Modify abbrvnat bibliography style so that last name comes first in typeset entries

Only just noticed your posting; I hope the following answer will still be useful to you.

If I understand your objective correctly, you want the surnames to be listed before the initials of the first (and, if present, any middle) names in the references, with a comma separating the surname from the first and middle names.

Starting out from the bibliography style file abbrvnat.bst, your objective may be achieved as follows:

• Locate the file abbrvnat.bst in your TeX distribution. Make a copy of this file, and name the copy, say, myabbrvnat.bst. (Don't modify a file that's part of the TeX distribution directly.

• Open the file myabbrvnat.bst in your favorite text editor. (The one you use to edit your .tex files will do.) Seach for the following line:

  { s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ 't :=
  

  (it'll be in the function called format.names) and change it to

  { s nameptr "{vv~}{ll}{, jj}{, f.}" format.name$ 't :=
  

  You can probably guess that "vv" stands for "von part" of a name, "ll" stands for "last name", etc. The ordering suggested above conforms to U.S. usage, which places the "von part" before the last name, as in "von der Vogelweide, W." If, instead, you want the "von part" to come after the first names' initials, i.e., if you want the name to be typeset as "Vogelweide, W. von der", you should change the line above to

  { s nameptr "{ll}{, jj}{, f. }{, vv}" format.name$ 't :=
  

• Save the file myabbrvnat.bst either in the directory where your main .tex file is located or in a directory that's searched by your TeX distribution. If you choose the latter option, be sure to update the TeX filename database in a way that's appropriate for your TeX distribution.

• Start using the new style file by issuing the command \bibliographystyle{myabbrvnat}. Be sure to run LaTeX, BibTeX, and LaTeX twice more with this new setup so that all changes are propagated fully.

For instance, suppose the bib entry you provided in a comment to the other answer, viz.,

@ARTICLE{KoBaTr00, 
    author = {D. Komatitsch and C. Barnes and J. Tromp}, 
    title  = {Wave propagation near a fluid-solid interface: 
             a spectral element approach}, 
    journal = geophysics, 
    year    = {2000}, 
    volume  = {65}, 
    pages   = {623-631}, 
    number  = {2}, 
    doi     = {10.1190/1.1444758}, 
}

is stored in a file called temp.bib. Then, the following MWE

\documentclass{article}
\usepackage{natbib,url}
\bibliographystyle{myabbrvnat}
\begin{document}
\nocite{*}
\bibliography{temp}
\end{document}

will produce the following output: