Introduction

Picking the traveltimes of the events on seismic sections plays an important role in many velocity inversion methods. For example, in traveltime tomography using cross-well data, the first step is to pick traveltimes of the events on recorded sections. There are many factors that can cause errors in traveltime picking. First, the wavelets of the events to be picked are often band-limited. Determining the exact picking positions of the finite duration wavelets is rather difficult. And precursors introduced in the preprocessing and noises in the data make this picking task even harder to accomplish.

In practice, a tentative rule for traveltime picking is to identify the first breaks of the wavelets. However, this rule cannot be applied to the cases where precursors are introduced by preprocessing. An extreme example is the data collected with a vibrator-type source. After we cross-correlate data with the known source signature, the wavelets in the data have a zero phase spectrum; hence the central points of the wavelets should be picked. Such situations suggest that the determination of the picking position should depend on the type of wavelet.

In this paper, we describe a picking algorithm that chooses the picking position according to the phase spectrum of the wavelets. The paper is organized in the following way. First, we relate the traveltime picking problem to the estimation of the time delay of the source wavelet in the recorded data, and define our convention for determining the picking position by factorizing the spectrum of the source wavelet. A formula is then derived to calculate the time delay from the phase spectrum of the data. We describe two methods for calculating the phase spectrum of data (Oppenheim and Schafer, 1975). The first method uses the Fourier transform to find the principal phase spectrum and performs phase-unwrap by adding appropriate multiples of $2\pi$. The second method finds the phase spectrum by averaging the group delay over the frequencies. Then, taking into consideration the presence of noises in field data, we modify the second method by including a weighting function in the integration. We use both synthetic wavelets and wavelets recorded in the field to demonstrate the picking results. We also show two picking results for Walk-Cross data.