Table 1 Coordinates of source-type diagrams

(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)