Optimizing the number of stations in arrays measurements: experimental outcomes for different array geometries and the f-k method

Array measurements have become a valuable tool for site response characterization in a non-invasive way. The array design, i.e. size, geometry and number of stations, has a great influence in the quality of the obtained results. From the previous parameters, the number of available stations uses to be the main limitation for the field experiments, because of the economical and logistical constraints that it involves. Sometimes, from the initially planned array layout, carefully designed before the fieldwork campaign, one or more stations do not work properly, modifying the prearranged geometry. Whereas other times, there is not possible to set up the desired array layout, because of the lack of stations. Therefore, for a planned array layout, the number of operative stations and their arrangement in the array become a crucial point in the acquisition stage and subsequently in the dispersion curve estimation. In this paper we carry out an experimental work to analyze which is the minimum number of stations that would provide reliable dispersion curves for three prearranged array configurations (triangular, circular with central station and polygonal geometries). For the optimization study, we analyze together the theoretical array responses and the experimental dispersion curves obtained through the f-k method. In the case of the f-k method, we compare the dispersion curves obtained for the original or prearranged arrays with the ones obtained for the modified arrays, i.e. the dispersion curves obtained when a certain number of stations n is removed, each time, from the original layout of X geophones. The comparison is evaluated by means of a misfit function, which helps us to determine how constrained are the studied geometries by stations removing and which station or combination of stations affect more to the array capability when they are not available. All this information might be crucial to improve future array designs, determining when it is possible to optimize the number of arranged stations without losing the reliability of the obtained results.

FFT Interpolation From Nonuniform Samples Lying in a Regular Grid

This paper presents a method to interpolate a periodic band-limited signal from its samples lying at nonuniform positions in a regular grid, which is based on the FFT and has the same complexity order as this last algorithm. This kind of interpolation is usually termed “the missing samples problem” in the literature, and there exists a wide variety of iterative and direct methods for its solution. The one presented in this paper is a direct method that exploits the properties of the so-called erasure polynomial and provides a significant improvement on the most efficient method in the literature, which seems to be the burst error recovery (BER) technique of Marvasti’s The paper includes numerical assessments of the method’s stability and complexity.

Estimation of Time-Limited Channel Spectra From Nonuniform Samples

This paper deals with the estimation of a time-invariant channel spectrum from its own nonuniform samples, assuming there is a bound on the channel’s delay spread. Except for this last assumption, this is the basic estimation problem in systems providing channel spectral samples. However, as shown in the paper, the delay spread bound leads us to view the spectrum as a band-limited signal, rather than the Fourier transform of a tapped delay line (TDL). Using this alternative model, a linear estimator is presented that approximately minimizes the expected root-mean-square (RMS) error for a deterministic channel. Its main advantage over the TDL is that it takes into account the spectrum’s smoothness (time width), thus providing a performance improvement. The proposed estimator is compared numerically with the maximum likelihood (ML) estimator based on a TDL model in pilot-assisted channel estimation (PACE) for OFDM.