Signatures of Emerging Subsurface Structures in Acoustic Power Maps

We show that under certain conditions, subsurface structures in the solar interior can alter the average acoustic power observed at the photosphere above them. By using numerical simulations of wave propagation, we show that this effect is large enough for it to be potentially used for detecting emerging active regions before they appear on the surface. In our simulations, simplified subsurface structures are modeled as regions with enhanced or reduced acoustic wave speed. We investigate the dependence of the acoustic power above a subsurface region on the sign, depth, and strength of the wave speed perturbation. Observations from the Solar and Heliospheric Observatory/Michelson Doppler Imager (SOHO/MDI) prior and during the emergence of NOAA active region 10488 are used to test the use of acoustic power as a potential precursor of magnetic flux emergence.Comment: 7 pages, 5 figures, accepted for publication in Solar Physics on 21 March 201

Estimation of aquifer lower layer hydraulic conductivity values through base flow hydrograph rising limb analysis

The estimation of catchment-averaged aquifer hydraulic conductivity values is usually performed through a base flow recession analysis. Relationships between the first time derivatives of the base flow and the base flow values themselves, derived for small and large values of time, are used for this purpose. However, in the derivation of the short-time equations, an initially fully saturated aquifer without recharge with sudden drawdown is assumed, which occurs very rarely in reality. It is demonstrated that this approach leads to a nonnegligible error in the parameter estimates. A new relationship is derived, valid for the rising limb of a base flow hydrograph, succeeding a long rainless period. Application of this equation leads to accurate estimates of the aquifer lower layer saturated hydraulic conductivity. Further, it has been shown analytically that, if base flow is modeled using the linearized Boussinesq equation, the base flow depends on the effective aquifer depth and the ratio of the saturated hydraulic conductivity to the drainable porosity, not on these three parameters separately. The results of the new short-time expression are consistent with this finding, as opposed to the use of a traditional base flow recession analysis. When base flow is modeled using the nonlinear Boussinesq equation, the new expression can be used, without a second equation for large values of time, to estimate the aquifer lower layer hydraulic conductivity. Overall, the results in this paper suggest that the new methodology outperforms a traditional recession analysis for the estimation of catchment-averaged aquifer hydraulic conductivities

Helioseismology of Sunspots: Confronting Observations with Three-Dimensional MHD Simulations of Wave Propagation

The propagation of solar waves through the sunspot of AR 9787 is observed using temporal cross-correlations of SOHO/MDI Dopplergrams. We then use three-dimensional MHD numerical simulations to compute the propagation of wave packets through self-similar magneto-hydrostatic sunspot models. The simulations are set up in such a way as to allow a comparison with observed cross-covariances (except in the immediate vicinity of the sunspot). We find that the simulation and the f-mode observations are in good agreement when the model sunspot has a peak field strength of 3 kG at the photosphere, less so for lower field strengths. Constraining the sunspot model with helioseismology is only possible because the direct effect of the magnetic field on the waves has been fully taken into account. Our work shows that the full-waveform modeling of sunspots is feasible.Comment: 21 pages, Accepted in Solar Physic

Reduced order modeling of subsurface multiphase flow models using deep residual recurrent neural networks

We present a reduced order modeling (ROM) technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrent neural network for modeling the evolution of dynamical systems. The DR-RNN architecture is inspired by iterative update techniques of line search methods where a fixed number of layers are stacked together to minimize the residual (or reduced residual) of the physical model under consideration. In this manuscript, we combine DR-RNN with proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM) to reduce the computational complexity associated with high-fidelity numerical simulations. In the presented formulation, POD is used to construct an optimal set of reduced basis functions and DEIM is employed to evaluate the nonlinear terms independent of the full-order model size. We demonstrate the proposed reduced model on two uncertainty quantification test cases using Monte-Carlo simulation of subsurface flow with random permeability field. The obtained results demonstrate that DR-RNN combined with POD-DEIM provides an accurate and stable reduced model with a fixed computational budget that is much less than the computational cost of standard POD-Galerkin reduced model combined with DEIM for nonlinear dynamical systems

Influence of Non-Uniform Distribution of Acoustic Wavefield Strength on Time-Distance Helioseismology Measurements

By analyzing numerically simulated solar oscillation data, we study the influence of non-uniform distribution of acoustic wave amplitude, acoustic source strength, and perturbations of the sound speed on the shifts of acoustic travel times measured by the time-distance helioseismology method. It is found that for short distances, the contribution to the mean travel time shift caused by non-uniform distribution of acoustic sources in sunspots may be comparable to (but smaller than) the contribution from the sound speed perturbation in sunspots, and that it has the opposite sign to the sound-speed effect. This effect may cause some underestimation of the negative sound-speed perturbations in sunspots just below the surface, that was found in previous time-distance helioseismology inferences. This effect cannot be corrected by artificially increasing the amplitude of oscillations in sunspots. For large time-distance annuli, the non-uniform distribution of wavefields does not have significant effects on the mean travel times, and thus the sound-speed inversion results. The measured travel time differences, which are used to determine the mass flows beneath sunspots, can also be systematically shifted by this effect, but only in an insignificant magnitude.Comment: 16 pages, 6 figures, accepted for publication in Ap

Testing Helioseismic-Holography Inversions for Supergranular Flows Using Synthetic Data

Supergranulation is one of the most visible length scales of solar convection and has been studied extensively by local helioseismology. We use synthetic data computed with the Seismic Propagation through Active Regions and Convection (SPARC) code to test regularized-least squares (RLS) inversions of helioseismic holography measurements for a supergranulation-like flow. The code simulates the acoustic wavefield by solving the linearized three-dimensional Euler equations in Cartesian geometry. We model a single supergranulation cell with a simple, axisymmetric, mass-conserving flow. The use of simulated data provides an opportunity for direct evaluation of the accuracy of measurement and inversion techniques. The RLS technique applied to helioseismic-holography measurements is generally successful in reproducing the structure of the horizontal flow field of the model supergranule cell. The errors are significant in horizontal-flow inversions near the top and bottom of the computational domain as well as in vertical-flow inversions throughout the domain. We show that the errors in the vertical velocity are due largely to cross talk from the horizontal velocity.Comment: 22 pages, 12 figues, accepted for publication in Solar Physic