Ergodic sampling: A new geophysical data acquisition method to save cost and gather more information

The cost of collecting geophysical data can be so high that it may hinder the effective application of geophysical methods in many important problems such as mineral exploration, geothermal exploration, and carbon storage monitoring. The primary factor that increases the cost of acquisition is the large number of spatial sampling stations distributed uniformly as required by the Nyquist sampling. To overcome this challenge, we propose a new sampling strategy referred to as ergodic sampling theory. Ergodic sampling requires only a subset of samples but can obtain nearly the same information as the entire set of uniform dense samples. In contrast to Nyquist sampling, which requires a sufficient but larger than necessary sample set, ergodic sampling only acquires the core subset of samples that is both necessary and sufficient to gather the same information. Therefore, ergodic sampling can significantly decrease the number of samples compared with Nyquist sampling. We present our new sampling theory and demonstrate its application in the geophysical data acquisition. Our simulation and field data example show that the cost can be reduced by a factor up to 5. Equivalently, this result also means that it is possible to acquire 5 times more information when the same number of samples used in the traditional equi-spaced sampling is deployed using the ergodic sampling strategy.