The effects of spatial sampling on refraction statics

The use of seismic refraction data to determine the long wavelength statics correction not adequately addressed by residual statics routines, is widespread. While the importance of accurate traveltimes is well known, the effects of the geophone array on the inversion process are not.

This study used two coincident sets of data recorded with two recording systems at Cobar in southeastern Australia. One system used a 60 m trace interval with end-to-end arrays consisting of 16 detectors, while the other recording system used single detectors, which were 10 m apart.

The temporal resolution achieved with the 60 m groups is poor, and does not accurately measure the thickness of weathering as determined with the data using the 10 m trace spacing. One factor limiting the achieved resolution is the finite length of the geophone array. With extended arrays, the location of the effective receiving point, depends upon the direction from which the seismic signal arrives. For signals traveling in the forward direction, the effective receiving point is the first detector in the array, while for signals traveling in the reverse direction, it is the last detector. For the data used in this study, the forward and reverse traveltimes which are referenced to the same station number, represents a lateral interval of the sub-weathering interface of approximately 100 m, when both the length of the geophone array and the offset distances are added. The traveltime differences of the refracted arrivals over this interval can be up to 20 milliseconds, which implies that an accuracy of only about 10 milliseconds is meaningful with model based inversion methods, unless the effect of the length of the array is accommodated.

An analysis using the generalized reciprocal method, which uses refraction migration in multiples of the array length, shows that a migration distance of one station interval essentially removes the effect of the finite array length, when end-to-end arrays are employed. However, the static then applies to each end of the array, and in the study area, there can be a variation of up to 7 milliseconds in the weathering correction from one end of the array to the other. Therefore, it is necessary to further increase the refraction migration by an additional array length, in order to determine the static in the central region of the geophone array, which is then taken as the static correction for the entire array. Although there is an improvement in the resolution achieved with the 60 m groups, it is still poor, when compared with that achieved using the 10 m single detectors.

Further analysis of the data will be carried out to confirm that the finite length of the 60 m geophone arrays is the significant factor limiting the resolution of the refraction data, rather than the variable signal-to-noise ratios of the data.