Effect of non-uniform station coverage on the inversion for earthquake rupture history for a Haskell-type source model

In order to determine how reliably one can invert accelerograms to determine the rupture process details, when the station configuration is less than optimal, we use the vertical component of synthetic accelerograms for a Haskell-type earthquake rupture model, at stations in the vicinity of a dip-slip fault and solve the inverse problem. Of the various station configurations used, one is a uniform distribution and the others are very non-uniform. Faults of two different aspect ratios are considered. We mainly use much larger spatial and temporal cell sizes in the inversion than we use to construct the artificial data. The fault mechanism and the fault area are taken as known in the inversions. To solve the inverse problem, we use the method of linear programming and stabilize the solution by the use of physical constraints. The constraints of positivity of the slip rates on the fault is used in all cases in this study. In some cases, additional physical constraints such as preassigning the final moment, the rupture speed, and so on, are also used. We find that using a cell size almost double the wavelength of interest, we are able to reproduce the solution of the problem, even when we add a small amount of random noise to the artificial data, provided the source medium structure is known. We show that the best station configuration is when the stations are on the hanging wall, due to the fact that they provide the best illumination of the fault surface. This provides an incentive to install permanent ocean bottom strong ground motion stations in subduction zones. We also analyzed the effect of the rupture propagation direction on the results of the inversion showing that even four stations are sufficient to retrieve the rupture process if they are in the forward direction of the rupture propagation; the results for this case are better than when the four stations are placed in the backward direction, even when their positions are such that they illuminate the fault in exactly the same way as the four stations in the forward direction. Thus azimuthal distribution and the resulting illumination of the fault as well as the relation of the position of the stations to the direction of rupture propagation are more important than simply the number of stations. Finally, we find that proper knowledge of source medium structure is essential to recover the source process details reliably and that poor knowledge of crustal structure cannot be compensated by adding stations or by additional constraints.