Computation of Acoustic Velocity of Natural Gases With an Alternative Heat Capacity Ratio Equation and Application to Seismic Modeling

We investigate three formulations for computing acoustic velocity of natural gas and derive an equation for the heat capacity ratio, which plays a central role in these formulations. The first formulation is a compilation of fundamental equations available in the engineering literature, referred to as the DASH formulation. The second formulation is a development from the first, in which we use the derived equation for the heat capacity ratio (modified DASH). The third formulation is a mainstream method implemented in Geoscience (BW formulation). All three formulations stem from virial Equations of State that take preponderance in the exploration stage, when the detailed fluid composition is unknown and compositional methods are frequently inapplicable. We test the formulations on an extensive experimental data set of acoustic velocity of natural gases and compare the resulting accuracies. Both DASH and modified DASH formulations provide significantly higher accuracy when compared to the BW formulation. Additionally, the modified DASH, as we derive in this work, has the highest accuracy at pressures above 7000 psi, a condition typically encountered in the Brazilian pre-salt reservoirs. In a final step, we investigate how these different formulations and corresponding accuracies in velocity computation may affect seismic modeling, using a single interface model between a dense gas reservoir and a sealing rock. A direct comparison of amplitude versus offset modeling using our modified DASH formulation and the BW formulation shows up to 50% difference in amplitude calculation in a sensitivity exercise, especially at the longer offsets and higher pressures.

Enabling efficient uncertainty quantification for seismic modeling via projection-based model reduction

<p>This talk focuses on the application of projection-based reduced-order models (pROMs) to seismic elastic shear waves. Specifically, we present a method to efficiently propagate parametric uncertainties through the system using a novel formulation of the Galerkin ROM that exploits modern many-core computing nodes.</p><p>Seismic modeling and simulation is an active field of research because of its importance in understanding the generation, propagation and effects of earthquakes as well as artificial explosions. We stress two main challenges involved: (a) physical models contain a large number of parameters (e.g., anisotropic material properties, signal forms and parametrizations); and (b) simulating these systems at global scale with high-accuracy requires a large computational cost, often requiring days or weeks on a supercomputer. Advancements in computing platforms have enabled researchers to exploit high-fidelity computational models, such as highly-resolved seismic simulations, for certain types of analyses. Unfortunately, for analyses requiring many evaluations of the forward model (e.g., uncertainty quantification, engineering design), the use of high-fidelity models often remains impractical due to their high computational cost. Consequently, analysts often rely on lower-cost, lower-fidelity surrogate models for such problems.</p><p>Broadly speaking, surrogate models fall under three categories, namely (a) data fits, which construct an explicit mapping (e.g., using polynomials, Gaussian processes) from the system's parameters to the system response of interest, (b) lower-fidelity models, which simplify the high-fidelity model (e.g., by coarsening the mesh, employing a lower finite-element order, or neglecting physics), and (c) pROMs which reduce the number of degrees of freedom in the high-fidelity model by a projection process of the full-order model onto a subspace identified from high-fidelity data. The main advantage of pROMs is that they apply a projection process directly to the equations governing the high-fidelity model, thus enabling stronger guarantees (e.g., of structure preservation or of accuracy) and more accurate a posteriori error bounds.</p><p>State-of-the-art Galerkin ROM formulations express the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern many-core and hybrid computing nodes. In this work, we introduce a reformulation, called rank-2 Galerkin, of the Galerkin ROM for linear time-invariant (LTI) dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound, and apply it to elastic seismic shear waves in an axisymmetric domain. Specifically, we present an end-to-end demonstration of using the rank-2 Galerkin ROM in a Monte Carlo sampling study, showing that the rank-2 Galerkin ROM is 970 times more efficient than the full order model, while maintaining excellent accuracy in both the mean and statistics of the field.</p>

Probing core overshooting using subgiant asteroseismology: The case of KIC10273246

Context. The size of convective cores remains uncertain, despite their substantial influence on stellar evolution, and thus on stellar ages. The seismic modeling of young subgiants can be used to obtain indirect constraints on the core structure during main sequence, thanks to the high probing potential of mixed modes. Aims. We selected the young subgiant KIC10273246, observed by Kepler, based on its mixed-mode properties. We thoroughly modeled this star, with the aim of placing constraints on the size of its main-sequence convective core. A corollary goal of this study is to elaborate a modeling technique that is suitable for subgiants and can later be applied to a larger number of targets. Methods. We first extracted the parameters of the oscillation modes of the star using the full Kepler data set. To overcome the challenges posed by the seismic modeling of subgiants, we propose a method that is specifically tailored to subgiants with mixed modes and uses nested optimization. We then applied this method to perform a detailed seismic modeling of KIC10273246. Results. We obtain models that show good statistical agreements with the observations, both seismic and non-seismic. We show that including core overshooting in the models significantly improves the quality of the seismic fit, optimal models being found for αov = 0.15. Higher amounts of core overshooting strongly worsen the agreement with the observations and are thus firmly ruled out. We also find that having access to two g-dominated mixed modes in young subgiants allows us to place stronger constraints on the gradient of molecular weight in the core and on the central density. Conclusions. This study confirms the high potential of young subgiants with mixed modes to investigate the size of main-sequence convective cores. It paves the way for a more general study including the subgiants observed with Kepler, TESS, and eventually PLATO.

Generation of 6-C Synthetic Seismograms in Stratified Vertically-Transversely-Isotropic Media Using a Generalized Reflection and Transmission Coefficient Method

Summary We develop a generalized reflection and transmission coefficient method (GRTM) for generating six-component (6-C) synthetic seismograms in horizontally layered vertically-transversely-isotropic (VTI) media. Compared with the traditional seismic modeling approaches that only consider translational motion, our method can simultaneously produce three-component translational and three-component rotational data excited by a point vector force or a moment tensor source in a layered half-space. Horizontally layered models are widely used in near surface applications as the properties of near surface formations generally show small lateral variations and change mainly along the depth direction. The use of the VTI constitutive relation can make our method applicable to more general situations because it takes into account the characteristics of sedimentary formations. We compare our method with a finite-difference method (FDM) for a variety of velocity models and acquisition geometries. The numerical results demonstrate that accurate 6-C synthetic seismograms can be calculated using our method. The computational efficiency of our method for 6-C seismic modeling is much higher than the finite-difference method, because it can reduce a 3D modeling problem to 2.5D by eliminating the azimuthal dimension. Also, our method does not require to perform additional spatial interpolations to obtain the rotational components. These advantages make our method suitable to serve as a forward modeling tool for rotational seismology.

Reduced memory implementation of a local elastic finite-difference solver

The recovery of elastic properties from seismic data often requires the iterative use of seismic modeling. Finite-difference (FD) simulation is a common component in seismic modeling, and it is usually the most computationally expensive step in methodologies such as inversion or reverse time migration. Local solvers attempt to reduce the cost of FD simulations by reducing the computational domain to small areas, updating the model within these areas without recomputing throughout the full domain. We have implemented a local elastic solver that allows us to propagate the elastic wavefield within a subvolume after local alterations of the model. We determine how the scattered wavefield due to the alterations can be extrapolated from the local domain to surface receivers. We extend existing works by using the method of multiple point sources to recompute the wavefield within the local domain. This method is memory efficient because it only requires the global wavefield to be recorded along the local domain boundary. By injecting these recordings as point sources, the global wavefield is emulated within the local domain. Thus, the method requires no modifications of standard FD solvers, merely the ability to record and inject data. We evaluate the capability of the local elastic solver to reconstruct the wavefield in a subvolume of the elastic SEAM elastic model.