Semi-automatic Picking of First Arrivals through Cross Correlation Using Spline Interpolation Applied to Near-surface Seismic Surveys

Cross-correlation between adjacent seismic traces is one of several ways to estimate the time shift between first arrivals on seismograms. The accuracy of this method is limited to the sampling interval of the recorded seismic energy and the signal-to-noise ratio and uniformity of the seismic wavelet. For situations where the sampling interval is large interpolation between samples can be used to refine and improve results from this technique. Simple linear interpolation, however, preserves the position of the maximum-recorded data value of the wavelet. Such an approach may not provide an exact estimation for the peak value of the wavelet and is therefore susceptible to errors due to noise influence. A spline function fit to the peak-value samples will better define the position of the wavelet maximum and as a result the first-arrival shift estimations are more accurate. Furthermore, the relatively small number of samples used in the spline fitting process can act as a second round refining correction of the time-shift estimate, which is especially valuable when data are noisy. This algorithm reduces the error of first-arrival picking algorithms that use simple cross correlation. Introduction First-arrival picking algorithms can be divided into several types of methods, including the coherence method (Gelchinski and Shtivelman, 1983), cross-correlation method (Peraldi and Clement, 1972; Lanz et al., 1998), neural network method (Veezhinathan et al., 1991). Coherence and neural network methods assume the existence of patterns in the first arrivals. Pattern recognition of this type is effective when a simple (layered) earth model can be used to approxmate the earth structure. This simple earth-model scenario rarely matches the near-surface conditions when studied with the detail required of most modern surveys. Cross-correlation methods are considered to be most appropriate for the near-surface surveys since their algorithm is based on trace-by-trace evaluation of the first-arrival times. The accuracy of cross-correlation methods is limited by the sampling interval of the data and consistency of the source wavelet. To overcome the sampling limitation Lanz et al. (1998) fitted a quadratic curve to the cross-correlation function. By doing this an additional component to the first arrival shift between traces can be estimated. Since this additional evaluation is controlled by the maximum of the cross-correlation function the maximum value resulting from this additional evaluation is smaller than one sampling interval. We propose a cross-correlation function method in which the additional evaluation may be greater than one sampling interval. This new proposed cross-correlation method is not fully automatic because of the need to select a starting point of the first-arrival wavelet of the first trace from a certain range of traces. Techniques, such as the MER (moving average ratio) to estimate the beginning of first arrivals can be used but these techniques perform poorly when the signal-to-noise ratio is low (Spagnolini, 1991). In practice, this is most often the case when different types of noise affect the first arrival picking algorithms. The crosscorrelation approach to first-arrival picking assumes that the phase and shape of the first arrival wavelet D ow nl oa de d 07 /0 3/ 14 to 1 29 .2 37 .1 43 .1 6. R ed is tr ib ut io n su bj ec t t o SE G li ce ns e or c op yr ig ht ; s ee T er m s of U se a t h ttp :// lib ra ry .s eg .o rg / are constant from trace to trace. In reality, the phase and shape of the first-arrival wavelet vary for different parts of the shot gathers. The main reason for this distortion is that the earth acts as a minimumphase low-pass filter (Aki and Richards, 1980). Noise can be another source of wavelet-shape alteration. Manual adjustment of the actual first-arrival time is necessary from time to time to account for the inconsistent shape of the first arrival wavelet and the lack of a consistent pattern in the first-arrival times from trace to trace, which is typical for many near-surface settings. The goal of this work is to demonstrate a method for first-arrival picking that takes into consideration the wavelet shape inconsistency, lack of first arrival patterns from trace to trace, and the presence of noise.