Abstract
The current interpretations of the travel-time measurements in quiet and active regions on the Sun are discussed. These interpretations are based on various approximations to the 3-D wave equation such as the Fermat principle for acoustic rays and the Born approximation. The ray approximation and its modifications have provided the first view of the 3-D structures and flows in the solar interior. However, more accurate and computationally efficient approximations describing the relation between the wave travel times and the internal properties are required to study the structures and flows in detail. Inversion of the large three-dimensional datasets is efficiently carried out by regularized iterative methods. Some results of time-distance inversions for emerging active regions, sunspots, meridional flows and supergranulation are presented. An active region which emerged on the solar disk in January 1998, was studied from SOHO/MDI for eight days, both before and after its emergence at the surface. The results show a complicated structure of the emerging region in the interior, and suggest that the emerging flux ropes travel very quickly through the depth range of our observations. The estimated speed of emergence is about 1.3 km s−1. Tomographic images of a large sunspot reveal sunspot `fingers' - long narrow structures at a depth of about 4 Mm, which connect the sunspot with surrounding pores of the same polarity.
Similar content being viewed by others
References
Aki, K. and Richards, P.: 1980, Quantitative Seismology. Theory and Methods, Freeman, San Francisco.
Birch, A. C. and Kosovichev, A. G.: 2000, Solar Phys. 192, 193 (this issue).
Bogdan, T. J., Braun, D. C., Lites, B. W., and Thomas, J. H.: 1998, Astrophys. J. 492, 379.
Braun, D. C.: 1997, Astrophys. J. 487, 447.
Duvall, T. L., Jr.: 1979, Solar Phys. 63, 3.
Duvall, T. L., Jr.: 1998, Proc. SOHO-6/GONG-98 Workshop, ESA, Noordwijk.
Duvall, T. L., Jr. and Gizon, L.: 2000, Solar Phys. 192, 177 (this issue).
Duvall, T. L., Jr., Jefferies, S. M., Harvey, J. W., and Pomerantz, M. A.: 1993, Nature 362, 430.
Duvall, T. L., Jr., D'Silva, S., Jefferies, S. M., Harvey, J. W., and Schou, J.: 1996, Nature 379, 235.
Duvall, T. L., Jr., Kosovichev, A. G., Scherrer, P. H., Bogart, R. S., Bush, R. I., De Forest, C., Hoeksema, J. T., Schou, J., Saba, J. L. R., Tarbell, T. D., Title, A. M., Wolfson, C. J., Milford, P. N.: 1997, Solar Phys. 170, 63.
Giles, P. M., Duvall, T. L., Jr, and Scherrer, P. H.: 1997, Nature 390, 52.
Jefferies, S. M., Osaki, Y., Shibahashi, H., Duvall, T. L., Jr., Harvey, J. W. and Pomerantz, M. A.: 1994, Astrophys. J. 434, 795.
Jensen, J. M., Jacobsen, B. H. and Christensen-Dalsgaard, J.: 1997, Proceedings, Interdisciplinary Inversion Workshop 5, Aarhus, pp. 57–67.
Jensen, J. M., Jacobsen, B. H. and Christensen-Dalsgaard, J.: 1999, 'Smooth versus Sharp Frechet Kernel in Time-Distance Helioseismology', preprint.
Kosovichev, A. G.: 1996, Astrophys. J. 461, L55.
Kosovichev, A. G.: 1999, J. Comput. Appl. Math 109, 1.
Kosovichev, A. G. and Duvall, T. L., Jr.: 1997: in F. P. Pijpers, J. Christensen-Dalsgaard, and C. S. Rosenthal (eds.), 'Acoustic Tomography of Solar Convective Flows and Structures', SCORe'96: Solar Convection and Oscillations and their Relationship, Kluwer Academic Publishers, Dordrecht, Holland, pp. 241–260.
Marquering, H., Dahlen, F. A., and Nolet, G.: 1999, Geophys. J. Int. 137, 805.
Paige, C. C. and Saunders, M. A.: 1982, ACM Trans. Math. Software 8, 43.
Rhodes, E. J. Jr., Kosovichev, A. G., Schou, J., Scherrer, P. H., Reiter, J.: 1997, Solar Phys. 175, 287.
Rickett, J. E. and Claerbout, J. F.: 2000, Solar Phys. 192, 203 (this issue).
Stark, P. B. and Nikolayev, D. I.: 1993, J. Geophys. Res. 98, 8095.
Title, A. M., Tarbell, T. D., Topka, K. P., Ferguson, S. H., and Shine, R. A.: 1989, Astrophys. J. 336, 475.
Woodard, M. F.: 1997, Astrophys. J. 485, 890.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kosovichev, A., Duvall, T. & Scherrer, P. Time-Distance Inversion Methods and Results – (Invited Review). Solar Physics 192, 159–176 (2000). https://doi.org/10.1023/A:1005251208431
Issue Date:
DOI: https://doi.org/10.1023/A:1005251208431