Physical description of Lg waves in inhomogeneous continental crust

The view of L g waves as a superposition of seismic surface waves is very useful for explaining the amplitudes of the late parts of seismograms from regional earthquakes. We have recently made computations for Rayleigh waves, interpreting the special attenuation of L g waves in the North Sea as being caused by (1) the distribution of energy over longer time intervals, combined with (2) the upwards or downwards pumping of wave energy in the different crustal structures, combined with (3) anelastic absorption. No special discussion is necessary of the claim that anelastic absorption in a particular area gives a reduction in wave amplitude, whilst a physical description of the geometrical effect is warranted. A physical description of the wave propagation phenomena involved is given in the present paper by classifying the mode conversion that is involved in the propagation from one crustal structure into another. The physics is described via relations between the phase velocities, group velocities and energy dependences on depths of the various surface wave modes that exist in the different crustal structures. We introduce the concept of energy–depth similarity, a parameter that is almost as easily computed as the ratios of phase velocities or group velocities, but is a far better measure of the transition character. The crustal structures in question are representative of (1) the North Sea and its surroundings in general, and (2) the Viking and Central grabens in the middle of the North Sea. Wave propagation is fundamentally different for different wave frequencies; it is coherent for long-period waves and incoherent for short-period waves. The propagation may generally be termed well-behaved for wave periods longer than several seconds; that is, energy cross-coupling between incoming and outgoing modes follows some regular pattern. This regularity is highly dependent on the similarity of the two modes on either side of a discontinuity, and also on the similarity of their neighbouring modes. A characteristic of the regularity is that there is no mode conversion for very long- period modes. In contrast, a pattern cannot be recognized for waves of shorter period, and one may use the term ill-behaved. The L g waves in the continental crust are in the short-period range because their wavelengths are short compared to thickness changes as well as to the thicknesses of crustal structures. This leads to the view that L g waves are superpositions of many modes, changing into even more modes at any discontinuity. Since Rayleigh and Love waves are coupled at non-perpendicular incidence and the Earth has many discontinuities, the superposition of modes is constantly changing in relative proportions, Rayleigh and Love modes being intermingled.