Box tomography: localized imaging of remote targets buried in an unknown medium, a step forward for understanding key structures in the deep Earth
We discuss an application of tomographic methods to the imaging of localized geological structures buried inside the Earth, where neither seismic sources nor receivers are necessarily present. We call this ‘box tomography’. The essential difference between box-tomography and standard tomographic methods is that the numerical modelling (i.e. the ray tracing in traveltime tomography and the wave propagation in waveform tomography or full waveform inversion) is completely confined within the small box-region imaged. Thus, box tomography is a lot more efficient than global tomography (i.e. where we invert for the velocity in the larger volume that encompasses all the sources and receivers), for imaging localized objects. The principal difficulty in the box tomography problem comes from the medium outside the box-region imaged, that masks the target structure. In the data recorded at the surface, the information carried by the waves about the target structure is mixed with that about the surrounding medium. The main focus of this paper is to evaluate how well box tomography can extract useful information to produce accurate images of remote buried objects, especially in the difficult situation where the velocity distribution above the target structure is not known a priori. We implemented traveltime box tomography, where first arrival times are inverted using ray theory, and, waveform box tomography or full waveform box inversion, where seismograms are inverted using either scattering integrals or adjoint methods. Whatever the method employed, we found that, in the simple situation where the velocity structure is known around the target region, box-tomography is faster and more accurate than global tomography. Most importantly, through examples and simple analysis, we show that box-tomography can produce accurate images of localized structures even though the velocity distribution is not a priori known around the box-region imaged. In the last section of this paper, we evaluate the usage of box-tomography for imaging geological structures in the deep Earth. We performed 2-D synthetic experiments in a fluid planet and we argue that box tomography can be employed for refining our current global tomographic models within arbitrary regions inside the Earth. This has important implications for understanding the composition and dynamics of the Earth’s interior.