Bayesian inference for ultralow velocity zones in the Earth's lowermost mantle: Complex ULVZ beneath the east of the Philippines

Abstract

Ultralow velocity zones (ULVZs) are small-scale structures with a sharp decrease in S and P wave velocity, and an increase in the density on the top of the Earth's core-mantle boundary. The ratio of S and P wave velocity reduction and density anomaly are important to understanding whether ULVZs consist of partial melt or chemically distinct material. However, existing methods such as forward waveform modeling that utilize 1-D and 2-D Earth-structure models face challenges when trying to uniquely quantify ULVZ properties because of inherent nonuniqueness and nonlinearity. This paper develops a Bayesian inversion for ULVZ parameters and uncertainties with rigorous noise treatment to address these challenges. The posterior probability density of the ULVZ parameters (the solution to the inverse problem) is sampled by the Metropolis-Hastings algorithm. To improve sampling efficiency, parallel tempering is applied by simulating a sequence of tempered Markov chains in parallel and allowing information exchange between chains. First, the Bayesian inversion is applied to simulated noisy data for a realistic ULVZ model. Then, measured data sampling the lowermost mantle under the Philippine Sea are considered. Cluster analysis and visual waveform inspection suggest that two distinct classes of ScP (S waves converted to, and reflected as, P waves) waves exist in this region. The distinct waves likely correspond to lateral variability in the lowermost mantle properties in a NE-SW direction. For the NE area, Bayesian model selection identifies a two-layer model with a gradual density increase as a function of depth as optimal. This complex ULVZ structure can be due to the percolation of iron-enriched, molten material in the lowermost mantle. The results for the SW area are more difficult to interpret, which may be due to the limited number of data available (too few waveforms to appropriately reduce noise) and/or complex 2-D and 3-D structures that cannot be explained properly by the 1-D models required by our inversion approach. In particular, the complex waveforms require highly layered 1-D models to fit the data. These models appear physically unreasonable and suggest that the SW region cannot be explained by 1-D structure.

New Candidate Ultralow-Velocity Zone Locations from Highly Anomalous SPdKS Waveforms

“…Therefore, the posterior probability density can be expressed in terms of the beta function. In contrast to previous studies of Bayesian waveform inversion of ULVZ properties [46,47], we have an analytical form for the posterior (Equation (5)). An alternative method using a numerical sampling approach could be employed.…”

Intermittent and lateral varying ULVZ structure at the northeastern margin of the Pacific LLSVP

“…Some regions may require a compositional origin to ULVZs, a suggestion coming from nearly equal yet strong V P and V S reductions along with a density increase [Brown et al, 2015]. Evidence for a two-layer ULVZ with a gradual increase in density toward the CMB has also been put forth [Pachhai et al, 2014]. To explain the density increase, iron enrichment alone may not be able to explain imaged properties [Muir and Brodholt, 2015].…”

A method of spherical harmonic analysis in the geosciences via hierarchical Bayesian inference

“…Treating σ in this way allows the data noise to be properly accounted for, without requiring the user to make arbitrary assumptions as to the scale of the noise. This technique has been employed with success to perform regional tomography (Bodin et al 2012a), calculate receiver functions from P-wave arrivals (Bodin et al 2012b), deconvolution of receiver functions (Kolb & Lekić 2014), sampling of autoregression parameters (Dettmer et al 2012) and identification of ultralow velocity zones (Pachhai et al 2014). The ability to extract the posterior probability distribution of the unknown data error gives the Bayesian MCMC approach presented in this paper a significant advantage over existing classical methods of spherical harmonic analysis; it also makes the problem nonlinear in the σ parameter, motivating our use of MCMC sampling.…”

“…A transdimensional type of sampling has recently been applied in many inverse problems to determine optimal model selection, despite the high computational burden (Malinverno 2002;Sambridge et al 2006;Dettmer et al 2010;Tkalčić et al 2013). Alternatively, an information criterion (IC) can be used at lower computational cost (Schwarz 1978;Pachhai et al 2014). Here, we utilize the corrected Akaike information criterion (AICc) to choose an appropriate maximum degree of expansion.…”