Bent O. Ruud

3-D finite-difference elastic wave modeling including surface topography

Three‐dimensional finite‐difference (FD) modeling of seismic scattering from free surface topography has been pursued. We have developed exact 3-D free surface topography boundary conditions for the particle velocities. A velocity‐stress formulation of the full elastic wave equations together with the boundary conditions has been numerically modeled by an eighth‐order FD method on a staggered grid. We give a numerical stability criterion for combining the boundary conditions with curved‐grid wave equations, where a curved grid represents the physical medium with topography. Implementation of this stability criterion stops instabilities from arising in areas of steep and rough topographies. We have simulated scattering from teleseismic P-waves using a plane, vertically incident wavefront and real topography from a 40 × 40 km area centered at the NORESS array of seismic receiver stations in southeastern Norway. Synthetic snapshots and seismograms of the wavefield show clear conversion from P-waves to Rg (sh...

Seismic Properties of Shales During Compaction

Shales, mudstones and their unconsolidated equivalents, constitute the vast majority of all sediments on Earth. The composition of such rocks may be roughly characterized (ignoring variation in clay mineralogy) by only two parameters: the water content (porosity) and the fraction of silt relative to total solid fraction (hereafter called the solid fraction of silt). The water content will decrease during compaction of the rock while the solid fraction of silt is unchanged. For shales and mudrocks the silt grains are mainly unconnected and the load-bearing component is the clay. Furthermore, it is reasonable to assume that the porosity of the uncompacted rock will decrease with increasing solid fraction of silt. The clay consists of small flakes (platelets) which after deposition have a random orientation, but which during compaction will become gradually more horizontally aligned. The degree of alignment will be reduced when silt is present since the platelets will drape around the much larger and rounder silt grains. Any alignment will result in an elastically anisotropic rock. For shales and mudstones without high carbonate content the compaction in the upper 2 km of the sediment column is mainly a mechanical process and it is then possible to calculate the orientation distribution function of the platelets as a function of the compaction (or porosity) of the rock. Given the composition (porosity and silt fraction) and the orientation distribution of the platelets one can use a variety of existing methods to model the elastic properties of the rock. All seismically observable properties of a shale (density, vertical Pand S-wave velocities, and the three anisotropy parameters of a transversally isotropic medium) are thus given by only two parameters, the porosity and the silt fraction. This reduction in the degrees of freedom would be very appealing for seismic inversion where the problem is seriously underdetermined.

3-D versus 2-D finite-difference seismic synthetics including real surface topography

Abstract We have pursued and compared two-dimensional (2-D) and three-dimensional (3-D) finite-difference (F-D) modeling of scattering from free surface topography. A velocity–stress formulation of the full elastic wave equations are combined with exact boundary conditions for the surface topography and numerically discretized by an eighth-order F-D method on a staggered grid. We have simulated scattering in 2-D and 3-D from teleseismic P-waves using a plane, vertically incident P-wave and real topography from a 60×60 km2 area including the NORESS array in southeastern Norway. Many field observations that are not easily explained by simpler 2-D cases are shown to better match qualitative effects from 3-D surface topography modeling. These include strong amplifications at hills, complex wave pattern caused by scattering, and directivity of scattered waves. Snapshots and seismograms show clear conversion from P- to Rg- (short period fundamental mode Rayleigh) waves in an area of rough topography in the vicinity of the array site. All results are consistent with numerous observations. By parallellization of the original software, possibilities have been opened for modeling with higher resolution and/or larger areas than before.

Combined inversion of 4D seismic waveform data and production data using ensemble Kalman filter

SUMMARY In this computational study we combine 4D seismic data with production data to continuously update the reservoir model during production. The inversion is based on the ensemble Kalman filter (EnKF ), and the forward method is a combination of a fast seismic modeling tool and a reservoir simulator. The EnKF method is a Monte Carlo approach, and state variables, as fluid saturations and pres sure, and model input parameters as the porosity and permeability, are updated in the reservoir model at each assimilation step. The assimilat ed measurements are seismic waveforms data and production data, which are measured gas-oil ratio, water cut and flowing bottomhole press ure. The updated models allow for improved estimation of the parameters and the state variables during the production, because additional well data and repeated seismic surveys are sequentially included in the inversion. The method is applied to a synthetic 2D reservoir model, and it is shown that introduction of production and seismic waveforms data gives a fairly good estimation of the porosity and permeability fields.

Shear-wave Reflection-seismic Pilot Study at the UNIS CO2 Lab site, Longyearbyen, Svalbard

As part of the world’s needs for CO2-injection test sites, the city of Longyearbyen in Svalbard is an interesting location for testing technologies related to carbon capture and storage (CCS) in a vulnerable arctic environment, being a closed energy system with a coal-fuelled power plant. Therefore, the University Centre in Svalbard (UNIS) established the UNIS CO2 Lab site a few km away of Longyearbyen. The local geological structures appear suited for storing CO2 at about 600-900 m depth and injection tests are carried out. Monitoring micro-seismicity during and after injection is important, but to properly analyse micro-seismicity, a good velocity model for both P- and S-wave is necessary. The top 100-m of the site, including permafrost, is however difficult to assess. In an attempt to improve the actual velocity model near the surface, a pilot study of S-wave reflection seismic was carried out in 2012 and is reported here. Despite numerous noise sources, including wind and strong surface waves, a profile acquired on a nearby filled road showed promising results, indicating very low S-wave velocity values down to 200 m/s, thus giving a much better image of the top 70-m than P-wave seismic earlier acquired. Lessons learned are given too.

Modeling seismic waves in orthorombic, viscoelastic media by finite‐differences

Realistic modeling of seismic wave propagation in heavily fractured rocks enforces us to account for anistropy and attenuation. For finite-difference (F-D) methods, this may be achieved by using relaxation functions in an anisotropic formulation of the stress-strain relations. When the relaxation functions are given by a set of standard linear solids (SLS), an efficient implementation is possible based on the introduction of so-called memory variables. The equations neccessary for a F-D scheme in an orthorombic, viscoelastic medium are given and results for an explosion source in a simple two layer model are shown and discussed.

The P‐P and P‐S response of a fractured reservoir

Understanding the seismic response from complex reservoirs is essential for remote sensing of properties relevant in reservoir characterization and production of hydrocarbons. In this paper we demonstrate the use of coupling rock physics and seismic modeling for understanding the seismic response of a fluid-filled reservoir with vertical fractures. We particularly focus on Amplitude Versus Offset signatures of both P-P and P-S waves using viscoelastic and anisotropic modeling, and compare these to results obtained using simpler modeling strategies. Our general conclusion is that the use of anisotropic and visco-elastic modeling seems important when the seismic spread makes an angle to the direction of the fractures.