Modelling S‐wave radiation for SP‐waves in isotropic and anisotropic media

Abstract

ABSTRACTUtilizing shear‐wave (S‐wave) data acquired with compressional waves (P‐waves) is becoming more common as joint imaging and inversion techniques improve. Interest in S‐waves radiated from vertical sources and buried explosives exploits conversion to P‐waves as primary reflections (SP‐waves) for reducing acquisition costs and for application to legacy data. However, recent investigations overstate the extent of SP‐wave illumination and show isotropic processing results with narrow bandwidth frequency and wavenumber data. I demonstrate that illumination with SP‐waves is limited in general to near vertical polar angles up to around 30° or 35° for VP/VS of 2 or 3, respectively. At greater angles, S‐waves are typically in the P‐wave evanescent range and cannot excite SP‐wave reflections. Contrary to recent claims, these sources for P‐wave do not radiate SH‐waves polarized in horizontal planes in all azimuths. I show these properties for isotropic media with radiation expressions for amplitude derived in vector slowness coordinates. Also, I extend these expressions to transversely isotropic media with a vertical symmetry axis to show agreement with synthetic seismic data that only quasi SV‐waves are radiated and become more narrowly focused towards 45°. Furthermore, in orthorhombic media, synthetic data show that fast S1‐ and slow S2‐waves polarized parallel and perpendicular to fractures may appear as SV‐ and SH‐waves. For the partially saturated fracture model studied here, S1‐wave radiation has broader azimuthal illumination than slow S2‐waves, which are more narrowly focused in azimuth. These produce SP‐wave splitting signatures on vertical component reflection data that are nearly identical to PS‐wave signatures on radial horizontal component data. Separating these fast and slow SP‐waves is an additional processing challenge.