Earth’s solid interior harbors the long-term memory of unending transformations, such as the formation & evolution of heterogeneous domains in the mantle. These dynamic transformations operate on influence regions that differ in their spatial wavelengths, depth ranges & lateral extents. Seismological signatures of heterogeneity (e.g. V_P & V_S variations) are proxies for intrinsic properties like temperature, composition, grain size, or crystal structure, which help elucidate mantle transformations.

Our approach leverages prior knowledge using physics-informed machine learning (PIML) & Bayesian inference. We reconcile features globally & beneath the US through: (1) analysis of features extracted using a multiscale wavelet method, (2) learning spatial- & scale-dependent blind spots based on existing models, (3) assimilating consistent features for a large suite of multiscale models, & (4) formulating a cascading validation scheme for rejecting scenarios based on agreement with data.

Machine Learning (ML) techniques permit feature extraction to detect consistent patterns & identify correlations across models. However, a challenge is the computational load while dealing with physical structure described at numerous interior locations (~10⁸ for a typical global mesh, see Komatitsch & Tromp, 2002). Global seismic tomography often incorporates dimensionality reduction during model construction by using basis functions (e.g. spherical splines or harmonics) & scaling between physical properties (dlnρ/dlnV_S)​​. However, extraction of localized features in a multiscale analysis requires an orthogonal basis set with built-in sensitivity to structure in both space & spatial-frequency domains (e.g. Daubechies 1992; Strang & Nguyen 1997; Mallat 2008). We use discrete wavelet transforms on a cubed sphere as the reduced basis set for feature extraction, modified from Simons et al. (2011). 

We formulated a method to analyze, learn & assimilate consistent features in the upper mantle to create an evolving  multiscale suite with uncertainties (ATLAS3D).

Analysis step has led to the development of a new wavelet-based method for characterizing both global and regional heterogeneity. Benchmarks were done against spherical-harmonic studies to reveal similar spectral variations in global structure, while also affording new insights into spectra beneath a region such as the US.

Learning step has led to (a) detection of blindspots (R<0.5) at smaller spatial scales and in the Eastern US, where strength of heterogeneity is low & modeling choices (i.e. parameterization, regularization, data) have stronger influences, and (b) detecting the threshold wavelet spatial scale where RMS amplitudes are stronger for regional models locally beneath the continental US. Temperature anomalies inferred in the western US are likely systematically underpredicted by regional models due to low RMS amplitudes at large spatial scales.

Assimilation step has led to the creation of a ATLAS3D suite by randomizing spectral slope and regional spectral prefactor for thresholded small-scale structure. These parameters are informed by the knowledge in existing models as gleaned from the learning step.

Validation data have been assembled and forward models formulated as part of the 3D reference Earth model (REM3D) project. Cascading validation steps are being automated for assessing multiscale scenarios in an efficient fashion. Waveform validation are done on a smaller subset of model scenarios that have already been validated with derived measurements.