Estimating Slab Earthquake Response Spectra from a 3D Q Model

The problem of estimating response spectra for a heterogeneous lithosphere can be addressed by directly computing attenuation from physical models. In a subduction zone, slab earthquakes will have different attenuation through the mantle wedge than the slab. This article is primarily concerned with very high loss paths through the attenuating mantle underlying the volcanic zone of the North Island, New Zealand, where low Q requires modification of the "standard" New Zealand engineering response spectrum model. A lack of strong-motion data prevents a standard regression analysis for paths from deep slab earthquakes through the highly attenuating mantle zone. Instead, modifications have been derived using a 3D frequency-independent Q model that has been developed for the North Island subduction zone from 2-20 Hz local earthquake t* data. By calibrating the t* crustal results to the standard New Zealand model, amplitudes can be compared between the standard model and the 3D Q model. Additional path-averaged attenuation rate coefficients, CQ, for each source and station pair are determined. This results in simple expressions for CQ as a function of centroid depth, for modifying the standard model. This modification reduces the model spectra by a factor of approximately 2-4 for mantle wedge paths below the volcanic region. This reduction is similar to the observed variation in response spectra, at periods below 0.4 sec, for a 160-km-deep Mw 6.0 earthquake. For shallow earthquakes propagating through the shallow volcanic region, the new model gives results that are similar to a volcanic-path attenuation term derived by regression analysis.