The inversion of geodetic data to obtain earthquake parameters is often performed by assuming that the medium is isotropic, elastic and either homogeneous or layered. The layered medium often offers the best estimate of the structure of the crust; however, predicted displacements and observed data may differ beyond the measurement errors. The slip distribution on the fault plane is usually obtained by dividing the best uniform slipping fault into an arbitrarily large number of subfaults and minimizing a cost function that includes a smoothness (Laplacian) term and a data misfit term. The smoothing factor controls the trade-off between the smoothness and the goodness-of-fit. The main focus of this work is the determination and effect of the smoothing parameter. We conducted several inversion tests of noiseless synthetic surface displacement due to faults embedded in media with properties consistent with the geology of the Central Apennines (Italy), where the 2009 April 6, L’Aquila earthquake occurred. We used the following three-step procedure: (i) global optimization with no smoothness constraint for a fault divided into a small number of equally sized equal-rake subfaults; (ii) selection of the best fault parameters using information criteria and (iii) evaluation of the slip amplitude distribution on an expanded fault after choosing the smoothing factor from trade-off curves or from cross-validation for different numbers of subfaults. We show that all of the fault features obtained by the inversion procedure, including the slip distribution, agree with those (‘true’) used in the forward modelling when the data cover the majority of the displacement field. Notable departures from the true slip distribution occur when a suboptimal smoothing factor (obtained from the trade-off curves or cross-validation) is used. If different crustal stratifications are used in the inversions, the best results are obtained for the stratification that is the closest to the true crustal structure. When we use more realistic GPS distributions, prominent spurious slip patches can be obtained. Modellers should use synthetic tests and sensitivity analyses as an initial step in the data inversion for source parameters.
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