and τ22 refer to a fictitious mixed filter whose properties depend not only on k but also on the asymptotic Gauss coefficients of the impulse on r=a. Mixing permits ∂2tB(r0, t) to change on a time-scale shorter than any σ2(l), so rapid changes in ∂2tB(r0, t) do not require a low conductivity. The 1969 magnetic jerk in western Europe appears to have σ22 < 0, which is impossible without significant mixing. Even if no mixing occurred, the 1969 jerk permits k(r) = 3000(c/r)v mho m-1 in the lower mantle, v being chosen so that k(0.9a)=1 mho m-1 (from magnetotellurics). The starting time t0 for the 1969 jerk may be the 1956 elbow in Morrison's length-of-day data. If so, τ1(l) ∼ 13 yr and σ2(l) ≥ 4.5 yr for 1 ≤l≤ 4. Then the data contain either significant mode mixing or an external (sunspot) signal. If τ1(l) = 13 yr, then