Multiple and single snapshot compressive beamforming

For a sound field observed on a sensor array, compressive sensing (CS) reconstructs the direction-of-arrival (DOA) of multiple sources using a sparsity constraint. The DOA estimation is posed as an underdetermined problem by expressing the acoustic pressure at each sensor as a phase-lagged superposition of source amplitudes at all hypothetical DOAs. Regularizing with an $\ell_1$-norm constraint renders the problem solvable with convex optimization, and promoting sparsity gives high-resolution DOA maps. Here, the sparse source distribution is derived using maximum a posteriori (MAP) estimates for both single and multiple snapshots. CS does not require inversion of the data covariance matrix and thus works well even for a single snapshot where it gives higher resolution than conventional beamforming. For multiple snapshots, CS outperforms conventional high-resolution methods, even with coherent arrivals and at low signal-to-noise ratio. The superior resolution of CS is demonstrated with vertical array data from the SWellEx96 experiment for coherent multi-paths.Comment: In press Journal of Acoustical Society of Americ

Variational inverse methods for transport problems

Variational inverse data assimilation schemes are developed for three types of parameter identification problems in transport models: (1) the tracer inverse for the Lagrangian mean transport velocity in a long-term advection-diffusion transport model; (2) determination of inflow salinity open boundary condition in an intra-tidal salinity transport model; and (3) determination of settling velocity and resuspension rate for a cohesive sediment transport model. The gradient of the cost function with respect to the control variables is obtained by the adjoint model. A series of twin experiments are conducted to test the inverse models for the three types of problems. Results show that variational data assimilation can successfully retrieve poorly known parameters in transport models. The first problem is associated with the long-term advective transport, represented by the Lagrangian mean transport velocity which can be decomposed into two parts: the Eulerian transport velocity and the curl of a 3-D vector potential A. The optimal long-term advective transport field is obtained through adjusting the vector potential using a variational data assimilation method. Experiments are performed in an idealized estuary. Results show that the variational data assimilation method can successfully retrieve the effective Lagrangian mean transport velocity in a long-term transport model. Results also show that the smooth best fit model state can still be retrieved using a penalty method when observations are too sparse or contain noisy signals. A variational inverse model for optimally determining open boundary condition is developed and tested in a 3-D intra-tidal salinity transport model. The maximum inflow salinity open boundary value and its recovery time from outflow condition are treated as control variables. Effects of scaling, preconditioning, and penalty are investigated. It is shown that proper scaling and preconditioning can greatly speed up the convergence rate of the minimization process. The spatial oscillations in the recovery time of the inflow boundary condition can be effectively eliminated by an penalty technique. A variational inverse model is developed to estimate the settling velocity and resuspension constant. The settling velocity &w\sb{lcub}s{rcub}& and resuspension constant &M\sb{lcub}o{rcub}& are assumed to be constant in the whole model domain. The inverse model is tested in an idealized 3-D estuary and the James River, a tributary of the Chesapeake Bay. Experimental results demonstrate that the variational inverse model can be used to identify the poorly known parameters in cohesive sediment transport modeling

Monitoring the sea environment using acoustics the role of the acoustical observatories

The presentation deals with theoretical factors and technical specifications pertinent to the design of an acoustical observatory for the monitoring of the marine environment. Two types of observatories are mentioned, namely active and passive. Among the various cases of active observatories, the ones related to ocean acoustic tomography are presented in some detail and the inverse problem of retrieving information from measured acoustic data is explained. Some basic issues related to the type of measurements that should be made for optimal use of the acoustic field are also given with related references. Finally, the basic features of passive observatories are underlined without going into details

Stochastic Parameter Estimation of Poroelastic Processes Using Geomechanical Measurements

Understanding the structure and material properties of hydrologic systems is important for a number of applications, including carbon dioxide injection for geological carbon storage or enhanced oil recovery, monitoring of hydraulic fracturing projects, mine dewatering, environmental remediation and managing geothermal reservoirs. These applications require a detailed knowledge of the geologic systems being impacted, in order to optimize their operation and safety. In order to evaluate, monitor and manage such hydrologic systems, a stochastic estimation framework was developed which is capable of characterizing the structure and physical parameters of the subsurface. This software framework uses a set of stochastic optimization algorithms to calibrate a heterogeneous subsurface flow model to available field data, and to construct an ensemble of models which represent the range of system states that would explain this data. Many of these systems, such as oil reservoirs, are deep and hydraulically isolted from the shallow subsurface making near-surface fluid pressure measurements uninformative. Near-surface strainmeter, tiltmeter and extensometer signals were therefore evaluated in terms of their potential information content for calibrating poroelastic flow models. Such geomechanical signals are caused by mechanical deformation, and therefore travel through hydraulically impermeable rock much more quickly. A numerical geomechanics model was therefore developed using Geocentric, which couples subsurface flow and elastic deformation equations to simulate geomechanical signals (e.g. pressure, strain, tilt and displacement) given a set of model parameters. A high-performance cluster computer performs this computationally expensive simulation for each set of parameters, and compares the simulation results to measured data in order to evaluate the likelihood of each model. The set of data-model comparisons are then used to estimate each unknown parameter, as well as the uncertainty of each parameter estimate. This uncertainty can be inuenced by limitations in the measured dataset such as random noise, instrument drift, and the number and location of sensors, as well as by conceptual model errors and false underlying assumptions. In this study we find that strain measurements taken from the shallow subsurface can be used to estimate the structure and material parameters of geologic layers much deeper in the subsurface. This can signicantly mitigate drilling and installation costs of monitoring wells, as well as reduce the risk of puncturing or fracturing a target reservoir. These parameter estimates were also used to develop an ensemble of calibrated hydromechanical models which can predict the range of system behavior and inform decision-making on the management of an aquifer or reservoir

Adjoint models of mantle convection with seismic, plate motion, and stratigraphic constraints: North America since the Late Cretaceous

We apply adjoint models of mantle convection to North America since the Late Cretaceous. The present-day mantle structure is constrained by seismic tomography and the time-dependent evolution by plate motions and stratigraphic data (paleoshorelines, borehole tectonic subsidence, and sediment isopachs). We infer values of average upper and lower mantle viscosities, provide a synthesis of North American vertical motions (relative sea level) from the Late Cretaceous to the present, and reconstruct the geometry of the Farallon slab back to the Late Cretaceous. In order to fit Late Cretaceous marine inundation and borehole subsidence, the adjoint model requires a viscosity ratio across 660 km discontinuity of 15:1 (reference viscosity of 10^(21) Pa s), which is consistent with values previously inferred by postglacial rebound studies. The dynamic topography associated with subduction of the Farallon slab is localized in western North America over Late Cretaceous, representing the primary factor controlling the widespread flooding. The east coast of the United States is not stable; rather, it has been experiencing continuous dynamic subsidence over the Cenozoic, coincident with an overall eustatic fall, explaining a discrepancy between sea level derived from the New Jersey coastal plain and global curves. The east coast subsidence further constrains the mantle viscosity structure and requires an uppermost mantle viscosity of 10^(20) Pa s. Imposed constraints require that the Farallon slab was flat lying during Late Cretaceous, with an extensive zone of shallow dipping Farallon subduction extending beyond the flat-lying slab farther east and north by up to 1000 km than previously suggested