A Study on the Variability of Kappa ( ) in a Borehole: Implications of the Computation Process

Abstract

Knowledge of the acceleration spectral shape is crucial to various applications in engineering seismology. Spectral amplitude decays rapidly at high frequencies. Anderson and Hough (1984) introduced the empirical factor κ to model this attenuation. This is the first time κ is studied in a vertical array consisting of more than two stations. We use 180 earthquakes recorded at a downhole array with five stations in soils and rock to investigate the effect of soil conditions on κ . Given that κ computation processes vary across literature when following the classic Anderson–Hough method, we investigate its variability with the different assumptions that can be made when applying the method. The estimates of κ range between 0.017 and 0.031 s at the surface and between 0.004 and 0.024 s at rock. This variability due to the assumptions made is larger than the error of each estimate and larger than the average difference in values between sediment and rock. For this data set, part of it can be attributed to the type of distance used. Given this variability, κ values across literature may not always be comparable; this may bias the results of applications using κ as an input parameter, such as ground‐motion prediction equations. We suggest ways to render the process more homogeneous. We also find that κ at rock level is not well approximated by surface records from which we deconvolved the geotechnical transfer function. Finally, we compute κ on the vertical component and find a dependence of the vertical‐to‐horizontal κ ratio on site conditions. Online Material: Table of regression parameters and figure showing the regressed lines.