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Table 1 Coordinates of source-type diagrams

From: Mathematical review on source-type diagrams

   Horizontal axis Vertical axis Normalization Reference
(a) Cubic \(u\) \(v\) \(\left( { - u, v} \right)\) Hudson et al. (1989)
(b) Hexagonal bi-pyramid \(\tau\) \(k\) \(\left( { - \tau , k} \right)\) Hudson et al. (1989)
Vavryčuk (2015)
(c) Modified hexagonal bi-pyramid \(T = \frac{\tau }{1 - \left| k \right|}\) \(k\) \(\left( { - T, k} \right)\) Hudson et al. (1989)
Vavryčuk (2015)
(d) Conjugate bi-pyramid \(\eta\) \(\xi\) \(\left( { - \eta , \xi } \right)\) Vavryčuk (2015)
(e) Spherical equirectangular \(\gamma\) \(\delta\) \(\left( { - \frac{6\gamma }{\pi }, \frac{2\delta }{\pi }} \right)\) Chapman and Leaney (2012)
Tape and Tape (2012)
(f) Spherical orthogonal \(R = \sin \gamma \cos \delta\) \(\zeta = \sin \delta\) \(\left( { - 2R,\zeta } \right)\)
(g) Modified spherical orthogonal \(r = R\left| R \right|\) \(s = \zeta \left| \zeta \right|\) \(\left( { - 4r, s} \right)\) Zhu and Ben-Zion (2013)
Vavryčuk (2015)
(h) Spherical azimuthal \(p = \frac{\sqrt 2 \sin \gamma \cos \delta }{{\sqrt {1 + \cos \gamma \cos \delta } }}\) \(q = \frac{\sqrt 2 \sin \delta }{{\sqrt {1 + \cos \gamma \cos \delta } }}\) \(\left( {\frac{ - 2p}{\sqrt 6 - \sqrt 2 },\frac{q}{\sqrt 2 }} \right)\) Chapman and Leaney (2012)
Tape and Tape (2013)
Vavryčuk (2015)
(i) Spherical cylindrical \(\gamma\) \(\zeta\) \(\left( { - \frac{6\gamma }{\pi }, \zeta } \right)\) Tape and Tape (2012)
(j) Modified spherical cylindrical \(a = \frac{6}{\pi }\gamma \sqrt {1 - \left| \zeta \right|}\) \(b = \frac{\zeta }{{1 + \sqrt {1 - \left| \zeta \right|} }}\) \(\left( { - a, b} \right)\)
(k) Spherical cylindrical orthogonal \(\chi = \sin \gamma\) \(\zeta\) \(\left( { - 2\chi ,\zeta } \right)\) Zhu and Ben-Zion (2013)
(l) Percentile \(\epsilon\) \(v\) \(\left( { - 2\epsilon , v} \right)\) Vavryčuk (2001)
(m) Modified percentile \(c = 2\epsilon \left( {1 - \left| v \right|} \right)\) \(v\) \(\left( { - c, v} \right)\) Vavryčuk (2001)