# Surface-Wave Extraction Based on Morphological Diversity of Seismic Events
## 1 Introduction  
Seismic surface waves are widely used in crustal and mantle structure studies as well as engineering prospecting. They are characterized by low attenuation with offset, a high signal-to-noise ratio, and dispersion [1; 2]. The dispersion characteristics of surface waves reflect the near-surface S-wave velocity structure. Dispersion curves of fundamental-mode surface waves are inverted to obtain a near-surface S-wave velocity structure for PS-wave static corrections in seismic exploration [3; 4]. Recently, some studies have found that fundamental- and higher-mode surface waves have different sensitivities to elastic properties and thicknesses of near-surface materials [5; 6]. Thus, joint inversion of fundamental- and higher-mode surface waves is of widespread interest for less ambiguity and higher accuracy of S-wave velocities in engineering seismic prospecting, ambient seismic noise tomography, and microtremor surveys [7; 8]. To obtain accurate S-wave velocities, extraction of accurate dispersion curves of multi-mode surface waves is essential. Fundamental-mode surface waves are dominant in vertical-component seismic data, while higher-mode surface waves are generally more evident on horizontal components or X components in two-dimensional (2D) surveys [9]. Because they are disturbed by reflections, it is usually difficult to extract accurate dispersion curves of higher-mode surface waves from X-component seismic data, causing ambiguity in the inverted S-wave velocities. [PERSON] et al. [10] propose high-resolution linear Radon transform (LRT) to image the surface-wave dispersive energy, which improves the resolution of phase velocities. However, when disturbed by body waves or strong noise, the dispersive energy may not be smooth, and, thus, it becomes hard to distinguish between different modes; this is known as \"mode kissing\" [11]. This phenomenon is vulnerable to mode misidentification [12], resulting in less reliable inversion or even wrong inverted S-wave velocities. To extract dispersion curves, surface waves are extracted on the basis of different characteristics between surface waves and interference waves. Methods of surface-wave suppression are based on single-component processing or multicomponent processing. Methods of single-component processing include f-k filtering, curvelet transform, and other transform methods [13; 14; 15], while methods of multicomponent processing are polarization filtering and vector median filtering, which preserve the vector characteristics and the spectral bandwidth of reflections [16; 17]. By a hybrid linear-hyperbolic Radon transform, [PERSON] et al. [18] separate surface waves successfully in a signal model that consists of both surface waves with linear events and reflections with hyperbolic events. However, raw data are transformed into the conventional intercept-slowness (\(\tau\)-p) domain, which is not sparse enough to separate surface waves according to their dispersion characteristics. Using high-resolution LRT, [PERSON] et al. [19] transform raw data into the frequency-velocity (f-v) domain to implement surface-wave separation. However, dispersive energy of higher-mode surface waves may overlap with that of reflections in the f-v domain, because the frequencies and velocities of PS-waves are close to those of higher-mode surface waves [16]. So, it may be difficult to extract surface waves from X-component seismic data. In this paper, we propose a method of surface-wave extraction to overcome the influence of reflections on surface-wave dispersive energy. The proposed method is based on the morphological differences between surface waves and reflections. We also exploit the advantages of wavefield separation by frequency-domain LRT and time-domain hyperbolic Radon transform (HRT). To implement surface-wave extraction, the sparse representation problem based on morphological component analysis (MCA) is optimally solved. We first describe the sparse representation problem and the selection of dictionaries.