Field array performance: Theoretical study of spatially correlated variations in amplitude coupling and static shift and case study in the Paris Basin

Abstract

Near‐surface propagation anomalies degrade the performance of field arrays. We studied this problem by modeling the signal detected by a field array. In our model, the signal arrival time and amplitude were each varied with distance along the array according to some arbitrary spatial trend. Given the intensity and the correlation distance of the signal variations, both wavenumber selectivity for noise rejection and frequency response for desired signal can be calculated. We begin by describing diagnostic graphs that show an array’s attainable signal bandwidth and noise rejection capability. Next, we discuss the mathematical relationships between the graphs and observable quantities such as correlations, array lengths, geophone spacing, etc. Exponential correlation functions are used in the modeling study for illustrative purposes. The same diagnostics are then generated from measured correlations derived from experimental data acquired in the Paris Basin with a densely sampled geophone spread. We found that the bandwidth diagnostic was useful and easy to calculate for this data set. Data sets with stronger noise waves should allow an accurate calculation of noise rejection capability. The diagnostic graphs can help in choosing the number of channels, array length, and weighting in a particular exploration area.