The primary reason for the thrust towards multiscale Earth models is a purely phenomenological one. Earth’s biosphere, atmosphere, ocean, cryosphere, surface & interior form a coupled system,  interacting through processes that operate over a wide range of spatial & temporal scales. Various physical, chemical & biological processes, such as meteorite impacts, glaciation & erosion, erase the geological memory of Earth’s outermost layers. The solid interior, in contrast, harbors the long-term memory of transformations that shape our planet. These dynamic transformations operate on influence regions that differ in their spatial wavelengths, depth ranges & lateral extents. For example, short-wavelength, dense slabs penetrating into the upper mantle may influence only the regional dynamics of subduction zones at short timescales (<100 Ma).

Moreover, our seismological understanding of the Earth's interior is inherently fuzzy due to the various amounts of knowledge provided at different spatial scales. In general, information about structure beneath the continents are better known than beneath the oceans due to the multifold number of stations on land. However, due to expanding networks of stations being deployed by various countries and institutions, we are at the crossroads in the geosciences where assimilation of structural knowledge is paramount. We need to gather finer-scale information on localized regions while honoring the constraints imposed by longer-period waves that average over longer spatial scales and are often measured with higher certainties. 

ATLAS3D is a suite of Earth models that is constructed by analyzing, learning & assimilating consistent features across various tomographic models. The likelihood of the each multiscale scenario in the suite is calculated using an objective function that optimizes fits to data and physics-informed expectations of the nature of heterogeneity (e.g. sharpness of variations, scaling between physical parameters). The multiscale scenario that maximizes the likelihood is reported as ATLAS3D and the variance is reported as uncertainty of structural parameters. The values reported are estimates of various physical parameters (e.g. shear velocity V_S) at various locations inside the Earth with a grid/pixel basis that is made finer as new datasets become available.

Long-wavelength models are constructed from long-period datasets (>20 seconds) that sense average heterogeneity over longer spatial scales. This large-scale structure is known with better fidelity due to the inherent limitations of data, and is also widely consistent across various Earth models. Regional models often use a teleseismic data correction (e.g. subtraction of average travel time to a local array in body-wave studies), either suppressing or completely obliterating the long-wavelength variations that the local variations are riding on top of. This is one of the major reasons why amplitudes of velocities are not interpretable in many seismic studies, and practitioners limit discussion to patterns of anomalies instead. Even for patterns of heterogeneity, such as along the active margin of the western United States, long-wavelength patterns are also not adequately captured in several tomographic models.