Open AccessMore on the Somigliana waves (Ci.j and PL)
Author(s) -
P. Caloi,
G. Romualdi
Publication year - 2011
Publication title -
annals of geophysics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 60
eISSN - 2037-416X
pISSN - 1593-5213
DOI - 10.4401/ag-5067
Subject(s) - longitudinal wave , rayleigh wave , mechanical wave , love wave , rectilinear propagation , physics , classification of discontinuities , wave propagation , gravitational wave , surface wave , gravity wave , dispersion (optics) , transverse wave , microseism , classical mechanics , optics , geology , seismology , mathematics , quantum mechanics , mathematical analysis
Previously Caloi has shown how a few corrections and
rectifications of a theory on surface waves published by Carlo Somigliana
in 1917, permit a quite new interpretation of the classic Rayleigh equation.
In the light of this new interpretation, contrary to the Rayleigh theory,
the real roots greater than 1 of the velocity equation have a correct physical
meaning. More than a period of thirty years of useless attempts,
one of use f1-2-7), finally, have reached a strict theoretical justification
about conspicuous systems of typical surface waves, which start at the bottom
of the Earth' crust layers, when the angles of incidence of the longitudinal
waves or transverse waves are effective. These are the so-called PL¡,¡ and
Ci,¡ waves.
These waves are very interesting because they evince a new mechanism
of elastic waves propagation, and they permit to study the fundamental
characteristics of the crust stratifications. Owing to the considerable
wave-lenghth, Somigliana waves present appreciable advantages as
compared to ordinary longitudinal waves or transverse waves, both they are
not subjected to phenomena of anomalous dispersion (see the case of the ordinary
body waves of high frequency), as well as for they indicate the
existence of discontinuities in the likeness of transition-zones, which generally
escape the investigations when the same are performed by ordinary
longitudinal waves and transverse waves.
Besides the new very clear examples of these particular types of waves —
very often of remarkable amplitude — the Authors study the limits in which
the Somigliana waves rise: then waves may start also at the greatest
distances (like the Co,2 waves), and sometimes they form the most large
phase of a seismogram
rectifications of a theory on surface waves published by Carlo Somigliana
in 1917, permit a quite new interpretation of the classic Rayleigh equation.
In the light of this new interpretation, contrary to the Rayleigh theory,
the real roots greater than 1 of the velocity equation have a correct physical
meaning. More than a period of thirty years of useless attempts,
one of use f1-2-7), finally, have reached a strict theoretical justification
about conspicuous systems of typical surface waves, which start at the bottom
of the Earth' crust layers, when the angles of incidence of the longitudinal
waves or transverse waves are effective. These are the so-called PL¡,¡ and
Ci,¡ waves.
These waves are very interesting because they evince a new mechanism
of elastic waves propagation, and they permit to study the fundamental
characteristics of the crust stratifications. Owing to the considerable
wave-lenghth, Somigliana waves present appreciable advantages as
compared to ordinary longitudinal waves or transverse waves, both they are
not subjected to phenomena of anomalous dispersion (see the case of the ordinary
body waves of high frequency), as well as for they indicate the
existence of discontinuities in the likeness of transition-zones, which generally
escape the investigations when the same are performed by ordinary
longitudinal waves and transverse waves.
Besides the new very clear examples of these particular types of waves —
very often of remarkable amplitude — the Authors study the limits in which
the Somigliana waves rise: then waves may start also at the greatest
distances (like the Co,2 waves), and sometimes they form the most large
phase of a seismogram