Estimates of the onset times of P phases from active source experiments can effectively be used in developing wavespeed models, and the large number of recordings typical of such experiments incentivizes the development of automated approaches to generate these estimates. The simplicity and repeatability of an airgun source such as that used in the 2016 Pisagua/Iquique Crustal Tomography to Understand the Region of the Earthquake Source (PICTURES) project in northern Chile suggested that a straightforward application of waveform cross-correlation would suffice for arrivals recorded by a network of inland seismic stations, but did not work well due to significant variations in waveform morphology. For similar reasons, the machine learning application PhaseNet also did not work well. Application of an alternative algorithm typically used in passive source investigations that is indifferent to waveform morphology, the Regressive ESTimator (REST) autopicking package, also proved unsatisfactory, largely because the limited spectral bandwidth of the airgun source and the frequent occurrence of local seismicity led to numerous false picks. This motivated the development of a new approach, named CORREL, that is a hybrid of REST and cross-correlation, with the addition of a constraint in the form of a polynomial function based on the REST picks that provides a reasonable prediction of an onset time. Compared to the results obtained originally from REST and simple waveform correlation, the application of CORREL to the PICTURES data both significantly increased the number of arrivals estimated and greatly reduced the number of outliers. The combination of techniques retains the precision afforded by cross correlation while taking advantage of the accuracy afforded by absolute time picking. The predictive polynomial also provides CORREL a better means to discriminate true shots from the abundant natural seismicity.