Rate Distortion Analysis of Wavefield Coding in Wireless Geophone Networks

Current and future trends in seismic acquisition point towards higher geophone densities (forecasted to be 1M nodes per survey). The geophones’ high operating precision and a sampling rate of a few milliseconds leads to a huge aggregate data rate in the geophone array. To handle this large data rate a hierarchy of multiplexed lines (including fiber optic cables) are used, resulting in substantial deployment costs. This work considers wireless geophone networks to mitigate these costs. Because of limited bandwidth of the wireless medium, compression of acquired data is needed. We assess lossy source coding (signal compression) performance using a rate-distortion tradeoff based on a physical model of the earth. The distortion criterion used is mean squared error. The earth’s physical model considered here consists of a randomly layered subsurface structure where the acoustic impedance of the earth varies as a homogeneous spatial random process. The rate distortion performance is assessed in terms of the parameters of this physical model e.g., the speed of sound underground and correlation length of acoustic impedance process. In comparison with previous work, this paper derives a closed form expression for the autocorrelation function for the reflection process for the 3D subsurface volume. We also show from the resulting rate-distortion curves that the compression performance improves both as the coding bock length increases and as the correlation length of the medium properties increases. The rate-distortion surface as a function of normalized MSE and sound of speed underground is also computed and validated through extensive simulations.