In this paper, I propose the scaling relation W C 1 L β (where β ≈ 2=3)to describe the scaling of rupture width with rupture length. I also propose a new displacement relation, where A is the area (LW). By substituting these equations into the definition of seismic moment (M 0 μ DLW), I have developed a series of self-consistent equations that describe the scaling between seismic moment, rupture area, length, width, and average displacement. In addition to β, the equations have only two variables, C 1 and C 2 , which have been estimated empirically for different tectonic settings. The relations predict linear log-log relationships, the slope of which depends only on β.These new scaling relations, unlike previous relations, are self-consistent, in that they enable moment, rupture length, width, area, and displacement to be estimated from each other and with these estimates all being consistent with the definition of seismic moment. I interpret C 1 as depending on the size at which a rupture transitions from having a constant aspect ratio to following a power law and C 2 as depending on the displacement per unit area of fault rupture and so static stress drop. It is likely that these variables differ between tectonic environments; this might explain much of the scatter in the empirical data.I suggest that these relations apply to all faults. For small earthquakes (M < ∼5) β 1, in which case L 3 fault scaling applies. For larger (M > ∼5) earthquakes β 2=3, so L 2:5 applies. For dip-slip earthquakes this scaling applies up to the largest events. For very large (M > ∼7:2) strike-slip earthquakes, which are fault widthlimited, β 0 and assuming D ∝ A p , then L 1:5 scaling applies. In all cases, M 0 ∝ A 1:5 fault scaling applies.
We investigate two intraplate earthquakes in a stable continental region of southwest Western Australia. Both small‐magnitude events occur in the top ∼1 km of crust and their epicenters are located with an accuracy of ∼100 m (1σ) using satellite Interferometric Synthetic Aperture Radar (InSAR). For the Mw 4.7 Katanning earthquake (10 October 2007) the average slip magnitude is 42 cm, over a rupture area of ∼1 km2. This implies a high static stress drop of 14–27 MPa, even for this very shallow earthquake, which may have important implications for regional seismic hazard assessment. The earthquake rupture extends from a depth of around 640 m to the surface, making it a rarely observed intraplate, surface‐rupturing event. Using InSAR observations, we estimate the coseismic slip distribution of the shallow earthquake, such estimates being rarely available for small magnitude events. For the Mw 4.4 composite Kalannie earthquake sequence (21–22 September 2005), we use a long‐term time series analysis technique to improve the measurement of the co‐seismic signal, which is a maximum of 27 mm in the line‐of‐sight direction. Double difference seismic analysis shows some relocated cluster seismicity which corresponds in timing, location, and source parameters to the InSAR‐observed deformation. This earthquake is the smallest magnitude seismic event to have been investigated using InSAR and demonstrates the capability of the technique to provide important constraints on small‐magnitude coseismic events. The shallow depth of both these events adds weight to the suggestion that earthquakes associated with tectonic processes in this area of Western Australia often initiate in the upper 1 km of crust.
The onset times for 78 teleseismic iP phases are picked by four seismic analysts and by three automatic picking algorithms, on both the single trace and on an array beam. The difference in the onset times picked by different analysts is on average 760.0ע sec with a standard deviation of 0.15 sec. The analysts on average pick times 0.1 sec earlier on the beam than on the single trace.The three automatic pickers are the picker described by Earle and Shearer (1994), an autoregressive-Akaike information criteria (AR-AIC) picker (Leonard and Kennett, 1999) and an adjusted AR-AIC picker, which is described in this article. Of the three automatic pickers, the adjusted AR-AIC picker picks onset times closest to an experienced analyst. Compared to the three most experienced analysts, the difference in onset time is on average ע 0.043 sec, with a standard deviation of 0.19 sec. These values are very similar to the differences between the analysts, suggesting that for many applications, the time estimated by the adjusted AR-AIC picker can be used without review by a seismic analyst.
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