Surface wave tomography with compressive sensing

The development of dense seismic arrays has led to the emergence of new surface wave tomography methods, such as Eikonal/Helmholtz tomography, wavefield gradiometry, and seismic noise gradiometry. All these methods need to calculate spatial derivatives of some attributes of the wavefields, for example travel time, amplitude, or the displacement itself. Usually, the waveforms contain noise and are observed on an irregular grid. Interpolation and smoothing are necessary to mitigate the problems, but also limit the resolution of tomography. Here, we propose a new data pre-processing method based on compressive sensing (CS). The new method uses sparsity promoting inverse techniques and curvelet transform to achieve simultaneous seismic data interpolation and denoising in frequency domain. The resulted wavefields can then be used in any wavefield-based surface wave tomography method. Preliminary tests with finite-difference synthetics show improved tomographic images, compared with images from the same methods applied to the original synthetics.