The wave equation is linear, and it scales in time and space. As a consequence, wave phenomena that occur during fractions of a millisecond in human tissue often have a close correspondence in waves travelling for hours through the interior of the Earth. The scale invariance of the wave equation is the foundation for collaboration and technology transfer between medical ultrasound and seismic imaging - the promotion of which is the main goal of this contribution.
In the first part of our presentation, we review the current state of the art in seismic imaging, with a focus on regional to global scales. Special emphasis will be on (1) high-performance modelling of seismic wave propagation through a heterogeneous, attenuating and anisotropic Earth, (2) the nature of seismic data and the resulting characteristics of the inverse problem, (3) recent images of 3D deep-Earth structure, and (4) future challenges in the field.
In the second part, we highlight efforts to translate techniques from seismic imaging to medical ultrasound. This includes optimal design to position transducers, finite-frequency traveltime tomography to image out of plane, reverse-time migration, and 3D multi-parameter full-waveform inversion.
Finally, we discuss several non-mathematical challenges that still impede technology transfer, and that remain to be addressed. These include the acceptable time to solution, and the ability of well-trained radiologists and seismic interpreters to handle entirely new types of images (and artifacts).