You must contact Seagate support. they will send you a link to a downloadable ISO disc image file. You use Disk utility to burn an ISO CD-ROM with the image. On a MacPro you restart from the disc you created and it will load DOS. It is a DOS based program that installs the new firmware. Only a MacPro can run the DOS OS (or a PC of course).
From the Accelerte your Mac site:
As a caution, the download page says:
Upgrade file for Seagate ST31500341AS SD1A
Use for 9JU138 -300 and -336 part numbers only (firmware SD15- SD19). DO NOT use on any other part number or firmware.
The firmware upgrade involves burning an ISO CD and then booting it on your (Intel-based) Mac (hold Option key while rebooting). The CD has a copy of FreeDOS and the firmware updater. Tech support mentioned that I should only have one drive installed at a time while doing the update. When the update finished, you press any key to “continue” which powers down your machine. The drive needs to be power cycled for the firmware to be installed. After each power down, I inserted a different drive and rebooted into the firmware updater. I just pulled all drives out a few inches and pushed in the drive I wanted to update. It took about 2 minutes per drive to perform the firmware update.
There is no generic direct download link. The download link is built based on your certificate number. I suppose I could give it out, but it looks like it violates the terms of the download license agreement.