Joint inversion of InSAR and broadband teleseismic waveform data using ABIC: application to the 1997 Manyi, Tibet earthquake
Gareth Funning(1) , Yukitoshi Fukahata(2)
, Yuji Yagi(3)
, and Barry Parsons(2)
University of California,
215 McCone Hall,
Berkeley, CA, 94720,
(2) University of Oxford, Parks Rd, Oxford OX1 3PR, United Kingdom
(3) IISEE, 1 Tatehara, Ibaraki 305-0802, Japan
There now exist numerous cases in which InSAR data have been used to estimate the distribution of coseismic slip on faults during earthquakes. InSAR data are largely very well suited for this task, having both high spatial resolution and large areal coverage on the ground, which translate to good spatial resolution at depth. The disadvantage with using InSAR to estimate earthquake slip is its lack of temporal resolution, limited by the often long time duration between satellite passes, which means that the evolution of slip on the fault cannot be determined, nor can the proportion of the observed deformation that is not coseismic. Detailed information about the temporal history of an earthquake rupture can be obtained seismologically; however such data have lower spatial resolving power than InSAR, and may be subject to tradeoffs between depth and origin time. Ideally, an earthquake source model would make use of the complimentary strengths of these two data types by inverting them simultaneously to find a model with good resolution in both space and time.
In order to accommodate these two different datasets in a single inversion, we derive and utilise a method based upon Akaike's Bayesian Information Criterion (ABIC) for such a problem for the first time. The ABIC method requires prior information to be imposed on the form of the final model in order to limit the range of possible solutions; we therefore use a spatial smoothing criterion - to limit large oscillations in slip which would imply unphysical strains on a fault - and a temporal smoothing criterion to similarly limit large accelerations on a fault. The InSAR and seismological datasets themselves are similarly treated as constraints on the model. The ABIC function, a statistical construct based upon the principle of maximum likelihood, has the property that when minimised numerically, the three hyperparameters that control the inversion - two weighting parameters controlling the relative importance of the spatial and temporal smoothing constraints on the model to the observed data in the inversion and another controlling the relative weighting of the two datasets in the inversion - can be obtained objectively, and an optimal inverse model thus generated.
We apply this technique to the Mw 7.6, 8th November 1997 Manyi earthquake in central northern Tibet. The input datasets are three short-interval ERS-2 interferograms from adjacent tracks that cover the coseismic deformation, and vertical component (P-wave) data from 10 Global Seismic Network stations at teleseismic distances from the epicentre. The Manyi fault is approximated by a 180 km x 18 km vertical fault, divided into 6 x 6 km subfaults. We invert both datasets separately, and then jointly, using the ABIC method.
We find that the InSAR data place a very strong constraint on the spatial pattern of fault slip obtained, with the joint inverse model strongly resembling the slip pattern obtained from the InSAR data alone, from both this simplified case and more complex models. Despite the difference in slip pattern between these models and that obtained by inverting the seismic data alone, the joint model can be accommodated by the seismic data with very little degradation to the fit over the seismic-only case. The slip history of the earthquake is consistent with that proposed in published seismic studies, with bilateral rupture for the first 20 seconds, followed by 32 seconds of unilateral westward rupture. The ABIC method is therefore demonstrated to be an excellent technique for objectively combining datasets, and has a lot of promise for further joint inversion studies of this kind.