Seismic data have a number of unique characteristics that differentiate them from the still image and video data that are the focus of most lossy coding research efforts. Seismic data occupy three or four dimensions, and have a high degree of anisotropy with substantial amounts of noise. Two-dimensional coding approaches based on wavelets or the DCT achieve only modest compression ratios on such data because of these statistical properties, and because 2D approaches fail to fully leverage the redundancy in the higher dimensions of the data. We describe here a wavelet-based algorithm that operates directly in the highest dimension available, and which has been used to successfully compress geophysical data with no observable loss of geophysical information at compression ratios substantially greater than 100:1. This algorithm was successfully field tested on a vessel in the North Sea in July 1995, demonstrating the feasibility of performing on-board real-time compression and satellite downloading from marine seismic data acquisition platforms.