Resolution, a Gedanken tale: Sampling, Blueness and Noise

Resolution is of the essence in many different fields and in many different formats. In exploration seismology, it is generally assumed that the bandwidth of the seismic wavelet is the parameter that dictates the limit of achievable resolution. In other words, if the cut-off frequency is 100Hz, there is no point in sampling at less than 4ms. Following an initially Gedanken experiment, we show in this paper that, in fact, achievable resolution is not dictated by the wavelet. Sampling at intervals which are less than the corresponding wavelet Nyquist frequency, together with a sparse inversion algorithm, can provide a very useful scenario.