Investigations Into Early Magnitude Estimation From Predominant Period, Using Synthetic Rupture Models

Considerable interest has been shown in a method for estimating predominant period in the time domain (TpMax), first proposed by Nakamura (1988) and currently being developed for other early warning systems (e.g. Lockman and Allen, BSSA, 2005). Issues still exist as to the causes of the scatter evident in empirical work, and how effective the method is for characterising large events whose time to rupture is longer than the few seconds desired to estimate the magnitude. Our work on applying this method to an aftershock dataset motivated us to investigate the method through the use of synthetic rupture models. The rupture model we use prescribes a stress-drop with a prescribed rise-time over a small patch of the fault surface. This stress-drop is propagated to other patches of the fault according to a prescribed rupture rate. The same finite difference model geometry and fault patch size was then used to model events ranging from magnitude 3.7 to 7.2. Moment Magnitude was calculated directly by integrating the resultant slip on the fault, and TpMax was calculated from seismograms recorded on surface 50 km from the centre of the fault. The initial modelling used a homogenous stress drop, rise-time, and rupture rate. A dataset of 165 events, showed a significant increasing relationship between the TpMax calculation and magnitude. Isolating similar events initiating at the same point on the fault, gave a near straight-line trend. Scatter in the relationship is shown to result from variations in the position, initiation point, stress drop, rise time, and rupture velocity. Low frequency filtering was found to significantly affect the TpMax calculations and trends. Without filtering, the relationship saturated from just after magnitude 6, as the time to rupture becomes longer than the window used to calculate TpMax. However, low frequency filtering actually reduces the time to reach a maximum in the calculation, and this can cause the increasing trend to continue into somewhat higher magnitudes. This mapping may explain some of the previously reported results that TpMax can often be calculated in less time than the time to rupture (Olson and Allen, Nature, 2005). Extensions to this work are being made to look at whether these conclusions remain true for heterogenous rupture, and whether any advantages can be gained by using either displacement or acceleration seismograms in the calculation rather than velocity seismograms.