ALBERT

Description: The cratonic cores of the continents are remarkably stable and long-lived features. Their ability to resist destructive tectonic processes is associated with their thick (∼250 km), cold, chemically-depleted, buoyant lithospheric keels that isolate the cratons from the convecting mantle. The formation mechanism and tectonic stability of cratonic keels remains under debate. To address this issue, we use P- and S-wave relative arrival-time tomography to constrain upper-mantle structure beneath southeast Canada and the northeast USA, a region spanning three quarters of Earth's geological history. Our models show three distinct, broad zones: Seismic wavespeeds increase systematically from the Phanerozoic coastal domains, through the Proterozoic Grenville Province, to the Archean Superior craton in central Québec. We also recover the NW-SE-trending track of the Great Meteor hotspot that cross-cuts the major tectonic domains. The decrease in seismic wavespeed from Archean to Proterozoic domains across the Grenville Front is consistent with predictions from models of two-stage keel formation, supporting the idea that keel growth may not have been restricted to Archean times. However, while crustal structure studies suggest that Archean Superior material underlies Grenvillian-age rocks up to ∼300 km SE of the Grenville Front, our tomographic models show a near-vertical boundary in mantle wavespeed directly beneath the Grenville Front. We interpret this as evidence for subduction-driven metasomatic enrichment of the Laurentian cratonic margin, prior to keel stabilization. Variable chemical depletion levels across Archean-Proterozoic boundaries worldwide may thus be better explained by metasomatic enrichment than inherently less-depleted Proterozoic composition at formation.

Description: The geological record of SE Canada spans more than 2.5Ga, making it a natural laboratory for the study of crustal formation and evolution over time. We estimate the crustal thickness, Poisson's ratio, a proxy for bulk crustal composition, and shear velocity (Vs) structure from receiver functions at a network of seismograph stations recently deployed across the Archean Superior craton, the Proterozoic Grenville and the Phanerozoic Appalachian provinces. The bulk seismic crustal properties and shear velocity structure reveal a correlation with tectonic provinces of different ages: the post-Archean crust becomes thicker, faster, more heterogenous and more compositionally evolved. This secular variation pattern is consistent with a growing consensus that crustal growth efficiency increased at the end of the Archean. A lack of correlation among elevation, Moho topography, and gravity anomalies within the Proterozoic belt is better explained by buoyant mantle support rather than by compositional variations driven by lower crustal metamorphic reactions. A ubiquitous ∼20km thick high-Vs lower-crustal layer is imaged beneath the Proterozoic belt. The strong discontinuity at 20km may represent the signature of extensional collapse of an orogenic plateau, accommodated by lateral crustal flow. Wide anorthosite massifs inferred to fractionate from a mafic mantle source are abundant in Proterozoic geology and are underlain by high Vs lower crust and a gradational Moho. Mafic underplating may have provided a source for these intrusions and could have been an important post-Archean process stimulating mafic crustal growth in a vertical sense.

Description: Plate-scale deformation is expected to impart seismic anisotropic fabrics on the lithosphere. Determination of the fast shear wave orientation ( ) and the delay time between the fast and slow split shear waves ( t ) via SKS splitting can help place spatial and temporal constraints on lithospheric deformation. The Canadian Appalachians experienced multiple episodes of deformation during the Phanerozoic: accretionary collisions during the Palaeozoic prior to the collision between Laurentia and Gondwana, and rifting related to the Mesozoic opening of the North Atlantic. However, the extent to which extensional events have overprinted older orogenic trends is uncertain. We address this issue through measurements of seismic anisotropy beneath the Canadian Appalachians, computing shear wave splitting parameters ( , t ) for new and existing seismic stations in Nova Scotia and New Brunswick. Average t values of 1.2 s, relatively short length scale (≥100 km) splitting parameter variations, and a lack of correlation with absolute plate motion direction and mantle flow models, demonstrate that fossil lithospheric anisotropic fabrics dominate our results. Most fast directions parallel Appalachian orogenic trends observed at the surface, while t values point towards coherent deformation of the crust and mantle lithosphere. Mesozoic rifting had minimal impact on our study area, except locally within the Bay of Fundy and in southern Nova Scotia, where fast directions are subparallel to the opening direction of Mesozoic rifting; associated t values of 〉1 s require an anisotropic layer that spans both the crust and mantle, meaning the formation of the Bay of Fundy was not merely a thin-skinned tectonic event.

Description: 〈span〉〈div〉SUMMARY〈/div〉We consider the case where the ‘solution’ to an inverse problem is an ensemble (e.g. drawn from the conditional probability density function $p( {{{\bf m}}|{{{\bf d}}^{obs}}} )$ of 〈span〉M〈/span〉 model parameters ${{\bf m}}$ given observed data ${{{\bf d}}^{obs}}$). Here we presume that the ${{\bf m}}$s have a natural ordering, say in position 〈span〉x〈/span〉, so that ‘resolution’ means the ability of the inverse problem to distinguish physically adjacent model parameters. The trade-off curve for resolution and variance is constructed using the following steps: (1) the single solution ${{{\bf m}}^{est}}$ and its covariance ${{{\bf C}}_m}$ are estimated as the ensemble mean and covariance; (2) the eigenvalue decomposition ${{{\bf C}}_m} = {\rm{\ }}{{{\bf V} {\boldsymbol \Lambda} }}{{{\bf V}}^{\rm{T}}}$ is computed and the submatrix ${{{\boldsymbol \Lambda }}^{( N )}}$ of the 〈span〉N〈/span〉 smallest eigenvalues, and submatrix ${{{\bf V}}^{( N )}}$of the 〈span〉N〈/span〉 corresponding eigenvectors, are formed; (3) the equation ${{{\boldsymbol \mu }}^{( N )}} = {{{\boldsymbol \Phi }}^{( N )}}\ {{\bf m}}$ with ${{{\boldsymbol \mu }}^{( N )}} = [ {{{{\bf V}}^{( N )}}} ]{\boldsymbol{\ }}{{{\bf m}}^{est}}$〈strong〉and〈/strong〉${{{\boldsymbol \Phi }}^{( N )}} = {[ {{{{\bf V}}^{( N )}}} ]^{\rm{T}}}$ is formed, as is its covariance ${{\bf C}}_\mu ^{( N )} = {{{\boldsymbol \Lambda }}^{( N )}}{\boldsymbol{\ }}$; (4) the equation is solved to yield a localized average ${\langle {{\bf m}} \rangle ^{( N )}} = \ {{{\boldsymbol \Phi }}^{ - g}}{{{\boldsymbol \mu }}^{( N )}}$, where ${{{\boldsymbol \Phi }}^{ - g}}$ is either the minimum length or Backus–Gilbert generalized inverse of ${{\boldsymbol \Phi }}$; (5) the resolution and covariance are computed as ${{{\bf R}}^{( N )}} = {{{\boldsymbol \Phi }}^{ - g}}{\boldsymbol{\ }}{{{\boldsymbol \Phi }}^{( N )}}$ and ${{\bf C}}_m^{( N )} = {{{\boldsymbol \Phi }}^{ - g}}{\boldsymbol{\ }}{{\bf C}}_\mu ^{( N )}{( {{{{\boldsymbol \Phi }}^{ - g}}} )^{\rm{T}}}$; (6) the spread ${K^{( N )}}$ of resolution and size ${J^{( N )}}\ $of covariance are computed using either the Dirichlet or Backus–Gilbert measures and (7) the process is repeated for $1 \le N \le M$ to build up the trade-off curve $K( J )$. We show that, in the Dirichlet case, ${K^{( N )}} = \ M - N$ and ${J^{( N )}} = \ {\rm{tr}}( {{{{\boldsymbol \Lambda }}^{( N )}}} )$. We also consider the case where the model parameters correspond to spline coefficients and a sequence ${y_i}( {{{\bf m}},{x_i}} )$ derived from these coefficients possesses natural ordering. Layered models are an example of such a parametrization. We construct the trade-off curve for ${{\bf y}}$ by converting each member of the ensemble from ${{\bf m}}$ to ${{\bf y}}$ and applying the above procedure to them. We demonstrate the method by applying it to several simple examples.〈/span〉

Description: 〈span〉〈div〉Summary〈/div〉We consider the case where the ‘solution’ to an inverse problem is an ensemble (e.g. drawn from the conditional probability density function $p( {{{\bf m}}{\rm{|}}{{{\bf d}}^{obs}}} )$ of 〈span〉M〈/span〉 model parameters ${{\bf m}}$ given observed data ${{{\bf d}}^{obs}}$). Here we presume that the ${{\bf m}}$s have a natural ordering, say in position 〈span〉x〈/span〉, so that ‘resolution’ means the ability of the inverse problem to distinguish physically adjacent model parameters. The trade-off curve for resolution and variance is constructed using the following steps: (1) the single solution ${{{\bf m}}^{est}}$ and its covariance ${{{\bf C}}_m}$ are estimated as the ensemble mean and covariance; (2) the eigenvalue decomposition ${{{\bf C}}_m} = {\rm{\ }}{{\bf V\Lambda }}{{{\bf V}}^{\rm{T}}}$ is computed and the submatrix ${{{\bf \Lambda }}^{( N )}}$ of the 〈span〉N〈/span〉 smallest eigenvalues, and submatrix ${{{\bf V}}^{( N )}}$of the 〈span〉N〈/span〉 corresponding eigenvectors, are formed; (3) the equation ${{{\bf \mu }}^{( N )}} = {{{\bf \Phi }}^{( N )}}\ {{\bf m}}$ with ${{{\bf \mu }}^{( N )}} = [ {{{{\bf V}}^{( N )}}} ]{\boldsymbol{\ }}{{{\bf m}}^{est}}$〈strong〉and〈/strong〉${{{\bf \Phi }}^{( N )}} = {[ {{{{\bf V}}^{( N )}}} ]^{\rm{T}}}{\boldsymbol{\ }}$ is formed, as is its covariance ${{\bf C}}_\mu ^{( N )} = {{{\bf \Lambda }}^{( N )}}{\boldsymbol{\ }}$; (4) the equation is solved to yield a localized average ${{{\bf m}}^{( N )}} = \ {{{\bf \Phi }}^{ - g}}{{{\bf \mu }}^{( N )}}$, where ${{{\bf \Phi }}^{ - g}}$ is either the minimum length or Backus-Gilbert generalized inverse of ${{\bf \Phi }}$; (5) the resolution and covariance are computed as ${{{\bf R}}^{( N )}} = {{{\bf \Phi }}^{ - g}}{\boldsymbol{\ }}{{{\bf \Phi }}^{( N )}}$ and ${{\bf C}}_m^{( N )} = {{{\bf \Phi }}^{ - g}}{\boldsymbol{\ }}{{\bf C}}_\mu ^{( N )}{( {{{{\bf \Phi }}^{ - g}}} )^{\rm{T}}}$; (6) the spread ${K^{( N )}}$ of resolution and size ${J^{( N )}}\ $of covariance are computed using either the Dirichlet or Backus-Gilbert measures; and (7) the process is repeated for $1 \le N \le M$ to build up the trade-off curve $K( J )$. We show that, in the Dirichlet case, ${K^{( N )}} = \ M - N$ and ${J^{( N )}} = \ {\rm{tr}}( {{{{\bf \Lambda }}^{( N )}}} )$. We also consider the case where the model parameters correspond to spline coefficients and a sequence ${y_i}( {{{\bf m}},{x_i}} )$ derived from these coefficients possesses natural ordering. Layered models are an example of such a parameterization. We construct the trade-off curve for ${{\bf y}}$ by converting each member of the ensemble from ${{\bf m}}$ to ${{\bf y}}$ and applying the above procedure to them. We demonstrate the method by applying it to several simple examples.〈/span〉