Seismic traces abound in singularity, which is essentially attributed to the first arrival of wavelets. Spline functions are of discontinuity and continuity. In some sense, the first arrival is the discontinuity for seismicity. The algorithm for singularity detection has been presented. The procedure includes some steps. Taking spline functions as scale function, constructing one low-pass filter and defining one operator with the theory of wavelet packet, one can isolate the low frequency of signal iteratively and decompose seismic traces singularly. Based on the processing of the model and field data, the algorithm can evidently improve the resolution and desirably eliminate ground-roll; Moreover, the algorithm has no limitation for any hypothesis.