For the 3 different technologies you mentioned, X-ray, sonogram, and MRI, they each have their pros and cons.
X-ray (regular or CT scan) gives you small doses of radiation, is good at detecting body tissues that contain calcium such as bones, but doesn't show soft tissues (discs, ligaments, muscles) very well. Adding dye can help show additional problems such as torn discs (discogram) or compressed nerve roots (myelogram). This is also a very quick test so this is why CT scans are used so extensively for emergency rooms where time is critical.
MRI is good at showing soft tissues such as disc herniations that an X-ray would miss, but doesn't show certain types of tissues well such as nerves. This test is time consuming and expensive.
Sonograms are very safe and work wonderfully for showing certain tissues and movement (heart valve problems, uterine fibroiRAB, babies, prostrate issues), but can't pass through air. Therefore, an abdominal sonogram would pick up certain structures well but the air in your bowels scatters the picture for certain areas. Again, this test is time consuming but not nearly as expensive as an MRI.
What one technology may miss, another one may or may not pick up.
Thoracic disc herniations are much more rare than lurabar or cervical, but they can and do happen. What are your symptoms or suspected problem(s) for which you are seeking answers?