Normal modes in seismic data — Revisited

Abstract

At long distances from a seismic shot, the recorded signal is dominated by reflections and refractions within the water layer. This guided wave signal is complex and often is referred to as normal or harmonic modes. From the period equation, we derive a new approximate expression for the local minima in group velocity versus frequency. We use two data sets as examples: one old experiment where the seismic signal is recorded at approximately 13 km offset and another example using life of field seismic data from the Valhall Field. We identify four and five normal modes for the two examples, respectively. A fair fit is observed between the estimated and modeled normal mode curves. Based on the period equation for normal modes, we derive a simple, approximate equation that relates the traveltime difference between various modes directly to the velocity of the second layer. Using this technique for offsets ranging from 6 to 10 km (in step of 1 km), we find consistent velocity values for the second layer. We think that this method can be extended to estimate shallow lateral velocity variations if the method is applied for the whole field. We find that the simple equations and approximations used here offer a nice tool for initial investigations and understanding of normal modes, although a multilayered method is needed for detailed analysis. A comparison of three vintages of estimated normal mode curves for the Valhall field example representing seabed locations shifted by 1 km indicates that minor shifts in group velocity minima for the various modes are detectable.