## 5 Discussion
Thus, when earthquake properties, such as the magnitude and focal mechanism, are difficult to determine, the HYDE algorithm can still provide seismotectonic information. We can generalize that the HYDE algorithm can be useful as an alternative or complementary tool to other investigation methods to reduce the uncertainties inherent in each method. In this regard, it should be stressed that fault parameter estimates are also affected by uncertainties when using approaches other than focal mechanisms. Statistical approaches such as Bayesian estimation, as well as numerical modeling methods, are useful to provide an understanding of geological processes and kinematic models [39; 40; 41]. However, these approaches require a priori information that is not always available, and the results depend on the boundary conditions and the accuracy of the many input parameters. Instead, our algorithm requires only the coordinates of the hypocenters as input data and does not require any constraints or boundary conditions, but does not provide slip angles. As a consequence, the size dip and strike obtained by HYDE may also be used as input parameters to reduce the uncertainties in slip estimates obtained by Bayesian estimation and numerical modeling methods. The value of the proposed algorithm becomes even more evident in terms of its application in the various fields in which knowledge of fault parameters is fundamental. Indeed, accurate knowledge of active fault geometries is also essential for earthquake ground motion evaluation, which, in turn, is crucial for seismic hazard assessments [41]. Thus, the HYDE algorithm may also be useful for subsoil characterization in the framework of performance-based earthquake engineering, reducing uncertainties in seismic fragility estimates [42; 43; 44]. General approaches to estimating fault strike and dip require collapsing the earthquake data onto a flat plane. For example, using the double-difference method, the data are transformed into a collinear dataset and then inverted using an L\({}_{1}\) or L\({}_{2}\) norm or another more robust norm. Other algorithms--such as the planar best-fitting method [45], which is based on the inertia tensor--are, like the double-difference method [37], heavily influenced by earthquakes located outside the fault zone. This trade-off is typically managed by carefully selecting the dataset. Our algorithm, however, automatically ignores all earthquakes outside the fault zone and can estimate the fault parameters without any prior data selection. This makes it particularly efficient and useful when rapid estimation of an active fault's strike, dip and mean location is needed. In particular, for the 2009 L'Aquila seismic sequence, we used the complete earthquake dataset to run our HYDE algorithm and determine the main fault plane parameters, in contrast to [32], who used a selection of hypocenters near the main fault to delineate its structure. Moreover, when refined seismic catalogs are not available, it is still possible to successfully use our algorithm, calibrating the thickness of the explorer parallelepiped according to the localization error magnitude. There are very few limitations when using the HYDE algorithm. However, when earthquake hypocenters are distributed on a curved structure, the algorithm will typically identify the fault in the area of lower curvature where event density is highest. Currently, we are unable to estimate the fault parameters for a curved structure or determine the location, strike and depth of the main shock if it occurs far from the lower-curvature region. Moreover, in the case of a highly segmented fault--i.e., a sequence of small segments of varying lengths separated by step-overs--the algorithm will identify a fault plane that encompasses all segments, with dip and strike parameters corresponding to the principal alignment, thereby providing only an approximate result.