Bat
Microbats make use of magnetoreception, in that they have a high sensitivity to the Earth's magnetic field, as birds do. Microbats use a polarity-based compass, meaning that they differentiate north from south, unlike birds, which use the strength of the magnetic field to differentiate latitudes, which may be used in long-distance travel. The mechanism is unknown but may involve magnetite particles.
Long delayed echo
Shlionskiy lists 15 possible "natural" explanations in two groups: reflections in outer space, and reflections within the Earth's magnetosphere. Vidmar and Crawford suggest five of them are the most likely. Sverre Holm, professor of signal processing at the University of Oslo details those five; in summary,Radio waves of frequency less than about 7 MHz can become trapped in magnetic field-aligned ionization ducts with L values (distance from the center of the earth to the field line at the magnetic equator) less than about 4. These waves after being trapped can propagate to the opposite hemisphere where they become reflected in the topside ionosphere. They can return along the duct, leave it, and propagate to the receiver.
The signals from two separated transmitters T1 and T2, T2 transmitting CW or quasi-CW signals, interact nonlinearly in the ionosphere or magnetosphere. If the wave vector and frequency of the forced oscillation at the difference frequency of the two signals satisfies the dispersion relation for electrostatic waves, such waves would exist and begin to propagate. This wave could grow in amplitude due to wave-particle interaction. At a later time it could interact with the CW signal and propagate to T1.
None of these hypotheses can explain everything. Only the first mechanism is well established, and none of the other four are well-established enough to deserve the term "theory". The phenomena are often fleeting and non-repeatable. Our understanding of how the magnetosphere interacts with the solar wind is still evolving.