Basis Pursuit Receiver Function

Abstract

Receiver functions (RFs) are derived by deconvolution of the horizontal (radial or transverse) component of ground motion from the vertical component, which segregates the PS phases. Many methods have been proposed to employ deconvolution in frequency as well as in time domain. These methods vary in their approaches to impose regularization that addresses the stability problem. Here, we present application of a new time-domain deconvolution technique called basis pursuit deconvolution (BPD) that has recently been applied to seismic exploration data. Unlike conventional deconvolution methods, the BPD uses an L1 norm constraint on model reflectivity to impose sparsity. In addition, it uses an overcomplete wedge dictionary based on a dipole reflectivity series to define model constraints, which can achieve higher resolution than that obtained by the traditional methods. We demonstrate successful application of BPD based RF estimation from synthetic data for a crustal model with a near-surface thin layer of thickness 5, 7, 10, and 15 km. The BPD can resolve these thin layers better with much improved signal-to-noise ratio than the conventional methods. Finally, we demonstrate application of the BPD receiver function (BPRF) method to a field dataset from Kutch, India, where near-surface sedimentary layers are known to be present. The BPRFs are able to resolve reflections from these layers very well.

De-noising receiver function data using the Seislet Transform

“…Additionally, there exist various sparsity promoting transforms, for example, Wavelet transform (Mallat 2009), Curvelets (Starck et al 2002), Shearlets (Guo & Labate 2007), Basis pursuit deconvolution (e.g. Chen et al 1998;Sen et al 2014), Radon transform (Foster & Mosher 1992), Empirical wavelet transforms (Liu et al 2016), etc. In general, the Wavelet transform has poor directionality and does not provide shift variance, as a result of which it cannot capture the curves and edges of a constructed image precisely.…”

Seismicity and structure of the Indian subcontin

“…Recently, Maurya et al (2016) presented a high-resolution 3-D velocity model including anisotropy, and imaged the lithosphere asthenosphere boundary (LAB) and the mid-lithospheric discontinuities of the Indian plate based on surface wave tomography using a massive dataset of 550 seismic broadband stations. In addition, some theoretical studies on receiver function, such as obtaining the response at the receiver without deconvolution (Kumar et al, 2010), sparsely constrained compressive time domain deconvolution (Sen et al, 2014) and transmitted P-to-S amplitude variation with ray parameter (Kumar et al, 2014) are made that show promising results.…”