Estimation of spectral attenuation relation in the Zagros Region

Amplitudes of seismic waves decrease with distance according to anelastic properties of the earth and geometrical spreading. The attenuation of ground-motion amplitudes in the frequency domain is an important problem in engineering seismology. It is of particular practical interest in the regions such as Zagros (Iran). The Zagros fold- thrust belt, as a part of Alpine- Himalayan orogenic belt is one of the most active continental collision zones on the earth, which extends from the Tarus mountains in southeastern Turkey to the Minab fault in the east of the Strait of Hormoz in southern Iran.
Structurally, its formation is related to the continuing convergent movement between the Arabian plate to the southwest and the Central Iranian Micro continent to the northeast, resulting from the north- northeastward drift of Afro-Arabia against Eurasia and so this region is seismically active. Hence, attenuation studies as well as other seismic studies seem to be necessary. The ground-motion relations are key inputs to seismic hazard analysis for engineered structures. In such cases, an empirical attenuation model determined from events provides critical input to the models of ground-motion generation. The attenuation model is used to play back attenuation effects to determine the apparent source spectrum for each earthquake in the database. The lack of an appropriate ground-motion prediction model may result in undesirable outcomes, such as unrealistically high or low loading standards in the design and construction of critical infrastructure such as large dams, power stations, and hospitals. For seismological purposes, appropriate attenuation models make it possible to calculate more accurately the source parameters such as magnitude and seismic moment.
In this study about 10000 records due to 998 events recorded at the International Institute of Earthquake engineering and Seismology (IIEES) stations during 2006-2013 across the Zagros region, were selected in order to estimate the average attenuation relation parameters. All data were divided into two parts: a) acceleration data (that is derived from velocity data) with moment magnitude between 4-7and b) velocity data with moment magnitude between 2-4. We combined the two north–south and east–west seismograms into a single seismogram for a given azimuth. For each rotated combined horizontal record, a shear-wave window was selected and a 5% taper was applied at each end of the window. After correcting for instrument response, the Fourier spectrum of the shear-wave window and a noise window with the same length as the shear-wave window were calculated and binned in increments of 0.2 log frequency units for a central frequency range of 1-10 Hz. We fit the observed Fourier velocity amplitudes at each frequency to a Hinged-Trilinear function. The distances at which the nature of geometrical spreading attenuation changes significantly was graphically found for both data in 110 km and 200 km using a locally weighted scatterplot smoothing (LOWESS, local regression smoothing method) called robust LOWESS.
A trilinear function with hinges at distances of about 110 and 200 km can describe the geometric spreading attenuation with distance. Using unconstrained Nonlinear Optimization algorithm, we found that for acceleration data with  and for velocity data with  minimize the average absolute value of the Fourier spectrum amplitude residuals. Using an anelastic attenuation coefficient at different frequencies, the direct average of calculated quality factor for both dataset, Q in the Zagros region is obtained as