Possibilities of trans-dimensional parameterization for Deep Earth joint inversion

Abstract:

Commonly, the physical properties of the Earth (velocity, density) are parameterized as continuous fields. The most popular representation are grids and basis functions like spherical harmonics or splines. In an inversion context it is quite common that not all the parameters are fully constrained by the available input data. This relates to the common issues of insufficient resolution, incomplete coverage, and trade-offs due to non-uniqueness. By applying some form of regularization to the inverse problem, a well-behaved and unique solution can be obtained, but this solution depends on the details of the chosen regularization.

Trans-dimensional approaches address this problem by using a model representation with a variable number of parameters. The number of parameters is adjusted according to the requirements of the input data using the reversible jump Monte Carlo Markov Chain (rj-MCMC) algorithm. The output is an ensemble of variable resolution models that provides insight into the required model complexity and trade-off between parameters.

Here, we will present synthetic tests from a joint inversion of satellite gravity gradients and normal modes for the Earth's velocity and density structure. The mantle's seismic velocity and density inside a 2-D spherical annulus are described by a variable number of discrete anomalous volumes, each with a variable size, shape, location and strength of velocity and density anomaly. We will test how the recovery of velocity and density depends on the distribution and noise level of the input data.