T-matrix approach to seismic forward modelling in the acoustic approximation

Forward seismic modelling in the acoustic approximation, for variable velocity but constant density, is dealt with. The wave equation and the boundary conditions are represented by a volume integral equation of the Lippmann-Schwinger (LS) or Fredholm type. A T-matrix (or transition operator) approach from quantum mechanical potential scattering theory is used to derive a family of linear and nonlinear approximations (cluster expansions), as well as an exact numerical solution of the LS equation. For models of 4D anomalies involving small or moderate contrasts, the Born approximation gives identical numerical results as the first-order t-matrix approximation, but the predictions of an exact T-matrix solution can be quite different (depending on spatial extention of the perturbations). For models of fluid-saturated cavities involving large or huge contrasts, the first-order t-matrix approximation is much more accurate than the Born approximation, although it does not lead to significantly more time-consuming computations. If the spatial extention of the perturbations is not too large, it is practical to use the exact T-matrix solution which allows for arbitrary contrasts and includes all the effects of multiple scattering.     

A Compilation of Radiocarbon Dates from Disko Bugt,Central West Greenland/Meteorological Observations in 1996 at the Arctic Station,Qeqertarsuaq (Godhavn), Central West Greenland/A Discussion on Pingos in Mellemfjord,Disko, Central West Greenland/Open System Pingos in Mellemfjord,Disko, Central West Greenland: A Reply to Gurney and Worsley

188 new and previously published radiocarbon dates on Holocene material from Disko Bugt, central West Greenland, are presented together with relevant informations (laboratory number, place name, dated material, geografic coordinates, altitude and δ¹³C-value) about the dates.

In October 1990 an automatic weather station was established at the Arctic station (65 °15′N,53 °31′W), Qeqertarsuaq (Godhavn), Central West Greenland. The Station register parameters each 20 min., and the parameters have been described in an earlier paper in this journal by Nielsen et al. (1995). The present paper summarises main points of the climate during 1996.

Open system, or more correctly, hydraulic pingos, are genetically poorly understood. A continuing problem concerns their need for a perennial groundwater supply (intra- or sub-permafrost). This has to be maintained despite the existence of continuous permafrost in many areas where they are located. Recent work on Disko Island has suggested a new type of hydraulic pingo developing only in a “marsh environment”. It is argued that the marsh setting is not relevant to the formation of these features and that they are simply hydraulic pingos.

Abstract

A group of marsh initiated open system pingo remnants from the Iterdlagssûp kûgssua valley mouth, in Mellemfjord, Disko Island, Central West Greenland was described in Christiansen (1995). Gurney and Worsley (1997) state that the location of this group of pingo remnants in the Iterdlagssûp kûgssua valley mouth is of no relevance to their genesis, and that they presumably were the result of an assumed late Holocene sea level regression, causing permafrost to be established in the valley bottom. In this reply the arguments by Gurney and Worsley (1997) on the Iterdlagssûp kûgssua valley pingos are commented, and it is argued by way of sea level information, frost penetration and water supply that the special setting must indeed have caused pingo initiation and growth. Furthermore, the area has experienced a relative sea level rise during the late Holocene.     

Assessment of Erythemal UV Level in Nepal Based on Solar UV Estimates from Total Ozone Mapping Spectrometer

Nepal lies on the southern slope of Himalaya in Asia. In a width ranging between 150 and 250 km, the altitude varies greatly from about 100 m at its southern border to a maximum of 8848 min the northern part. Like the variation in altitude, climatic condition varies quite a lot. Long-term monthly mean erythemal UV daily dose values for Nepal are evaluated using Total Ozone Mapping Spectrometer (TOMS) estimation from the time of its overpass between 1996 and 2003. The results are presented as summer and winter maps of mean UV levels in each satellite grid. The mean winter erythemal UV daily dose ranges between 2.1 and 3.6 kJ m-2 whereas summer values are found to lie between 4.6 and 9.7 kJ m-2. The altitude variation increases the UV levels by about 0.2 kJ km-1 in winter months, and 0.9 kJ km-1 in summer. A multiyear monthly average erythemal daily dose in most of the areas shows that the summer value is about three times higher than that in winter. Although year-to-year variation is not pronounced in high- and mid-elevation regions, UV levels seemed to decrease from 1997 to 2002 in the southern part of the country in the low elevation region by about 5.35%. Due to the combined effects of the altitude, low ozone concentration in the troposphere, and thin air, surface UV radiation at higher altitudes is found to be higher than in the surrounding regions.     

Seismic characterization of reservoirs with multiple fracture sets using velocity and attenuation anisotropy data

Knowledge about the spatial distribution of the fracture density and the azimuthal fracture orientation can greatly help in optimizing production from fractured reservoirs. Frequency-dependent seismic velocity and attenuation anisotropy data contain information about the fractures present in the reservoir. In this study, we use the measurements of velocity and attenuation anisotropy data corresponding to different seismic frequencies and azimuths to infer information about the multiple fracture sets present in the reservoir. We consider a reservoir model with two sets of vertical fractures characterized by unknown azimuthal fracture orientations and fracture densities. Frequency-dependent seismic velocity and attenuation anisotropy data is computed using the effective viscoelastic stiffness tensor and solving the Christoffel equation. A Bayesian inversion method is then applied to measurements of velocity and attenuation anisotropy data corresponding to different seismic frequencies and azimuth to estimate the azimuthal fracture orientations and the fracture densities, as well as their uncertainties. Our numerical examples suggest that velocity anisotropy data alone cannot recover the unknown fracture parameters. However, an improved estimation of the unknown fracture parameters can be obtained by joint inversion of velocity and attenuation anisotropy data.     

The Zn abundance and isotopic composition of diatom frustules,a proxy for Zn availability in ocean surface seawater

We have developed cleaning methods for extracting diatomopal from bulk marine sediment samples, for measurement of both zinc (Zn) abundance and isotope composition. This cleaning technique was then applied to a set of Holocene core-top samples from the Southern Ocean. The measured δ⁶⁶Zn (reported relative to the JMC_Lyon standard) and Zn/Si ratios from the Southern Ocean diatom_opal samples range from 0.7 to 1.5‰, and from 14 to 0.9 μmol/mol, respectively. The Zn abundance and isotope composition data show a clear correlation with opal burial rates and other oceanographic parameters. In common with previous work, we interpret the systematic changes in the Zn/Si ratio to be linked to the variability in the concentrations of bioavailable Zn in the ambient surface seawater where the diatom opal is formed. This variability is likely to be primarily controlled by the degree to which Zn is taken up into phytoplankton biomass. The observed systematic pattern in the δ⁶⁶Zn compositions of the diatom_opal core-top samples is, similarly, likely to reflect changes in the δ⁶⁶Zn composition of the ambient Zn in the surface waters above the core-top sites, which is progressively driven towards isotopically heavier values by preferential incorporation of the lighter isotopes into phytoplankton organic material. Thus, the systematic relationship between Zn isotopes and abundance observed in the core-top diatom_opal samples suggests a potential tool for investigating the biogeochemical cycling of Zn in the past surface ocean for down-core diatom_opal material. In this respect, it may be possible to test hypotheses that attribute variations in atmospheric CO₂ on glacial–interglacial timescales to the degree to which trace metals limited primary productivity in HNLC zones.     

Velocity variations in carbonate rocks due to dual porosity and wave-induced fluid flow

Stiffness variations in carbonates may be described as resulting from different concentrations of flat compliant pores or cracks, which can have a significant effect on the effective stiffness and acoustic properties (e.g., velocities and attenuations) of dry as well as saturated carbonates, although they carry extremely little porosity. As shown in this paper, the effects of dual porosity and wave-induced fluid flow or pore pressure communication may also play a significant role. On the basis of a previously published T-matrix approach to model the effective viscoelastic properties of cracked porous media, we illustrate the (frequency-dependent) effects of wave-induced fluid flow (mainly squirt flow) or pore pressure communication for a model structure consisting of a mixture of fluid-saturated porous grains and fluid-saturated cavities (vugs, etc.) that are embedded in a solid matrix associated with carbonates. We assume that the pores within the porous grains are decoupled from the pores in the solid matrix (and possibly saturated with different fluids) but that each pore system at the micro and/or mesoscale may or may not be connected. For each of four different connectivity models, we present numerical results for four different cases of microstructure (that emphasize the importance of cracks and flat compliant pores). Our numerical results indicate that the velocity and attenuation spectra of carbonates vary significantly, even when the crack density and all other volume concentrations are constant.     

Bayesian estimation of reservoir properties—effects of uncertainty quantification of 4D seismic data

This paper shows a history matching workflow with both production and 4D seismic data where the uncertainty of seismic data for history matching comes from Bayesian seismic waveform inversion. We use a synthetic model and perform two seismic surveys, one before start of production and the second after 1 year of production. From the first seismic survey, we estimate the contrast in slowness squared (with uncertainty) and use this estimate to generate an initial estimate of porosity and permeability fields. This ensemble is then updated using the second seismic survey (after inversion to contrasts) and production data with an iterative ensemble smoother. The impact on history matching results from using different uncertainty estimates for the seismic data is investigated. From the Bayesian seismic inversion, we get a covariance matrix for the uncertainty and we compare using the full covariance matrix with using only the diagonal. We also compare with using a simplified uncertainty estimate that does not come from the seismic inversion. The results indicate that it is important not to underestimate the noise in seismic data and that having information about the correlation in the error in seismic data can in some cases improve the results.