High-Efficiency Observations: Compressive Sensing and Recovery of Seismic Waveform Data

We present a new sampling scheme for seismic network observations and seismic exploration data acquisition based on compressive sensing theory. According to this theory, seismic data can be recovered with a compressive sampling scheme, using fewer samples than in traditional methods, provided that two prerequisites are met. The first prerequisite is sparse representation of the data in a transform domain. We use a one-dimensional wavelet transform to sparsely express the waveform data of the seismic network. For seismic exploration data, we use a curvelet transform as the sparse transform. The second prerequisite is incoherence between the sampling method and sparse transform. To enhance the incoherence, we propose a random sampling scheme for network and exploration observations, as random sampling is incoherent to most data transforms. In particular, we propose temporal random sampling for seismic network data observation and a full random sampling scheme in time and space for seismic exploration data. Compared with random sampling in spatial dimensions only, full random sampling further enhances incoherence because it adds the temporal dimension for randomization. Finally, seismic data are recovered from the compressive sampling data by calculating a sparsity-promoting algorithm in the sparse transform domain. We perform a real data test and synthetic data tests to illustrate that the proposed method can be used stably to achieve compressive sampling and successful recovery of high-resolution seismic waveform data. The results show that good sparse representation of the data and high incoherence between the sampling scheme and the data are important for successful recovery.