Abstract. We present new seismic data from a basement high beneath the southern Iberia Abyssal Plain that appears, from the latest Ocean Drilling Program (ODP) results and indirectly from various seismic observations, to consist of lower continental crustal material. This is a unique opportunity to use seismic profiles and other geophysical evidence to investigate the tectonic process which led to the exhumation of these rocks. We infer that the lower crust was exhumed at the seafloor and then uplifted toward the end of rifting. Our results lead to the following new observations: low-angle detachment faults, previously reported along the east-west Lusigal-12 profile across the southern Iberia Abyssal Plain, penetrate both the 3-10 km thick continental crust and, unusually, the uppermost mantle. Processing of new multichannel seismic reflection profiles across the basement high on which ODP Sites 900, 1067, and 1068 are located reveals that the high is bounded by a previously unsuspected steep, landward dipping normal fault on its east flank.Basement cores from the above ODP sites also reveal that the high is not capped by the previously predicted early syn-rift sediment but by rocks from the lower continental crust. These unexpected observations are incorporated into a new tectonic model of the development of this part of the west Iberia margin which is also consistent with other geophysical observations. A novel feature of this model is the proposal that the seaward edge of the continental crust is thinned to 3-6 km by a currently poorly understood process. The model implies three stages of deformation: (1) lithospheric extension, principally by symmetric pure shear, which leads to a-10 km thick crust in which the lower crust is largely absent over the axial zone and the crust-mantle boundary forms a shear zone, (2) further thinning and then dissection of the most distal continental crust by seaward dipping, low-angle normal faults, (3) inception of a high-angle, landward dipping normal fault that offsets the tectonized crust-mantle boundary and uplifts the lower crust to the crest of the basement high on which ODP Sites 900, 1067, and 1068 were drilled.

We have developed a new uncertainty estimation method that accounts for nonlinearity inherent in most geophysical problems, allows for the explicit search of model posterior space, is scalable, and maintains computational efficiencies on the order of deterministic inverse solutions. We accomplish this by combining an efficient parameter reduction technique, a parameter constraint mapping routine, a sparse geometric sampling scheme, and an efficient forward solver. In order to reduce our model domain and determine an independent basis, we implement both a typical principal component analysis, which factorizes the model covariance matrix, and an alternative compression method, based on singularvalue decomposition, which acts on training models, directly, and is storage efficient. Once we have a reduced base, we map parameter constraints, from our original model domain, to this reduced domain to define a bounded geometric region of feasible model space. We utilize an optimal scheme to sample this reduced model space that uses Smolyak sparse grids and minimizes the number of forward solves by finding the sparsest sampling required to produce convergent uncertainty measures. The result is an ensemble of equivalent models, consistent with our inverse solution structure, which is used to infer inverse uncertainty. We tested our method with a 1D synthetic example, a comparison with a published Metropolis-Hastings sampling example, and an extension to 2D problems using a field data inversion.

We analyze, through linear algebra, the topography of the cost functional in linear and nonlinear inverse problems with the aim of illuminating general characteristics. To a first-order approximation, the local data misfit function in any inverse problem is valley-shaped and elongated in the directions of the null space of the Jacobian and/or in the directions of the smallest singular values. In nonlinear inverse problems, valleys persist; however, local minima might also coexist in the misfit space and might be related to nonlinear effects ignored by the Gauss-Newton approximation to the Hessian, the regularization term designed to provide convexity to the misfit function, or to noise in the data. Furthermore, noise perturbs the size of the equivalence region making location of solutions easier but finding a global minimum harder (in the case of existence). Understanding the behavior of the cost functional is an important step in the developing techniques to appraise inverse solutions and estimate uncertainties caused by noise, incomplete sampling, regularization, and more fundamentally, simplified physical models.