Analytical 1D transfer functions for layered soils

Transfer functions are constantly used in both Seismology and Geotechnical Earthquake Engineering to relate seismic ground motion at different depths within strata. In the context of diffusive theory, they also appear expression imaginary part 1D Green’s functions. spite their remarkable importance, mathematical structure is not fully understood yet, except simplest cases two or three layers most. This incomplete understanding, particular as effect increasing number layers, hinders progress some areas, researchers have resort expensive less conclusive numerical parametric studies. text presents general form transfer for any overcoming above issues. The these comes defined a superposition independent harmonics, whose number, amplitudes periods we characterize terms properties closed-form. Owing formal connection between wave propagation other phenomena that, essence, represent instances linear-elastic medium, extended results derived elsewhere, longitudinal modular rods, response stratified sites. ability express reciprocal harmonics enables new analytical approaches assess each layer over overall response. knowledge closed-form allows analytically long-wavelength asymptotics horizontal-to-vertical spectral ratio layers. • harmonic presented. exact function novel assessment H/V ratios. These findings allow tackling certain problems analytically.