资源环境科技发展态势分析平台

We present a method to explore the effective nullspace of nonlinear inverse problems without Monte Carlo sampling. This is based on the construction of an artificial Hamiltonian system where a model is treated as a high-dimensional particle. Depending on its initial momentum and mass matrix, the particle evolves along a trajectory that traverses the effective nullspace, thereby producing a series of alternative models that are consistent with observations and their uncertainties. Variants of the nullspace shuttle enable hypothesis testing, for example, by adding features or by producing smoother or rougher models. Furthermore, the Hamiltonian nullspace shuttle can serve as a tunable hybrid between deterministic and probabilistic inversion methods: Choosing random initial momenta, it resembles Hamiltonian Monte Carlo; requiring misfits to decrease along a trajectory, it transforms into gradient descent. We illustrate the concept with a low-dimensional toy example and with high-dimensional nonlinear inversions of seismic traveltimes and magnetic data, respectively.

Plain Language Summary All geophysical data are inherently limited in their ability to constrain the properties and dynamics of the Earth, such as material parameters deep inside our planet, future atmospheric circulation, or fluid flow in a geothermal reservoir. As a consequence, there are generally many representations (also called models) of the Earth that explain our data to within their uncertainties. The ensemble of these admissible representations is the "nullspace." Here we present an efficient tool to explore the nullspace. This is based on treating an Earth model as an artificial particle under the influence of gravity. Much like a real planet, the particle travels in an orbit. Each position in the orbit corresponds to an admissible model of the Earth. In addition to developing the theory, we demonstrate the efficiency of our method using examples from traveltime tomography and magnetic surveying.