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Results
Summary In this study, rotated staggered-grid (RSG) scheme is optimized by introducing compact finite-difference operator and global optimization. RSG is widely used in seismic forward modeling field because it needs no elastic moduli interpolations, so it is better suited for anisotropic media forward modeling than standard staggered-grid (SSG). However, for the same size of grid cells, rotated staggered-grid needs longer step than standard staggered- grid and tend to produce spatial numerical dispersion. To solve this problem, we introduce the compact finite-difference operator. Although the compact finite-difference operator is more accurate and has less numerical dispersion than conventional finite-difference operator, there still is non-negligible numerical dispersion when the wavenumber is big. So to further broaden the wavenumber or frequency range without lengthening the operator length, global optimization is carried out. Both the dispersion analysis and modeling tests show that the optimized compact finite-difference rotated staggered-grid scheme (CRSG) has lower dispersion than conventional RSG scheme.
Summary We demonstrate a workflow to simulate seismicity generated by CO2 injection into the In Salah field, Algeria. Seismic activity in hydrocarbon reservoirs is caused by stress changes on pre-existing fractures that lead to their re-activation. As inputs to our workflow, a history-matched reservoir flow simulation is used to model changes in pressure caused by injection; while a geomechanical model gives the stress state at each node of the flow model. The locations, lengths, and orientations of pre-existing fractures in the reservoir are modeled via a mass-spring solver, which restores the faulted, folded reservoir to its initial, undeformed conditions. This algorithm predicts the intensity and orientation of strain through the model, from which fracture sets can be generated. To simulate seismicity during CO2 injection, we compute changes in effective stress caused by pore pressure changes, and map these stress changes into shear and normal stresses acting on the fractures. Where stresses exceed Mohr-Coulomb failure criteria, seismic events are predicted. We compare our modeled events with observed seismicity at In Salah, finding excellent agreement between model and observation in terms of event timing, event location, and event magnitude.
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Structural Geology > Tectonics > Plate Tectonics > Earthquake (0.70)
Summary Numerical modeling is an important tool in geophysical community. Due to the limitations of computational capability, most of the previous work in anisotropic simulation has concentrated on 2D cases, with inability of acquiring correct amplitude and waveform for generally 3D heterogeneous structures. Herein, we introduce 3D elastic finite-difference numerical modeling with flux correction transport (FCT) for general anisotropic media, which is valid for arbitrary anisotropic symmetry system, provided with the appropriate anisotropic parameters. Numerical simulations are performed over a variety of symmetric models, including isotropic (ISO), vertical transversely isotropic (VTI), horizontal transversely isotropic (HTI) and orthorhombic (ORT) media. Specifically, we present a fracture model experiment, verifying that this 3D numerical modeling scheme with FCT could not only effectively suppress numerical dispersion with less computational effort, but also has the advantage of improving modeling accuracy in fractured media.
Summary In this paper, we develop a weighted Runge-Kutta discontinuous Galerkin method for the wavefield modeling, which is simply called the WRKDG method. For this method, we first transform the seismic wave equations into a first-order hyperbolic system, and then combine the discontinuous Galerkin spatial discretization with a weighted Runge-Kutta (RK) time discretization. The time discretization is based on a diagonal implicit RK method. We employ an explicit technique to change the implicit RK into an explicit method. We also investigate the stability criteria and numerical dispersion for solving the 2D acoustic equation for this method. Afterwards, we apply the WRKDG method to simulate the wavefields for a 2D homogeneous transversely isotropic (TI) model and a water-filled fracture model. Linear and quadratic interpolations are typically used in this article.
Summary Full Waveform Inversion (FWI) has been widely studied in recent years but challenges remain. Issues include computational cost, slow convergence rate, cycle skipping problem and so on. Aiming at these obstacles, we develop the t-p domain waveform inversion with a assemblage of strategies and present the inversion results with different scaling methods in a companion paper (Pan et al., 2014b). Generally, for per iteration in FWI, slant stacking over a set of p values should be performed to balance the updates. To reduce the computational burden further, we illustrate slant update strategy with varied p values in which the model updates can be balanced as the iteration proceeds. The phase-encoding method in t-p domain can reduce the computational cost considerably, but unfortunately, it can also involve serious crosstalk artifacts especially for sparsely sampled sources. A further examination of the anti-aliasing rules in the Random transform reveals that the source spacing has a negative relationship with ray parameter spacing. Different ray parameters are responsible to illuminate the subsurface layers with different dip angles. So, in this paper, we analyze the influences of source spacing and ray parameter range on the t-p domain FWI. In practical application, the presence of noise can increase the ill-posedness of the least-squares inversion problem. Hence, we also analyze the stability of t-p domain FWI with noise data.
- Geophysics > Seismic Surveying > Seismic Processing > Seismic Migration (0.95)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (0.35)
Summary Reverse time migration produces an image by crosscorrelating the solution of the wave equation solved forward in time with the wave equation solved backwards in time. Solution of the wave equation can be computationally prohibitive for large subsurface regions. Therefore one typically combines a finite difference discretization of the wave equation with a parallel computing paradigm such as domain decomposition. Operator or subgrid upscaling is an alternate technique which produces a coarse scale solution of the wave equation that captures fine scale information. In the computationally intensive part of the algorithm one achieves ideal speedup without ghost cell allocation or communication. In this work we show the first images from reverse time migration (RTM) combined with operator upscaling. These upscaled images capture essentially the same velocity heterogeneities as RTM using the full fine grid solution.
Benefits of Frequent Seismic Monitoring and Computer Simulations in Thermal EOR Projects
Cabolova, Anastasija (Shell International Exploration & Production, Inc.) | Lopez, Jorge L. (Shell International Exploration & Production, Inc.) | Wills, Peter (Shell International Exploration & Production, Inc.)
Summary This paper discusses the results of seismic modeling using a history matched dynamic reservoir model for a heavy oil field undergoing thermal EOR in Canada. Through the use of 4D RMS and time-shifts maps in an integrated interpretation, we argue that there are important benefits in performing frequent seismic repeats commensurate with the time scale of the impact of steam injection on reservoir dynamics. These benefits may enable timely adjustments to production operations and more robust characterizations of reservoir behavior.
- Geophysics > Seismic Surveying (1.00)
- Geophysics > Time-Lapse Surveying > Time-Lapse Seismic Surveying (0.86)
- Reservoir Description and Dynamics > Reservoir Simulation (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Thermal methods (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management (1.00)
Summary Time Preserving Tomography is an accurate, efficient and flexible tool for constructing kinematically equivalent subsurface models given a background model and a set of model parameter perturbations. In this method, parameters of the background model are allowed to change while preserving traveltimes of all ray pairs. Perturbations can be applied for all types of model parameters. In the case of tilted transverse isotropy (TTI) the model parameters are the axial compressional velocity, Thomsen anisotropic interval parameters epsilon and delta, and the depth values of the model horizons. The traveltimes of all ray pairs traced during the tomographic inversion are kinematic invariants. In the migrated domain, all the kinematically equivalent models should provide more or less flat reflection events along common image gathers (CIG). In fact, time-preserving tomography does not require CIG at all. An example of the application of this type of method is the use of misties between well markers and seismic depth horizons to obtain Thomsen delta parameters (Mancini, 2013). Timepreserving tomography is a very useful tool for depth interpretation, uncertainty analysis and risk management.
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling (0.70)
Summary Solving the frequency-domain elastic wave equations relies on an efficient linear solver for the large, sparse, indefinite and ill-conditioned linear system derived from the discretization of the elastic wave equation. Direct solvers, which are mostly based on LU decomposition, are efficient for multiple right-hand sides problems, but the memory requirement is huge due to the fill-in effects. On the contrary, iterative solvers fully benefit from the sparsity of the system, but they require problem-specific preconditioners to ensure the convergence because of the ill-conditioning of the system. In this study, we investigate the performance of a robust iterative method named CARP-CG for frequency-domain elastic wave modeling. CARP-CG method turns the original system into a symmetric positive semi-definite system by Kaczmarz row-projections. Such a system can be efficiently solved by the conjugate gradient (CG) method. The row-projections can be seen as a purely algebraic preconditioning technique which is general and is easy to implement. The parallelization is straightforward through a row-block decomposition combined with a component-averaging method. We discretize the 2D frequency-domain elastic wave equation through a 4th order finite difference scheme. Numerical experiments on the Marmousi2 model exhibit a good scalability of CARP-CG. Comparisons between CARP-CG and standard Krylov iterative solvers (GMRES and CGNR) further emphasize the robustness and the fast convergence of CARP-CG method.
- Geophysics > Seismic Surveying > Seismic Processing (0.96)
- Geophysics > Seismic Surveying > Seismic Modeling (0.68)
Cosmic-Ray Neutron Intensity Measurements of Soil Moisture – A Case Study in the Skjern Catchment, Denmark
Andreasen, Mie (University of Copenhagen) | Looms, Majken Caroline (University of Copenhagen) | Jensen, Høgh (University of Copenhagen) | Sonnenborg, Torben O. (Geological Survey of Denmark and Greenland) | Bogena, Heye (Agrosphere IBG-3) | Juelich, Forschungszentrum (GmbH) | Desilets, Darin (Hydroinnova LLC) | Zreda, Marek (University of Arizona)
Summary We estimate soil moisture content variation for an agricultural field in Denmark using a cosmic-ray neutron probe and compare the results with point measurements using capacitance probes, and modelling result using a one-dimensional hydraulic model. The cosmic-ray data are in good agreement with modelled soil moisture content variation using measured/estimated meteorological variables (i.e. precipitation, potential evapotranspiration, and temperature) as well as unsaturated hydraulic parameters. Introduction Soil moisture in the upper subsurface controls the amount of water returned to the atmosphere through evapotransporation, and thereby also controls the amount of water recharged to the underlying groundwater reservoirs. A detailed knowledge of the soil moisture variation over time is therefore crucial for water balance considerations in catchment modelling. Soil moisture measurements using point-scaled probes, such as Time Domain Reflectrometry (TDR) probes and capacitance probes (e.g. 5TE, Decagon Devices), have been applied in soil moisture networks in several catchments (e.g. Bogena et al., 2010; Bircher et al., 2012), due to the fairly robust and inexpensive equipment now available. Furthermore, the petrophysical equations needed to convert the dielectric permittivity values measured to estimated moisture content are fairly wellestablished and universal for coarse-grained mineral soils (Topp et al., 1980). However, the measurement volume of such a sensor is on centimeter to decimeter scale, and upscaling to catchment models may be challenging. Cosmic-ray neutron probes provide soil moisture estimates at a scale that is more in concurrence with the large-scale hydrological models as the measurement footprint has a diameter of approx. 600 m (Zreda et al., 2008; Desilets and Zreda, 2013). These measurements bridge the considerable gap in scale between point measurements and remotely sensed data (e.g. SMOS satellite, Bircher et al., 2012).
- Europe > Denmark (0.72)
- North America > United States (0.69)