Abstract
To maintain a stable and computationally feasible inverse problem, standard methods of inversion of ground motions for slip distribution on earthquake faults have to limit the size of the fault-discretization grid, with no clearly established criteria for setting the cell size. The subfault dimensions typically scale with earthquake magnitude. Also, the solution of a linear matrix equation, being the basis for the standard inversion techniques, assumes the slip weight on subfaults to be the only rupture parameter to solve for. This approach does not consider the fact that fault radiation is controlled by two independent rupture parameters – the slip U and peak slip rate vm – except at very low frequencies. These two parameters trade off with each other. Sensitivities of slip images to the selection of the grid and the assumption of a particular slip velocity (through a subfault’s rise time) cause ambiguities in the inverted models. Such sensitivities can be investigated by discretizing the representation integral of elasticity. For a heterogeneous fault, containing both a deterministic and a stochastic components, the subfault size of approximately 3 × 2.5 km leads to significant unphysical oscillations in the radiated ground-velocity pulse, caused by imprecise representation of the continuous integral; any coarser grid will cause distortions of the true slip distribution. The trade-off between U and vm results in offsetting large changes in subfault slip by relatively minor changes in slip velocity. The consequences of inadequate choices of mesh size and fixing the value of slip velocity (via slip duration), inevitable in the formulation of the matrix inversion, are the distortions of true slip of unknown severity. The artifacts produced are exacerbated by the use of the triangular slip-velocity function, compared to the omega-square one, as well as by the retention of only the far-field terms in the matrix equation.
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Beresnev, I.A. Uncertainties in Finite-Fault Slip Inversions, Part II: Fault Discretization and Parameterization of Slip Function. Pure Appl. Geophys. 180, 59–68 (2023). https://doi.org/10.1007/s00024-022-03216-4
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DOI: https://doi.org/10.1007/s00024-022-03216-4