Main Article Content
Two methods for tracing seismic rays between 2 given end points through three dimensional, continuously varying velocity structures are available. This paper describes and compares them for problems of practical interest and for analytical ray paths through an idealized velocity structure. One method involves "shooting" the ray from one point with a given starting direction and then modifying this starting direction until the ray emerges at the desired target, while the other method involves "bending" an initial path between the end points until it satisfies the principle of stationary time. For most of the models investigated, "bending" is computationally faster than "shooting" by a factor of 10 or more. The "bending" method can be modified to deal with discontinuities in the velocity model, and can also be adapted for use in conjunction with a table of distances as a function of ray parameter when the three dimensional anomaly influences only a small fraction of the total ray path. The geometrical spreading effect on the amplitude of the ray may be retrieved easily from the "bending" solution.
Authors who publish with this journal as of Vol. 63 agree to the following terms:
a. Authors share the copyright with this journal in equal parts (50% to the journal, 50% to the lead author), and grant the journal right of first publication, with the work after publication simultaneously licensed under Creative Commons Attribution License CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
b. Authors may enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal, and a reference to this copyright notice.
c. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) during the submission process, as this can lead to productive exchanges and earlier and greater citation of published work and better sales of the copyright.
- Authors retain copyright and grant the Journal of Geophysics right of first publication, with the work two years after publication simultaneously licensed under the Creative Commons BY-NC-ND 4.0 License that allows others to share the work (with an acknowledgment of the work's authorship and initial publication in this journal), except for commercial purposes and for creating derivatives.
- Authors can enter into separate, additional, but non-commercial contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository, but not publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) before and during the submission process, as that can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
This journal is one of a handful of scholarly journals that publish original scientific works under CC BY-NC-ND 4.0 - the only Creative Commons license affording the authors' intellectual property absolute worldwide protection.
Journal of Geophysics is published under the scholar-publishers model, meaning authors do not surrender their copyright to us. Instead, and unlike corporate publishers like Elsevier or Springer Nature that resell copyright to third-parties for up to $80,000 (per paper, per transaction!), the Journal of Geophysics authors share copyright equally with this journal.
Therefore, all the proceeds from reselling copyright to third parties get shared to equal parts (50% to the journal, 50% to the lead author). Under the Berne Convention, this protection is an inheritable right that lasts for as long as the rightsholder lives + 50 years.
By submitting to this journal, the lead author, on behalf of all co-authors, grants permission to this journal to represent all co-authors in negotiating copyright sales and collecting proceeds. The lead author should negotiate with his/her co-authors the modalities of distributing the lead author's portion of the proceeds. Usually, this is per pre-agreed percentage of each co-author's contribution to creating the copyrighted work. (more...)
Barnes, A., Solomon, L.P. (1973) Some curious analytical ray paths for some interesting velocity profiles in geometrical acoustics. J. Acoustical Soc. Am. 53:147-155
Bulirsch, R., Stoer, J. (1966) Numerical treatment of ordinary differential equations by extrapolation methods. Numer. Math. 8:1-13
Chander, R. (1975) On tracing seismic rays with specified end points. J. Geophys. 41:173-177
Chernov, L.A. (1960) Wave propagation in a random medium. Dover, New York
Davies, D. (1972) Julian, B.R.: A study of short period P-wave signals from Longshot. Geophys. J. 29:185-202
Eliseevnin, V.A. (1965) Analysis of waves propagating in an inhomogeneous medium. Soviet PhysicsAcoustics 10:242-245
Engdahl, E.R. (1973) Relocation of intermediate depth earthquakes in the central Aleutians by seismic ray tracing. Nature Phys. Sci. 245:23-25
Engdahl, E.R., Sleep, N.H., Lin, M.T. (1977) Plate effects in North Pacific subduction zones. Tectonophysics 37:95-116
Jacob, K.H. (1970) Three-dimensional seismic ray tracing in a laterally heterogeneous spherical earth. J. Geophys. Res. 75:6685-6689
Jacob, K.H. (1972) Global tectonic implications of anomalous seismic P travel times from the nuclear explosion Longshot. J. Geophys. Res. 77:2556-2573
Julian, B.R. (1970) Ray tracing in arbitrarily heterogeneous media. Tech. Note 1970-45, Lincoln Laboratory. MIT, Lexington, MA USA
Keller, H.B. (1968) Numerical methods for two-point boundary-value problems. Blaisdell, Waltham, MA USA
Roberts, S.M., Shipman, J.S. (1972) Two-point boundary value problems: Shooting methods. Elsevier, New York
Sleep, N.H. (1973) Teleseismic P-wave transmission through slabs. Bull. Seism. Soc. Am. 63:1349-1373
Solomon, S.C., Julian, B.R. (1974) Seismic constraints on ocean-ridge mantle structure: Anomalous faultplane solutions from first motions. Geophys. J. 38:265-285
Sorrels, G.G., Crowley, J.B., Veith, K.F. (1971) Methods for computing ray paths in complex geological structures. Bull. Seism. Soc. Am. 61:27-53
Toksi:iz, M., Nafi, J., Minear, W., Julian, B.R. (1971) Temperature field and geophysical effects of a downgoing slab. J. Geophys. Res. 76:1113-1138
Wesson, R.L. (1971) Travel-time inversion for laterally inhomogeneous crustal velocity models. Bull. Seism. Soc. Amer. 61:729-746
Wilkinson, J.H. (1965) The algebraic eigenvalue problem. Clarendon Press, Oxford