Quantifying resolving power of seismic systems

Abstract

Abstract A quantitative formulation of vertical resolving power of seismic exploration systems is presented and is offered as a proposed characteristic, or standard, resolving power identified with individual systems. The formulation broadens the classical concept of resolution by taking into account the reflection waveform and the noise, in addition to the classical time variable. The principal feature in the formulation is the stipulation that the intratrace distribution of reflections and of noise be treated as random (Gaussian) distribution, which is regarded as the most general representation for seismic sections as a whole.Through this quantification of vertical resolving power and therefore of intratrace reflection quality, a number of elemental reflection properties that have been described only qualitatively in the past are expressed by simple formulas. The quantification is consistent with the concept that the resolving power of a noise-free zero-phase system with a flat spectral band response is proportional to the bandwidth. The derived basic formula for the proposed characteristic resolving power is a 2m /E, where a m is the maximum (absolute) amplitude of the signal wavelet of a seismogram interval, E is the energy of the signal wavelet, and noise is neglected. The quantification of the reflection properties, including taking the noise into account, stems from this formula.The classical concept of resolution, which considers only the time variable, such as the dominant period of signal wavelets, is applicable essentially only in cases of two noise-free equal-strength reflections. In contrast, the proposed formulation of resolving power accommodates a wide scope of applications and might be considered basic to seismic systems. I present theoretical material for evaluating the merits of the proposal. Suitable comparisons by seismic modeling would be useful in the overall evaluation.