Statistically perturbed geophone array responses

Abstract

Seismic‐receiver arrays implemented under typical field conditions are subject to a variety of perturbing influences. The array responses that are actually achieved differ, perhaps substantially, from the nominal response associated with ideal conditions (precise positioning, vertical plants, identical geophones, perfect ground coupling, etc.). Variations in receiver array response may degrade the effectiveness of multichannel processing and analysis schemes that rely upon channel‐to‐channel waveform constancy. In effect, array‐response variation is a form of noise added to recorded waveforms and is thus potentially harmful. A rigorous physical treatment of the response of a geophone array to incident plane‐wave elastic radiation forms the point of departure for assessing the importance of response perturbations. The hard‐wired multiple seismometer group, long transmission line, and recording‐system input impedance are considered an electromechanical system. An individual geophone may have arbitrarily specified position and axial orientation and is modeled as a ground‐motion transducer that incorporates, to first order, the effect of compliant coupling to the earth. Elastic waves (of either vibratory mode) can be incident from any direction. This generality built into the mathematical description of receiver‐array response allows numerous array types (including those designed to record shear waves) to be analyzed. All parameters that determine the response value are then subjected to controlled random perturbations in order to evaluate the statistical variability of the complex valued array‐response function. Transformation of the perturbed responses to the time domain indicates the extent of waveform variability induced by geophone‐array diversity. Computational studies indicate that, for vertical or near‐vertical plane P‐wave incidence, reasonable variations in the controlling parameters do not reduce waveform coherence by any major amount. Peak times of reflection signal recorded on well planted geophone arrays typically vary by up to 4 ms. As the angle of incidence increases or the quality of the field‐array implementation degrades, the wavelets exhibit increasing amplitude loss, wave‐shape alteration, and incoherence that may affect an interpretation.