Estimation of wave velocity (or slowness) from array waveform data is
a basic and very important process in acoustic logging and seismic pro
cessing. A predictive method is developed to process array waveform da
ta containing multiple wave modes. These wave modes may overlap in bot
h time and frequency and are inseparable using conventional techniques
. In this new technique, the waveform at a receiver is modeled by a co
mbination of wave data at other receivers using a time-domain predicti
on theory. It is assumed that the array data contain a number of propa
gating modes. A minimization procedure is formulated to optimize the m
atch between the predicted and measured waveforms. yielding slowness e
stimates of the wave modes across the array. Most important, the optim
ization is performed directly in the time domain using the entire arra
y wave data set, including all possible data combinations. This strate
gy effectively reduces the noise effects and enhances the robustness o
f the estimation. Furthermore, the estimated slowness values can be us
ed in formulating a procedure to split the array data into individual
wave modes, allowing their behavior to be analyzed. Examples are shown
to demonstrate the ability of the technique to extract wave slowness
from multiple wave-mode data.