linux - Search through tar files for a pattern and print the full path of what's found

I have directory tree with many tar files. Each tar file contains many other files. I want to search through all the tar files for a given pattern, and print the full path of any files within a tar that are found.

I got this far:
find . -type f -name '*.tar' -exec tar tf {} \; | egrep ''

Now my problem is that the above command only prints the name of the file within the tar that it finds. Ie, the output of the above is:
pattern.jpg
foundMe.txt

I would like the output to contain also the full path and the tar name where the file was found. How would I do this?

Thank you!