In the field of earthquake engineering, Fragility Curves (FCs) have become indispensable for regional risk assessments due to their efficacy in estimating the failure probabilities of diverse structures, including buildings and bridges, based on certain intensity measures. FCs are typically derived from either mechanical simulations or on -site observations, encapsulating crucial information about local stratigraphy and topography. The dependency of FCs on these local parameters, such as soil and topographic conditions, may vary depending on the selected intensity measure. When a spectral ordinate at a specific period is used as an intensity measure, FCs tend to be largely site -independent. On the other hand, if the intensity measure is chosen to be the acceleration ag at the bedrock substrate, as often occurs, then the FC is site -dependent. This distinction implies that identical structures at different locations, or even the same location with different soil and topographic conditions, have different FCs. This can significantly influence the results of regional risk studies, as using FCs for a specific building type at diverse locations with different hazards, stratigraphy, and topography can result in significantly different failure probabilities. The goal of this study is to develop a method so that ag-based FCs, developed at a certain location, can be used at any other location and on any other soil, preserving consistency in terms of spectral ordinate. This is done by a fully analytical approach, using a spectrum -consistent transformation. As an application, risk maps for Italy are generated and compared with an alternative method based on shifting the hazard curve.

A microwave radiation model with coherent surface scattering is developed for analyzing the topographic effects of the lunar permanently shadowed region (PSR) on microwave radiometric observations. The coherent surface scattering to the observer, which comes from the nearby surface due to the variation in the surface slope, is quantified by the ray-tracing method. In addition, the vertical distribution of temperatures of the PSR is estimated by a 1-D thermal model with 3-D shading and scattering effects. The impact of coherent scattering on microwave brightness temperatures (TBs) by a nadir-look radiometer becomes more noticeable with high-resolution microwave TB data, such as 4 pix/degrees by 4 pix/degrees in this study. The rise in TB at certain locations in PSR may reach up to similar to 8 K at 37 GHz. However, when compared with the low resolution of the TB by Chang'E-2, the averaged contribution of coherent surface scattering is less than 1 K. Meanwhile, there is a discrepancy between the model-generated microwave TB and the measured TB of Chang'E-2, both in small and large craters. This discrepancy may be explained by a calibration issue or the uncertainty of model parameters. Nonetheless, the trend in the model-generated TB is consistent with the measurements, indicating that the proposed model has the potential to predict TB effectively within the PSR.