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Seismic tomography
This protocol is extracted from research article:
Upper and lower plate controls on the great 2011 Tohoku-oki earthquake
Sci Adv, Jun 20, 2018; DOI: 10.1126/sciadv.aat4396

We applied a tomographic method (18, 47) to invert 144,354 P-wave arrival-time data recorded at 382 permanent seismic stations in Tohoku from 4760 local shallow- and intermediate-depth earthquakes that occurred during January 2000 to June 2016 (Fig. 1). Lateral depth variations of the Conrad and Moho discontinuities in the overriding Okhotsk plate and the UBP were considered, and they were fixed in the tomographic inversion, because the existence of the three discontinuities in the study region has been established well and their geometries have been determined reliably (18, 47). A 3D grid with a lateral-grid interval of 0.5° was set up in the modeling space to express the 3D Vp structure. The grid nodes were arranged at depths of 0 to 60 km with a vertical grid interval of 5 km and at depths of 60 to 200 km with a vertical grid interval of 20 to 50 km above the UBP, as well as at depths of 5, 25, and 75 km below the UBP. Vp perturbations at the grid nodes from a starting Vp model (47) and hypocentral parameters of the local earthquakes were taken as unknown parameters. In the starting 1D velocity model (47), Vp was 6.0 km/s in the upper crust and 6.7 km/s in the lower crust, and the Jeffreys-Bullen velocity model was adopted for the upper mantle. Following the previous tomographic studies in Tohoku (3, 4, 47), the initial Vp of the subducting Pacific slab was assigned to be 4% faster than the mantle velocity at the same depth. The Vp perturbation at any point in the modeling space was computed by linearly interpolating the Vp perturbations at the eight grid nodes surrounding that point. An efficient 3D ray tracing technique (47) was used to compute theoretical travel times and ray paths. The damped least-squares method with smoothing regularization (47) was used to solve the observation equations that relate the arrival-time data to the velocity and hypocentral parameters. The local earthquakes were relocated in the inversion process. The P-wave root-mean-square travel-time residuals before and after the tomographic inversion were 0.496 and 0.394 s, respectively, with a variance reduction of 37%.

After the 3D Vp model was obtained, we further determined a 2D Vp model for the overriding Okhotsk plate beneath the Tohoku forearc (Fig. 2D). For any point in the 2D forearc area above the UBP, we calculated travel times t1 and t3 for a vertical ray path with a length d from the UBP to Earth’s surface using the 1D Vp model (47) and the obtained 3D Vp model, respectively. Then, the Vp anomaly δVV1 at that point was obtained using a simple relation δVV1=(dt3dt1)/(dt1), which is shown in Fig. 2D.

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