• Processed and Derived Data

    Do different datasets "see" the same Earth?
    Processed and derived seismic data

    Processed waveform (Left) & spectrum (Right) at Charters Towers, Australia from MW 9.1 2004 Sumatra Earthquake. Derived data types are listed; those in yellow are array-based techniques. Do tomographic techniques that use processed versus derived measurements “see” the same heterogeneity?

  • Multiscale Wavelets

    Multiscale Wavelets

    Features of our multiscale wavelet configuration (four-tap Daubechies D4, resolution parameter N=8, scale J=5) for describing lateral variations (a) Cubed sphere centered on North America showing edges of 6 faces in red with 6 X 22N elements, (b) Approximate extent of spatial scales (1.5,3,6,12 deg.) overlain on topography, (c) Normalized power distribution with spherical harmonic degree, (d) Patterns & normalized amplitudes of orthogonal sets of scaling function, representing baseline structure, & wavelets for smaller-scale variations. Note that dashed circles for scales 2 & 1 (1.5 & 3 deg.) represent smaller variations than those for other scales.

Probing the interior structure of terrestrial planets is one of the most computationally intensive, big-data problems in the physical sciences. Multiscale models characterize geodynamic processes (e.g. mantle mixing) & underlying causes of heterogeneity (e.g. sinking slabs, volcanism). We analyze, learn & assimilate consistent features in the upper mantle to create an evolving multiscale suite with uncertainties (ATLAS3D). Read about the project below and checkout Goals, News and FAQs!


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. VP & VS variations) are proxies for intrinsic properties like temperature, composition, grain size, or crystal structure, which help elucidate mantle transformations.

Plethora of tomographic models at global (nominal resolution>1000 km), regional (~500-1000 km) & local scales (<500 km). Is there a way to integrate existing knowledge in global & regional models?

Seismic tomography uses waves generated by earthquakes to image the interior at global (nominal resolution ≥ 1000 km), regional (~500–1000 km) & local scales (≤ 500 km). Multiscale models characterize geodynamic processes (e.g. mantle mixing) & underlying causes of heterogeneity (e.g. sinking slabs, volcanism). While spectra for global VS variations are dominated by their long-wavelength components, regional VP & VS spectra beneath the US have not been quantified. Owing to the dense station coverage afforded by USArray, this region is particularly well suited for assessing the limitations in tomographic techniques & the convergence of structural knowledge.

We analyze, learn & assimilate consistent features in the upper mantle to create a multiscale suite with uncertainties (ATLAS3D), which can evolve with the state of community knowledge. The project leverages advancements in inverse theory, machine learning, data processing & wave propagation.

Reconciliation of techniques, models & data across traditionally siloed disciplines has emerged as a frontier area for deep Earth exploration. The outcomes & infrastructure arising from this work are relevant to answering several priority science questions in the Earth Sciences.

Overall Methodology

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.

Flowchart for creating ATLAS3D

Overarching modeling framework outlining steps (blue boxes) for creating the final ATLAS3D suite from a small set of Earth models using the Machine Learning (ML) concepts specified underneath.

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/dlnVS)​​. 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.