Balancing unevenly distributed data in seismic tomography: a global adjoint tomography example

The uneven distribution of earthquakes and stations in seismic tomography leads to slower convergence of nonlinear inversions and spatial bias in inversion results. Including dense regional arrays, such as USArray or Hi-Net, in global tomography causes severe convergence and spatial bias problems, against which conventional pre-conditioning schemes are ineffective. To save computational cost and reduce model bias, we propose a new strategy based on a geographical weighting of sources and receivers. Unlike approaches based on ray density or the Voronoi tessellation, this method scales to large full-waveform inversion problems and avoids instabilities at the edges of dense receiver or source clusters. We validate our strategy using a 2-D global waveform inversion test and show that the new weighting scheme leads to a nearly twofold reduction in model error and much faster convergence relative to a conventionally pre-conditioned inversion. We implement this geographical weighting strategy for global adjoint tomography.