The dynamic response of a fluid‐filled borehole under a normal point load on the free surface

The dynamic response of a semi‐infinite fluid‐filled borehole embedded in an elastic half‐space under a concentrated normal surface load is analysed in the long‐wavelength limit. The solution of the problem is obtained with integral transforms in the form of a double integral with respect to the slowness and frequency. The partial P‐ and SV‐wave responses are further transformed to path integrals along Cagniard paths in the complex slowness plane. Unlike the traditional Cagniard‐de Hoop technique based on the Laplace transform of time dependence, this paper is based on the Fourier transform. The tube‐wave response is presented as a causal integral over a slowness range. The resultant representation in the time‐domain is suitable for the numerical evaluation of the complete response in the fluid‐filled borehole, especially at large distances. Asymptotic analysis of seismic phases arising in the borehole is performed on the basis of the obtained solution. The complete asymptotic wavefield consists in P‐ and SV‐waves, the Rayleigh wave and the low‐frequency Stoneley (tube) wave. Pressure synthetics obtained by the use of the asymptotic formulas are shown to be in good agreement with straightforward calculations.     

Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid‐characteristic method

This paper introduces a novel method of modelling acoustic and elastic wave propagation in inhomogeneous media with sharp variations of physical properties based on the recently developed grid‐characteristic method which considers different types of waves generated in inhomogeneous linear‐elastic media (e.g., longitudinal, transverse, Stoneley, Rayleigh, scattered PP‐, SS‐waves, and converted PS‐ and SP‐waves). In the framework of this method, the problem of solving acoustic or elastic wave equations is reduced to the interpolation of the solutions, determined at earlier time, thus avoiding a direct solution of the large systems of linear equations required by the FD or FE methods. We apply the grid‐characteristic method to compare wave phenomena computed using the acoustic and elastic wave equations in geological medium containing a hydrocarbon reservoir or a fracture zone. The results of this study demonstrate that the developed algorithm can be used as an effective technique for modelling wave phenomena in the models containing hydrocarbon reservoir and/or the fracture zones, which are important targets of seismic exploration.     

Pseudo‐spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

Staggering grid is a very effective way to reduce the Nyquist errors and to suppress the non‐causal ringing artefacts in the pseudo‐spectral solution of first‐order elastic wave equations. However, the straightforward use of a staggered‐grid pseudo‐spectral method is problematic for simulating wave propagation when the anisotropy level is greater than orthorhombic or when the anisotropic symmetries are not aligned with the computational grids. Inspired by the idea of rotated staggered‐grid finite‐difference method, we propose a modified pseudo‐spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggered‐grid pseudo‐spectral method based on stiffness matrix decomposition and a possible alternative using the Lebedev grids, the rotated staggered‐grid‐based pseudo‐spectral method possesses the best balance between the mitigation of artefacts and efficiency. A 2D example on a transversely isotropic model with tilted symmetry axis verifies its effectiveness to suppress the ringing artefacts. Two 3D examples of increasing anisotropy levels demonstrate that the rotated staggered‐grid‐based pseudo‐spectral method can successfully simulate complex wavefields in such anisotropic formations.     

Extended reflectivity method for modelling the propagation of diffusive–viscous wave in dip‐layered media

The reflectivity method plays an important role in seismic modelling. It has been used to model different types of waves propagating in elastic and anelastic media. The diffusive–viscous wave equation was proposed to investigate the relationship between frequency dependence of reflections and fluid saturation. It is also used to describe the attenuation property of seismic wave in a fluid‐saturated medium. The attenuation of diffusive–viscous wave is mainly characterised by the effective attenuation parameters in the equation. Thus, it is essential to obtain those parameters and further characterise the features of the diffusive–viscous wave. In this work, we use inversion method to obtain the effective attenuation parameters through quality factor to investigate the characteristics of diffusive–viscous wave by comparing with those of the viscoacoustic wave. Then, the reflection/transmission coefficients in a dip plane‐layered medium are studied through coordinate transform and plane‐wave theory. Consequently, the reflectivity method is extended to compute seismograms of diffusive–viscous wave in a dip plane multi‐layered medium. Finally, we present two models to simulate the propagation of diffusive–viscous wave in a dip plane multi‐layered medium by comparing the results with those in a viscoacoustic medium. The numerical results demonstrate the validity of our extension of reflectivity method to the diffusive–viscous medium. The numerical examples in both time domain and time–frequency domain show that the reflections from a dip plane interface have significant phase shift and amplitude change compared with the results of horizontal plane interface due to the differences in reflection/transmission coefficients. Moreover, the modelling results show strong attenuation and phase shift in the diffusive–viscous wave compared to those of the viscoacoustic wave.     

Uncertainty analysis for the integration of seismic and controlled source electro‐magnetic data

We study the appraisal problem for the joint inversion of seismic and controlled source electro‐magnetic (CSEM) data and utilize rock‐physics models to integrate these two disparate data sets. The appraisal problem is solved by adopting a Bayesian model and we incorporate four representative sources of uncertainty. These are uncertainties in 1) seismic wave velocity, 2) electric conductivity, 3) seismic data and 4) CSEM data. The uncertainties in porosity and water saturation are quantified by a posterior random sampling in the model space of porosity and water saturation in a marine one‐dimensional structure. We study the relative contributions from the four individual sources of uncertainty by performing several statistical experiments. The uncertainties in the seismic wave velocity and electric conductivity play a more significant role on the variation of posterior uncertainty than do the seismic and CSEM data noise. The numerical simulations also show that the uncertainty in porosity is most affected by the uncertainty in the seismic wave velocity and that the uncertainty in water saturation is most influenced by the uncertainty in electric conductivity. The framework of the uncertainty analysis presented in this study can be utilized to effectively reduce the uncertainty of the porosity and water saturation derived from the integration of seismic and CSEM data.     

Wavenumber of the guided wave supported by a thin resistive layer in marine controlled‐source electromagnetics

This paper discusses the asymptotic behaviour of the electromagnetic fields received on the sea‐bed (target response), as well as the fields distributed inside a thin resistive target, generated by a horizontal electric dipole above the sea‐bed in marine controlled‐source electromagnetics for hydrocarbon exploration. It is found that the guided wave supported by a thin resistive target can be expressed as a single‐mode exponential function. A simple closed‐form expression is derived to relate the single‐mode wavenumber of the guided wave to the model parameters: the resistivity and thickness of the target layer, the sea‐bed resistivity and the frequency. When the air‐wave is removed, the guided wave is dominant among the fields received on the sea‐bed at far offset. Hence the wavenumber of the guided wave can be calculated from the fields measured on the sea‐bed. The closed‐form expression can then be used to invert the target property from the calculated wavenumber and hence, can be considered as a hydrocarbon indicator.     

Displacement produced in an elastic half-space by the impulsive torsional motion of a circular ring source

Summary In this paper the problem of disturbance in an elastic semi-infinite medium due to the torsional motion of a circular ring source on the free surface of a medium are studied. Two cases, when the medium is either homogeneous or inhomogeneous, are treated. In order to solve the problem, the Laplace transform and the Hankel transform and the Laplace inversion by Cagniard's method as modified byDe Hoop (1959) are applied. Finally, the integrals for displacement are evaluated numerically. The displacement on the free surface as a function of time is shown by means of graphs, in the case of both a homogeneous and an inhomogeneous medium, indicating clearly the variation in displacement due to the presence of an inhomogeneity.     

CO2 storage in the high Arctic: efficient modelling of pre‐stack depth‐migrated seismic sections for survey planning

The sequestration of CO₂ in subsurface reservoirs constitutes an immediate counter‐measure to reduce anthropogenic emissions of CO₂, now recognized by international scientific panels to be the single most critical factor driving the observed global climatic warming. To ensure and verify the safe geological containment of CO₂ underground, monitoring of the CO₂ site is critical. In the high Arctic, environmental considerations are paramount and human impact through, for instance, active seismic surveys, has to be minimized. Efficient seismic modelling is a powerful tool to test the detectability and imaging capability prior to acquisition and thus improve the characterization of CO₂ storage sites, taking both geological setting and seismic acquisition set‐up into account. The unique method presented here avoids the costly generation of large synthetic data sets by employing point spread functions to directly generate pre‐stack depth‐migrated seismic images. We test both a local‐target approach using an analytical filter assuming an average velocity and a full‐field approach accounting for the spatial variability of point spread functions. We assume a hypothetical CO₂ plume emplaced in a sloping aquifer inspired by the conditions found at the University of Svalbard CO₂ lab close to Longyearbyen, Svalbard, Norway, constituting an unconventional reservoir–cap rock system. Using the local‐target approach, we find that even the low‐to‐moderate values of porosity (5%–18%) measured in the reservoir should be sufficient to induce significant change in seismic response when CO₂ is injected. The sensitivity of the seismic response to changes in CO₂ saturation, however, is limited once a relatively low saturation threshold of 5% is exceeded. Depending on the illumination angle provided by the seismic survey, the quality of the images of five hypothetical CO₂ plumes of varying volume differs depending on the steepness of their flanks. When comparing the resolution of two orthogonal 2D surveys to a 3D survey, we discover that the images of the 2D surveys contain significant artefacts, the CO₂‐brine contact is misplaced and an additional reflector is introduced due to the projection of the point spread function of the unresolvable plane onto the imaging plane. All of these could easily lead to a misinterpretation of the behaviour of the injected CO₂. Our workflow allows for testing the influence of geological heterogeneities in the target aquifer (igneous intrusions, faults, pervasive fracture networks) by utilizing increasingly complex and more realistic geological models as input as more information on the subsurface becomes available.     

Zone of main contribution to the measured signal for a circular current loop source and receiver on the surface of a conductive half‐space

The electric and magnetic fields generated by an individual horizontal current ring induced inside a homogeneous conductive half‐space, originating from an external large circular loop source of current in the presence of a flat half‐space, are deduced. A check of self‐consistency for these expressions led to the known general functions for these fields due to the same external source in the presence of that medium. The current rings’ mutual coupling related to the magnetic field's radial component is thoroughly analysed and its specific members are presented. The existence of a relatively small zone inside the half‐space responsible for the main contribution for the signal measured at the observation point, with the source and receiver on the ground surface, is made evident. For increasing values of frequency, at a given transmitter‐receiver (T–R) configuration, this zone shrinks and its central point moves away from a maximum depth of about 30% and horizontal distance of nearly 85%, of the T–R separation, to a point very close to the receiver position. The coordinates of the central point of this zone of main contribution are provided as approximated functions in terms of the induction number .     

Seasonal variations of deuterium and oxygen‐18 isotopes and their response to moisture source for precipitation events in the subtropical monsoon region

Deuterium and oxygen‐18 are common environmental tracers in water used to investigate hydrological processes such as evaporation and groundwater recharge, and to trace moisture source. In this study, we collected event precipitation from 01 January 2010 to 28 February 2011 at a site in Changsha, Yangtze River Basin to estimate the influence of moisture source and atmospheric conditions on stable isotope compositions. The local meteoric water line, established as δD = (8.45 ± 0.13) δ¹⁸O + (17.7 ± 0.9) (r² = 0.97, n = 189), had a higher slope and intercept than global meteoric water line. Temperature–δ¹⁸O exhibited complex correlations, with positive correlations during Nov.–Apr. superior to during Jun.–Sep., which was attributed to distinctive moisture sources, but vague the overall period; amount effect examined throughout the year. Linear regressions between δ¹⁸O and δD value in different precipitation event size classes revealed progressively decreasing slope and intercept values with decreasing precipitation amount and increasing vapour pressure deficit, indicating that small rainfall events (0–5 mm) were subject to secondary evaporation effects during rainwater descent. In contrast, snowfall and heavy precipitation events exhibited high slope and intercepts for the regression equation between δ¹⁸O and δD. High concentrations of heavy isotopes were associated with precipitation events sourced from remote westerly air masses, degenerated tropical marine air masses from the Bay of Bengal (BoB), and inland moisture in the pre‐monsoon period, as determined from backward trajectories assessed in the HYSPLIT model. Meanwhile, low concentrations of heavy isotopes were found to correspond with remote maritime moisture from BoB, the South China Sea, and the west Pacific at three different air pressures in summer monsoon and post‐monsoon using HYSPLIT and records of typhoon paths. These findings suggest that stable isotope compositions in precipitation events are closely associated with the meteorological conditions and respond sensitively to moisture source in subtropical monsoon climates. Copyright © 2013 John Wiley & Sons, Ltd.     

Laboratory measurements of ‘porosity‐free’ intrinsic Vp and Vs in an olivine gabbro of the Oman ophiolite: Implication for interpretation of the seismic structure of lower oceanic crust

In order to determine ‘porosity‐free’ intrinsic ultrasonic compressional (Vp) and shear wave (Vs) velocities and Vp/Vs of an olivine gabbro from the Oman ophiolite, we developed a new experimental system using a piston‐cylinder type high‐pressure apparatus. The new system allowed us to measure velocities at pressures ranging from 0.20 to 1.00 GPa and at temperatures up to 300°C for Vp and 400°C for Vs. At room temperature, the Vp and Vp/Vs increase rapidly with pressure up to 0.40 GPa, while between 0.45 and 1.00 GPa the increase is more gradual. The change in increasing rate is attributed to closure of porosity at pressures above 0.45 GPa. Based on the linear regression of data obtained at higher pressures (0.45–1.00 GPa) and extrapolation to the lower pressures, combined with temperature derivatives of velocities of the sample measured at 1.00 GPa, we determined the intrinsic Vp and Vs of the sample as a function of pressure (P, in GPa) and temperature (T, in °C). The intrinsic velocities can be expressed as Vp (km/s) = 7.004 + 0.096 × P ? 0.00015 × T, and Vs (km/s) = 3.827 + 0.007 × P ? 0.00008 × T. We evaluated the intrinsic Vp and Vs of the olivine gabbro at oceanic crustal conditions and compared them with a velocity depth‐profile of the borehole seismic observatory WP‐2 area in the northwestern Pacific Basin. Although the intrinsic Vp (～7.0 km/s) and Vs (～3.8 km/s) for the olivine gabbro studied are comparable to those of seismic layer 3 in the WP‐2 area, the estimated vertical gradients of intrinsic velocities are significantly smaller than those reported from layer 3. These results suggest that velocity profiles of layer 3 in the WP‐2 area may reflect the presence of a minor porosity in lower oceanic crust, which closes with increasing depth and/or continuous changes in mineralogy of layer 3 rocks.