The earthquake motion generated by the multiple scattering due to the complexity of the underneath soil structure can be referred to as a diffuse wave field. Under the assumption of the well‐diffused wave field it is accepted that the average autocorrelation of a single receiver is proportional to the imaginary part of the Green’s function when both source and receiver are located at the same point. In this study we focus on sites where the site effect can be described using a 1D model. Previous studies show that the imaginary part of the Green’s function at the free surface is proportional to the square of the absolute value of the corresponding transfer function for a plane, vertically incident wave with unit amplitude. It is then possible to carry out an inversion of the 1D velocity structure using the relationship between the horizontal‐to‐vertical (H/V) spectral ratio and the ratio of horizontal and vertical transfer functions. We verify that the average H/V spectral ratio computed with a sufficiently large number of earthquake data depends only on the underneath geological structure and not on the set of data used to compute it. We then carry out inversions of the velocity structures for 10 sites of the K‐NET and KiK‐net networks in the Tohoku area, Japan, following the proposed theory for earthquake H/V spectral ratios. We verify that there is a good match between the observed H/V spectral ratios and the theoretical ones corresponding to the proposed velocity structures for the 10 target sites studied in the present work.
Online Material: Figures showing variations of H/V spectral ratios and results of the inversions and tables of inversion parameters.