In this study, we investigate the accuracy of approximating constant-Q wave propagation by series of Zener or standard linear solid (SLS) mechanisms. Modelling in viscoacoustic and viscoelastic media is implemented in the time domain using the finite-difference (FD) method. The accuracy of numerical solutions is evaluated by comparison with the analytical solution in homogeneous media. We found that the FD solutions using three SLS relaxation mechanisms as well as a single SLS mechanism, with properly chosen relaxation times, are quite accurate for both weak and strong attenuation. Although the RMS errors of FD simulations using a single relaxation mechanism increase with increasing offset, especially for strong attenuation (Q= 20), the results are still acceptable for practical applications. The synthetic data of the Marmousi-II model further illustrate that the single SLS mechanism, to model constant Q, is efficient and sufficiently accurate. Moreover, it benefits from less computational costs in computer time and memory.

Full Tensor Gravity Gradiometry (FTG) data are routinely used in exploration programmes to evaluate and explore geological complexities hosting hydrocarbon and mineral resources. FTG data are typically used to map a host structure and locate target responses of interest using a myriad of imaging techniques. Identified anomalies of interest are then examined using 2D and 3D forward and inverse modelling methods for depth estimation. However, such methods tend to be time consuming and reliant on an independent constraint for clarification. This paper presents a semi-automatic method to interpret FTG data using an adaptive tilt angle approach. The present method uses only the three vertical tensor components of the FTG data (T_zx, T_zy and T_zz) with a scale value that is related to the nature of the source (point anomaly or linear anomaly). With this adaptation, it is possible to estimate the location and depth of simple buried gravity sources such as point masses, line masses and vertical and horizontal thin sheets, provided that these sources exist in isolation and that the FTG data have been sufficiently filtered to minimize the influence of noise. Computation times are fast, producing plausible results of single solution depth estimates that relate directly to anomalies. For thick sheets, the method can resolve the thickness of these layers assuming the depth to the top is known from drilling or other independent geophysical data. We demonstrate the practical utility of the method using examples of FTG data acquired over the Vinton Salt Dome, Louisiana, USA and basalt flows in the Faeroe-Shetland Basin, UK. A major benefit of the method is the ability to quickly construct depth maps. Such results are used to produce best estimate initial depth to source maps that can act as initial models for any detailed quantitative modelling exercises using 2D/3D forward/inverse modelling techniques.

In the last decade the seismic imaging industry has begun collecting data volumes with a substantial amount of data redundancy through new acquisition geometries including: wide-azimuth, rich-azimuth and full-azimuth geometries. The increased redundancy significantly improves image quality in areas with complex geology, but requires considerably greater computational power to construct an image because of the additional data and the need to use advanced imaging algorithms. One way to reduce the computational cost of processing such datasets is to blend shot-records, using shot-encoding, together prior to imaging which reduces the number of migrations necessary for imaging. The downside to doing so is that blending introduces strong, non-physical, cross-talk noise into the final image. By carefully choosing the shot-encoding scheme, we can reduce the additional noise inserted into the image and maximally reduce the number of migrations necessary. We describe a theory of blended imaging that explains all shot-encoding schemes, and use the theory to design a new class of encodings that use amplitude weights instead of phase-shifts or time-delays. We are able to use amplitude encoding to produce blended images of the same quality as previous encoding schemes at a similiar computational cost. Furthermore, we compare the results of amplitude encoding with the results from well-known shot-encoding schemes from previous work including: plane-wave migration, random-time delay, modulated-shot migration, and decimated shot-record migration. In our comparison, we find that plane-wave migration is in many ways an optimal shot-encoding scheme. However, we find that plane-wave migration produces results that are comparable to decimated shot-record migration when the total cost of imaging is taken into account, thereby calling into question the utility of shot-encoding in general. Overall, this work questions the potential for shot-encoding in standard (shot-record) seismic imaging because blended imaging does not appear to sufficiently reduce the cost of imaging given the quality of the blended image compared to decimated shot-record migration.

Lake sediments may serve as archives on paleoclimatic fluctuations, geomagnetic field variations and volcanic activities. Lake Holzmaar in Eifel/Germany is a maar lake and its lacustrine sediments provide paleoclimatic proxy data. Therefore, knowledge about the geometry and, especially, about the thickness of the sediments is very important for determining an optimum drilling location for paleoclimatic studies.

We have developed a floating in-loop transient electromagnetic method field set up (Float-transient electromagnetic method) with a transmitter and receiver size of 18 × 18 m² and 6 × 6 m² respectively. This special set up enables in-loop transient electromagnetic method measurements on the surface of freshwater lakes that define the geometry and the thickness of sediments beneath such lakes thus helping to determine optimum drilling locations. Due to the modular design of the new Float-transient electromagnetic method field set up, this system can be handled by two operators and can easily be transported.

Sixteen in-loop soundings were carried out on the surface of Lake Holzmaar. The transient electromagnetic method data could not be interpreted by conventional 1D inversions because of the 3D distribution of subsurface conductivity caused by the lake's geometry. Three-dimensional finite element modelling was applied to explain the observed transients and the 3D conductivity distribution beneath the lake was recovered by taking its geometry into account. The 3D interpretation revealed approximately 55 m thick sediments beneath 20 m deep water in the central part of the lake.

We develop a methodology to obtain a consistent velocity model from calibration shots or microseismicity observed on a buried array. Using a layered 1D isotropic model derived from checkshots as an initial velocity model, we invert P-wave arrival times to obtain effective anisotropic parameters with a vertical axis of symmetry (VTI). The nonlinear inversion uses iteration between linearized inversion for anisotropic parameters and origin times or depths, which is specific to microseismic monitoring. We apply this technique to multiple microseismic events from several treatments within a buried array. The joint inversion of selected events shows a largely reduced RMS error indicating that we can obtain robust estimates of anisotropic parameters, however we do not show improved source locations. For joint inversion of multiple microseismic events we obtained Thomsen anisotropic parameters ε of 0.15 and δ of 0.05, which are consistent with values observed in active seismic surveys. These values allow us to locate microseismic events from multiple hydraulic fracture treatments separated across thousands of metres with a single velocity model. As a result, we invert the effective anisotropy for the buried array region and are able to provide a more consistent microseismicity mapping for past and future hydraulic fracture stimulations.

Modern downhole microseismic surveys often employ geometries in which ray trajectories generated by a collection of locatable events provide full polar and azimuthal coverage, making it possible to estimate the in situ seismic anisotropy. We show that traveltimes and particle motions of the direct P- and shear-waves acquired in such geometries can constrain stiffness tensors of triclinic media. While obtaining all 21 stiffness coefficients of a homogeneous triclinic space simultaneously with locating pertinent microseismic events from data recorded in a single vertical well is relatively straightforward, the same methodology does not necessarily succeed in layered formations because the combination of their vertical heterogeneity and azimuthal anisotropy might invalidate the commonly adopted approximation of the event azimuths by those of the P-wave polarization vectors. When the event azimuths cannot be derived from the particle motions, traveltimes observed in two or more wells are required to locate the events and build layered triclinic or higher-symmetry azimuthally anisotropic velocity models. As our numerical tests indicate, the multi-well event-location methods are expected to perform better than their single-well counterparts because they rely solely on triangulation and eliminate the usually pronounced azimuthal uncertainties in the event locations that stem from noises adversely affecting hodogram analysis.

This paper discusses and addresses two questions in carbonate reservoir characterization: how to characterize pore-type distribution quantitatively from well observations and seismic data based on geologic understanding of the reservoir and what geological implications stand behind the pore-type distribution in carbonate reservoirs. To answer these questions, three geophysical pore types (reference pores, stiff pores and cracks) are defined to represent the average elastic effective properties of complex pore structures. The variability of elastic properties in carbonates can be quantified using a rock physics scheme associated with different volume fractions of geophysical pore types. We also explore the likely geological processes in carbonates based on the proposed rock physics template. The pore-type inversion result from well log data fits well with the pore geometry revealed by a FMI log and core information. Furthermore, the S-wave prediction based on the pore-type inversion result also shows better agreement than the Greensberg-Castagna relationship, suggesting the potential of this rock physics scheme to characterize the porosity heterogeneity in carbonate reservoirs. We also apply an inversion technique to quantitatively map the geophysical pore-type distribution from a 2D seismic data set in a carbonate reservoir offshore Brazil. The spatial distributions of the geophysical pore type contain clues about the geological history that overprinted these rocks. Therefore, we analyse how the likely geological processes redistribute pore space of the reservoir rock from the initial depositional porosity and in turn how they impact the reservoir quality.

The purpose of this paper is to develop an analytical method to decompose an observed anisotropic compliance tensor into two transversely isotropic (TI) tensors that are associated with layers and fractures. Specifically, the fracture parameters and the TI background medium parameters are obtained from a given monoclinic compliance tensor. Here the set of parallel fractures and TI medium can be arbitrarily oriented in ; they are not constrained to vertical and horizontal directions respectively. First the summation of the two TI tensors, which represent fractures and layerings, is obtained in order to have the form of the resultant monoclinic medium. The orientation of each TI medium is represented by one Euler angle once the mirror plane normal of the monoclinic tensor is determined. This is because the mirror plane normal of the monoclinic medium is perpendicular to the rotation axes of the two TI tensors. Thus a layered medium with one set of parallel fractures is represented by nine parameters; two for rotationally symmetric fractures, five for a generic background TI medium and two Euler angles for the orientations of the structures. The decomposition problem, which is to find these nine parameters from a given monoclinic compliance tensor with thirteen parameters, is solved in the paper. Finally, the decomposition method is extended to media with three structures, namely two sets of fractures and layerings whose rotation axes lie in the same plane.

Prestack seismic inversion plays an important role in estimating elastic parameters that are sensitive to reservoirs and fluid underground. In this paper, a simultaneous inversion method named FMR-AVA (Fluid Factor, Mu (Shear modulus), Rho (Density)-Amplitude Variation with Angle) is proposed based on partial angle stack seismic gathers. This method can be used for direct inversion for the fluid factor, shear modulus and density of heterogeneous reservoirs. Firstly, an FMR approximation equation of a reflection coefficient is derived based on poroelasticity with P- and S-wave moduli. Secondly, a stable simultaneous AVA inversion approach is presented in a Bayesian scheme. This approach has little dependence on initial models. Furthermore, it can be applied in heterogeneous reservoirs whose initial models for inversion are not easy to establish. Finally, a model test shows the superiority of this FMR-AVA inversion method in stability and independence of initial models. We obtain a reasonable fluid factor, shear modulus and density even with smooth initial models and moderate Gaussian noise. A real data case example shows that the inverted fluid factor, shear modulus and density fit nicely with well log interpretation results, which verifies the effectiveness of the proposed method.

Assessment of deep buried basin/basement relationships using geophysical data is a challenge for the energy and mining industries as well as for geothermal or CO₂ storage purposes. In deep environments, few methods can provide geological information; magnetic and gravity data remain among the most informative and cost-effective methods. Here, in order to derive fast first-order information on the basement/basin interface, we propose a combination of existing and original approaches devoted to potential field data analysis. Namely, we investigate the geometry (i.e., depth and structure) and the nature of a deep buried basement through a case study SW of the Paris Basin. Joint processing of new high-resolution magnetic data and up-to-date gravity data provides an updated overview of the deep basin.

First, the main structures of the magnetic basement are highlighted using Euler deconvolution and are interpreted in a structural sketch map. The new high-resolution aeromagnetic map actually offers a continuous view of regional basement structures and reveals poorly known and complex deformation at the junction between major domains of the Variscan collision belt.

Second, Werner deconvolution and an ad hoc post-processing analysis allow the extraction of a set of magnetic sources at (or close to) the basin/basement interface. Interpolation of these sources together with the magnetic structural sketch provides a Werner magnetic basement map displaying realistic 3D patterns and basement depths consistent with data available in deep petroleum boreholes.

The last step of processing was designed as a way to quickly combine gravity and magnetic information and to simply visualize first-order petrophysical patterns of the basement lithology. This is achieved through unsupervised classification of suitably selected gravity and magnetic maps and, as compared to previous work, provides a realistic and updated overview of the cartographic distribution of density/magnetization of basement rocks.

Altogether, the three steps of processing proposed in this paper quickly provide relevant information on a deep buried basement in terms of structure, geometry and nature (through petrophysics). Notwithstanding, limitations of the proposed procedure are raised: in the case of the Paris Basin for instance, this study does not provide proper information on Pre-Mesozoic basins, some of which have been sampled in deep boreholes.

Vertical fractures with openings of less than one centimetre and irregular karst cause abundant diffractions in Ground-Penetrating Radar (GPR) records. GPR data acquired with half-wavelength trace spacing are uninterpretable as they are dominated by spatially undersampled scattered energy. To evaluate the potential of high-density 3D GPR diffraction imaging a 200 MHz survey with less than a quarter wavelength grid spacing (0.05 m × 0.1 m) was acquired at a fractured and karstified limestone quarry near the village of Cassis in Southern France. After 3D migration processing, diffraction apices line up in sub-vertical fracture planes and cluster in locations of karstic dissolution features. The majority of karst is developed at intersections of two or more fractures and is limited in depth by a stratigraphic boundary. Such high-resolution 3D GPR imaging offers an unprecedented internal view of a complex fractured carbonate reservoir model analogue. As seismic and GPR wave kinematics are similar, improvements in the imaging of steep fractures and irregular voids at the resolution limit can also be expected from high-density seismic diffraction imaging.

We propose a new method for estimating pore volume concentrations associated with inclusions with different aspect ratios and also the rock matrix and pore fluid moduli using very fast simulated annealing. We use the Kuster and Toksöz effective modulus formulations as a forward model that takes the pore shapes into consideration.

In order to provide this method, we first estimated the model parameters, then calculated the P- and S-wave velocities as a function of pressure in dry and saturated conditions and finally compared the calculated velocities with the measured ultrasonic velocities of sandstone, limestone and granite. The calculated velocity fitted well with the measured velocity. Furthermore, we verified the calculated bulk modulus and shear modulus of the rock matrix. As these moduli were consistent with the results from other experiments and were almost the same as those by the inversion method, we believe that this method can satisfactorily calculate the moduli.

Next, we conducted optimization under several cases of moduli setting. We obtained the best results using the independent shear modulus under saturated conditions. The result indicates that the shear modulus varies according to the fluid in the pores in sandstone.

Finally, we optimized the average aspect ratio of rock and found that the average aspect ratio may depend on the type of rock. The velocity calculated by the single aspect ratio is similar to the velocity calculated by using a spectrum of aspect ratios for the same rock.

Laboratory experiments are performed with soft synthetic reservoir sandstone cemented under stress and with synthetic overburden (caprock) material consisting of compacted clay (kaolinite) in brine. The rock-like materials are loaded mechanically under stress paths representative of stress changes occurring in the subsurface as a result of injection (increasing pore pressure) or depletion followed by injection into a storage reservoir. Static stress-strain behaviour and multidirectional P- and S-wave velocities are monitored during the tests. The tests with sandstone are performed on dry material and simple poroelastic modelling is performed to relate these data to the behaviour of fluid (water / CO₂) saturated samples under the same stress paths. The focus is on identifying 4D seismic attributes that may be used in the field to interpret monitoring measurements. This could help diagnose stress changes in the overburden, signalling the risk of CO₂ leakage from a reservoir if the compressive or tensile strength limit of the overburden is reached and of course to help quantify amounts of CO₂ stored.

The resistive and capacitive response of a multiphase subsoil can be analysed by amplitude and phase models of the electrical complex resistivity. The main goal of this work is to extend the 2D transformed formulation used for electrical site investigations for cylindrical laboratory models, solving the complex resistivity forward problem starting from the Complete Electrode Model approach. This formulation is tested by a comparison with the full 3D solution and is proven to be stable and accurate. Inversion of complex resistivity data is achieved through a Matlab interface included in the EIDORS environment, with the addition of numerous new functions. Three synthetic examples are discussed, to understand the potential and limits of this approach in comparison with the 3D inversion. Laboratory experiments on a cylindrical laboratory model with a horizontal cross-section of 10 electrodes validated synthetic results. The model having a height of 1 m and a diameter of 500 mm is made by sand contaminated from the top by an engineered fluid with electrical properties similar to chlorinated solvents.

In order to perform a good pulse compression, the conventional spike deconvolution method requires that the wavelet is stationary. However, this requirement is never reached since the seismic wave always suffers high-frequency attenuation and dispersion as it propagates in real materials. Due to this issue, the data need to pass through some kind of inverse-Q filter. Most methods attempt to correct the attenuation effect by applying greater gains for high-frequency components of the signal. The problem with this procedure is that it generally boosts high-frequency noise. In order to deal with this problem, we present a new inversion method designed to estimate the reflectivity function in attenuating media. The key feature of the proposed method is the use of the least absolute error (L1 norm) to define both the data and model error in the objective functional. The L1 norm is more immune to noise when compared to the usual L2 one, especially when the data are contaminated by discrepant sample values. It also favours sparse reflectivity when used to define the model error in regularization of the inverse problem and also increases the resolution, since an efficient pulse compression is attained. Tests on synthetic and real data demonstrate the efficacy of the method in raising the resolution of the seismic signal without boosting its noise component.

Reverse-time migration is a two-way time-domain finite-frequency technique that accurately handles the propagation of complex scattered waves and produces a band-limited representation of the subsurface structure that is conventionally assumed to be linear in the contrasts in model parameters. Because of this underlying linear single-scattering assumption, most implementations of this method do not satisfy the energy conservation principle and do not optimally use illumination and model sensitivity of multiply scattered waves. Migrating multiply scattered waves requires preserving the non-linear relation between the image and perturbation of model parameters. I modify the extrapolation of source and receiver wavefields to more accurately handle multiply scattered waves. I extend the concept of the imaging condition in order to map into the subsurface structurally coherent seismic events that correspond to the interaction of both singly and multiply scattered waves. This results in an imaging process referred to here as non-linear reverse-time migration. It includes a strategy that analyses separated contributions of singly and multiply scattered waves to a final non-linear image. The goal is to provide a tool suitable for seismic interpretation and potentially migration velocity analysis that benefits from increased illumination and sensitivity from multiply scattered seismic waves. It is noteworthy that this method can migrate internal multiples, a clear advantage for imaging challenging complex subsurface features, e.g., in salt and basalt environments. The results of synthetic seismic imaging experiments, including a subsalt imaging example, illustrate the technique.

Advances in seismics acquisition and processing and the widespread use of 4D seismics have made available reliable production-induced subsurface deformation data in the form of overburden time-shifts. Inversion of these data is now beginning to be used as an aid to the monitoring of a reservoir's effective stress. Past solutions to this inversion problem have relied upon analytic calculations for an unrealistically simplified subsurface, which can lead to uncertainties. To enhance the accuracy of this approach, a method based on transfer functions is proposed in which the function itself is calibrated using numerically generated overburden strain deformation calculated for a small select group of reference sources. This technique proves to be a good compromise between the faster but more accurate history match of the overburden strain using a geomechanical simulator and the slower, less accurate analytic method. Synthetic tests using a coupled geomechanical and fluid flow simulator for the South Arne field confirm the efficacy of the method. Application to measured time-shifts from observed 4D seismics indicates compartmentalization in the Tor reservoir, more heterogeneity than is currently considered in the simulation model and moderate connectivity with the overlying Ekofisk formation.

We develop a method to invert S-wave splitting (SWS) observations, measured on microseismic event data, for the ratio of normal to tangential compliance (Z_N/Z_T) of sets of aligned fractures. We demonstrate this method by inverting for Z_N/Z_T using SWS measurements made during hydraulic fracture stimulation of the Cotton Valley tight gas reservoir, Texas. When the full SWS data set is inverted, we find that Z_N/Z_T= 0.74 ± 0.04. Windowing the data by time, we were able to observe variations in Z_N/Z_T as the fracture stimulation progresses. Most notably, we observe an increase in Z_N/Z_T contemporaneous with proppant injection. Rock physics models and laboratory observations have shown that Z_N/Z_T can be sensitive to (1) the stiffness of the fluid filling the fracture, (2) the extent to which this fluid can flow in and out of the fracture during the passage of a seismic wave and (3) the internal architecture of the fracture, including the roughness of the fracture surfaces, the number and size of any asperities and the presence of material filling the fracture. These factors have direct implications for modelling the fluid-flow properties of fractures. Consequently, the ability to image Z_N/Z_T using SWS will provide useful information about fractured rocks and allow additional constraints to be placed on reservoir behaviour.

The basic physical properties of the magnetic source field, namely its homogeneity and spatial coherence, have been used for a variety of magnetotelluric processing techniques including remote reference processing. In the present work we propose a data acquisition and processing technique for a large number of stations distributed over a localized area ideally on a grid. For pseudo-remote reference processing it is necessary to use the following station setup: five-component MT data are only measured at some sites (base stations) while at the majority of sites (local stations) only the electric and vertical magnetic fields are recorded. The impedance tensor and vertical magnetic transfer functions at each local station are computed by assigning the magnetic fields of a base station to the local station as if they had been measured there. This approach can lead to biased or erroneous estimates of local transfer functions at stations in the vicinity of strong conductivity contrasts that can be corrected using the interstation transfer functions between the horizontal magnetic fields measured at the base station(s).

We test this approach with a data set collected in the vicinity of the Groß Schönebeck geothermal test site. Magnetotelluric data were collected at 146 local and 5 base stations distributed over an approximately 5 km × 25 km wide grid with site spacing ranging from 500 m × 500 m to 1000 m × 1000 m in the frequency range 128–0.001Hz. The obtained pseudo-remote reference transfer functions are generally smooth and consistent and conductivity models obtained from 2D inversion of the data are in agreement with previous conductivity models from the study area.

An approach is developed to estimate pore-pressure changes in a compacting chalk reservoir directly from time-lapse seismic attributes. It is applied to data from the south-east flank of the Valhall field. The time-lapse seismic signal of the reservoir in this area is complex, despite the fact that saturation changes do not have an influence. This complexity reflects a combination of pressure depletion, compaction and stress re-distribution throughout the reservoir and into the surrounding rocks. A simple relation is found to link the time-lapse amplitude and time-shift attributes to variations in the key controlling parameter of initial porosity. This relation is sufficient for an accurate estimation of pore-pressure change in the inter-well space. Although the time-lapse seismic estimates mostly agree with reservoir simulation, unexplained mismatches are apparent at a small number of locations with lower porosities (less than 38%). The areas of difference between the observations and predictions suggest possibilities for simulation model updating or a better understanding of the physics of the reservoir.

Mudrocks, defined to be fine-grained siliclastic sedimentary rocks such as siltstones, claystones, mudstones and shales, are often anisotropic due to lamination and microscopic alignments of clay platelets. The resulting elastic anisotropy is often non-negligible for many applications in the earth sciences such as wellbore stability, well stimulation and seismic imaging. Anisotropic elastic properties reported in the open literature have been compiled and statistically analysed. Correlations between elastic parameters are observed, which will be useful in the typical case that limited information on a rock's elastic properties is known. For example, it is observed that the highest degree of correlation is between the horizontal elastic stiffnesses C₁₁ and C₆₆. The results of statistical analysis are generally consistent with prior observations. In particular, it is observed that Thomsen's ɛ and γ parameters are almost always positive, Thomsen's ɛ and γ parameters are well correlated, Thomsen's δ is most frequently small and Thomsen's ɛ is generally larger than Thomsen's δ. These observations suggest that the typical range for the elastic properties of mudrocks span a sub-space less than the five elastic constants required to fully define a Vertical Transversel Isotropic medium. Principal component analysis confirms this and that four principal components can be used to span the space of observed elastic parameters.

In studies on heavy oil, shale reservoirs, tight gas and enhanced geothermal systems, the use of surface passive seismic data to monitor induced microseismicity due to the fluid flow in the subsurface is becoming more common. However, in most studies passive seismic records contain days and months of data and manually analysing the data can be expensive and inaccurate. Moreover, in the presence of noise, detecting the arrival of weak microseismic events becomes challenging. Hence, the use of an automated, accurate and computationally fast technique for event detection in passive seismic data is essential. The conventional automatic event identification algorithm computes a running-window energy ratio of the short-term average to the long-term average of the passive seismic data for each trace. We show that for the common case of a low signal-to-noise ratio in surface passive records, the conventional method is not sufficiently effective at event identification. Here, we extend the conventional algorithm by introducing a technique that is based on the cross-correlation of the energy ratios computed by the conventional method. With our technique we can measure the similarities amongst the computed energy ratios at different traces. Our approach is successful at improving the detectability of events with a low signal-to-noise ratio that are not detectable with the conventional algorithm. Also, our algorithm has the advantage to identify if an event is common to all stations (a regional event) or to a limited number of stations (a local event). We provide examples of applying our technique to synthetic data and a field surface passive data set recorded at a geothermal site.

We present two-and-a-half dimensional (2.5D) and three-dimensional (3D) integral equation modelling of the marine controlled source electromagnetic method. We implement 2.5D modelling using a point source and a two-dimensional reservoir and compare the results with point source responses from one-dimensional and three-dimensional reservoir models. These methods are based on an electric field domain integral equation formulation. We show how the 2.5D method performs in terms of both accuracy and computing speed with different configurations. We compare the results from 1D, 2.5D and 3D modelling, for a symmetrically placed reservoir and the in-line acquisition configuration, as a function of different reservoir sizes in the cross-line direction, thickness and for different frequencies and depths. Depending on the model’s parameters 2.5D modelling can be considered as an accurate and fast method for marine controlled source electromagnetic acquisition optimization and interpretation. If the thickness of the reservoir is less than one fifth of the skin depth of the embedding and if the depth of the reservoir is two or more times the skin depth of the embedding, the largest amplitude difference between two-dimensional and three-dimensional reservoirs is less than 10% when the source is above the centre of the reservoir. In this paper we discuss supporting examples with different configurations, where the 2.5D results lead to an optimistic detection estimate. Phase differences between 2.5D and 3D modelling are even smaller and the 2.5D solution can be used to assess the ability to detect the reservoir with a given acquisition configuration.

Numerical implementation of the gradient of the cost function in a gradient-based full- waveform inversion (FWI) is essentially a migration operator used in wave equation migration. In FWI, minimizing different data residual norms results in different weighting strategies of data residuals at receiver locations prior to back-propagation into the medium. In this paper, we propose different scaling methods to the receiver wavefield and compare their performances. Using time-domain reverse-time migration (RTM), we show that compared to conventional algorithms, this type of scaling is able to significantly suppress non-Gaussian noise, i.e., outliers. Our tests also show that scaling by its absolute norm produces better results than other approaches.

Velocity model building and impedance inversion generally suffer from a lack of intermediate wavenumber content in seismic data. Intermediate wavenumbers may be retrieved directly from seismic data sets if enough low frequencies are recorded. Over the past years, improvements in acquisition have allowed us to obtain seismic data with a broader frequency spectrum. To illustrate the benefits of broadband acquisition, notably the recording of low frequencies, we discuss the inversion of land seismic data acquired in Inner Mongolia, China. This data set contains frequencies from 1.5–80 Hz. We show that the velocity estimate based on an acoustic full-waveform inversion approach is superior to one obtained from reflection traveltime inversion because after full-waveform inversion the background velocity conforms to geology. We also illustrate the added value of low frequencies in an impedance estimate.

The forward (modelled) wavefield for conventional reverse time migration (RTM) is computed by extrapolating the wavefield from an estimated source wavelet. In the typical case of a smooth subsurface velocity, this wavefield lacks the components, including surface reflections, necessary to image multiples in the observed data. We, instead, introduce the concept of forward propagating the recorded data, including direct arrivals, as part of RTM. We analyse the influence of the main components of the data on the imaging process, which include direct arrivals, primaries and surface-related multiples. In our RTM methodology, this implies correlating the forward extrapolated recorded data wavefield with its reversely extrapolated version prior to applying the zero-lag cross-correlation imaging condition. The interaction of the data components with each other in the cross-correlation process will image primaries and multiples, as well as introduce cross-talk artefact terms. However, some of these artefacts are present in conventional RTM implementation and they tend to be relatively weak. In fact, for the surface seismic experiment, forward propagating the direct arrivals is almost equivalent to forward propagating a source and it tends to contribute the majority of the data imaging energy. In addition, primaries and multiples recorded in the data become multiples of one higher order. Forward propagating the recorded data to recreate the source will relieve us from the requirement of estimating the source function. It will also include near-surface information necessary to improve the image in areas with near-surface complexity. Data from a simple synthetic layered model, as well as the Marmousi model, are used to demonstrate some of these features.

In this study, importance is drawn to the role of engineering principles when interpreting dynamic reservoir changes from 4D seismic data. In particular, it is found that in clastic reservoirs the principal parameters controlling mapped 4D signatures are not the pressure and saturation changes per se but these changes scaled by the corresponding thickness (or pore volume) of the reservoir volume that these effects occupy. For this reason, pressure and saturation changes cannot strictly be recovered by themselves, this being true for all data interpretation. This understanding is validated both with numerical modelling and analytic calculation. Interestingly, the study also indicates that the impact of gas saturation on the seismic can be written using a linear term but that inversion for gas saturation can yield at best only the total thickness/pore volume of the distribution. The above provides a basis for a linear equation that can readily and accurately be used to estimate pressure and saturation changes. Quantitative updates of the static and dynamic components of the simulation model can be achieved by comparing thickness or pore volume-scaled changes from the simulator with the corresponding quantities on the inverted observations.

Estimating elastic parameters from prestack seismic data remains a subject of interest for the exploration and development of hydrocarbon reservoirs. In geophysical inverse problems, data and models are in general non-linearly related. Linearized inversion methods often have the disadvantage of strong dependence on the initial model. When the initial model is far from the global minimum, inversion iteration is likely to converge to the local minimum. This problem can be avoided by using global optimization methods.

In this paper, we implemented and tested a prestack seismic inversion scheme based on a quantum-behaved particle swarm optimization (QPSO) algorithm aided by an edge-preserving smoothing (EPS) operator. We applied the algorithm to estimate elastic parameters from prestack seismic data. Its performance on both synthetic data and real seismic data indicates that QPSO optimization with the EPS operator yields an accurate solution.

Despite being less general than 3D surface-related multiple elimination (3D-SRME), multiple prediction based on wavefield extrapolation can still be of interest, because it is less CPU and I/O demanding than 3D-SRME and moreover it does not require any prior data regularization. Here we propose a fast implementation of water-bottom multiple prediction that uses the Kirchhoff formulation of wavefield extrapolation. With wavefield extrapolation multiple prediction is usually obtained through the cascade of two extrapolation steps. Actually by applying the Fermat’s principle (i.e., minimum reflection traveltime) we show that the cascade of two operators can be replaced by a single approximated extrapolation step. The approximation holds as long as the water bottom is not too complex. Indeed the proposed approach has proved to work well on synthetic and field data when the water bottom is such that wavefront triplications are negligible, as happens in many practical situations.

Spectral decomposition, or local time-frequency analysis, tries to enhance the amount of information one can obtain from a seismic volume by finding the frequency content of the seismic data at each time sample. However, if a small amount of noise is present within the seismic amplitude volume, it has the potential to become more prominent in the spectrally decomposed data especially if high-resolution or sparsity promoting methods are utilized. To combat this problem post-processing noise removal has commonly been employed, but these techniques can potentially degrade the resolution of small-scale geological structures in their attempt to remove this noise. Rather than de-noising the spectrally decomposed data after they are generated, we propose to incorporate the ideas of f−x−y deconvolution within the spectral decomposition process to create an algorithm that has the ability to de-noise the time-frequency representation of the data as they are being generated. By incorporating the spatial prediction error filters that are utilized for f−x−y deconvolution with the spectral decomposition problem, a spatially smooth time-frequency representation that maintains its sparsity, or high-resolution characteristics, can be obtained. This spatially smooth high-resolution time-frequency representation is less likely to exhibit the random noise that was present in the more conventionally obtained time-frequency representation. Tests on a real data set demonstrate that by de-noising while the time-frequency representation is being constructed, small-scale geological structures are more likely to maintain their resolution since the de-noised time-frequency representation is specifically built to reconstruct the data.

A spectral sparse Bayesian learning reflectivity inversion method, combining spectral reflectivity inversion with sparse Bayesian learning, is presented in this paper. The method retrieves a sparse reflectivity series by sequentially adding, deleting or re-estimating hyper-parameters, without pre-setting the number of non-zero reflectivity spikes. The spikes with the largest amplitude are usually the first to be resolved. The method is tested on a series of data sets, including synthetic data, physical modelling data and field data sets. The results show that the method can identify thin beds below tuning thickness and highlight stratigraphic boundaries. Moreover, the reflectivity series, which is inverted trace-by-trace, preserves the lateral continuity of layers.

This paper compares three alternative algorithms for simultaneously estimating a source wavelet at the same time as an earth model in full-waveform inversion: (i) simultaneous descent, (ii) alternating descent and (iii) descent with the variable projection method. The latter is a technique for solving separable least-squares problems that is well-known in the applied mathematics literature. When applied to full-waveform inversion, it involves making the source wavelet an implicit function of the earth model via a least-squares filter-estimation process. Since the source wavelet becomes purely a function of medium parameters, it no longer needs to be treated as a separate unknown in the inversion. Essentially, the predicted data are projected onto the measured data in a least-squares sense at every function evaluation, making use of the fact that the filter estimation problem is trivial when compared to the full-waveform inversion problem. Numerical tests on a simple 1D model indicate that the variable projection method gives the best result; actually producing results in quality that are very similar to control experiments with a known, correct wavelet.

We describe a numerical study to quantify the influence of tool-eccentricity on wireline (WL) and logging-while-drilling (LWD) sonic logging measurements. Simulations are performed with a height-polynomial-adaptive (hp) Fourier finite-element method that delivers highly accurate solutions of linear visco-elasto-acoustic problems in the frequency domain. The analysis focuses on WL instruments equipped with monopole or dipole sources and LWD instruments with monopole excitation. Analysis of the main propagation modes obtained from frequency dispersion curves indicates that the additional high-order modes arising as a result of borehole-eccentricity interfere with the main modes (i.e., Stoneley, pseudo-Rayleigh and flexural). This often modifies (decreases) the estimation of shear and compressional formation velocities, which should be corrected (increased) to account for borehole-eccentricity effects. Undesired interferences between different modes can occur at different frequencies depending upon the properties of the formation and fluid annulus size, which may difficult the estimation of the formation velocities.

We review and describe the electromagnetic transmitters and receivers used to carry out magnetotelluric and controlled source soundings in the marine environment. Academic studies using marine electromagnetic methods started in the 1970s but during the last decade these methods have been used extensively by the offshore hydrocarbon exploration industry. The principal sensors (magnetometers and non-polarizing electrodes) are similar to those used on land but magnetotelluric field strengths are not only much smaller on the deep sea-floor but also fall off more rapidly with increasing frequency. As a result, magnetotelluric signals approach the noise floor of electric field and induction coil sensors (0.1 nV/m and 0.1 pT) at around 1 Hz in typical continental shelf environments. Fluxgate magnetometers have higher noise than induction coils at periods shorter than 500 s but can still be used to collect sea-floor magnetotelluric data down to 40–100 s. Controlled source transmitters using electric dipoles can be towed continuously through the seawater or on the sea-bed, achieving output currents of 1000 A or more, limited by the conductivity of seawater and the power that can be transmitted down the cables used to tow the devices behind a ship. The maximum source-receiver separation achieved in controlled source soundings depends on both the transmitter dipole moment and on the receiver noise floor and is typically around 10 km in continental shelf exploration environments. The position of both receivers and transmitters needs to be navigated using either long baseline or short baseline acoustic ranging, while sea-floor receivers need additional measurements of orientations from compasses and tiltmeters. All equipment has to be packaged to accommodate the high pressure (up to 40 MPa) and corrosive properties of seawater. Usually receiver instruments are self-contained, battery powered and have highly accurate clocks for timekeeping, even when towed on the sea-floor or in the water column behind a transmitter.

Seismic monitoring of an injected carbon dioxide (CO₂) distribution at depth is an important issue in the geological storage of CO₂. To help monitor changes in the subsurface during CO₂ injection a series of 2D seismic surveys were acquired within the framework of the CO2SINK and CO2MAN projects at Ketzin, Germany at different stages of the injection process. Here we investigate using seismic full waveform inversion as a qualitative tool for time-lapse seismic monitoring given the constraints of the limited maximum offsets of the 2D seismic data. Prior to applying the inversion to the real data we first made a number of benchmark tests on synthetic data using a similar geometry as in the real data. Results from the synthetic benchmark tests show that it is difficult to recover the true value of the velocity anomaly due to the injection but that it is possible to qualitatively locate the distribution of the injected CO₂. After the synthetic studies, we applied seismic full waveform inversion on the real time-lapse data from the Ketzin site along with conventional time-lapse processing. Both methods show a similar qualitative distribution of the injected CO₂ and agree well with expectations based upon more extensive 3D time-lapse monitoring in the area.

Gas hydrates are a potential energy resource, a possible factor in climate change and an exploration geohazard. The University of Toronto has deployed a permanent seafloor time-domain controlled source electromagnetic (CSEM) system offshore Vancouver Island, within the framework of the NEPTUNE Canada underwater cabled observatory. Hydrates are known to be present in the area and due to their electrically resistive nature can be monitored by 5 permanent electric field receivers. However, two cased boreholes may be drilled near the CSEM site in the near future. To understand any potential distortions of the electric fields due to the metal, we model the marine electromagnetic response of a conductive steel borehole casing. First, we consider the commonly used canonical model consisting of a 100 Ωm, 100 m thick resistive hydrocarbon layer embedded at a depth of 1000 m in a 1 Ωm conductive host medium, with the addition of a typical steel production casing extending from the seafloor to the resistive zone. Results show that in both the frequency and time domains the distortion produced by the casing occurs at smaller transmitter-receiver offsets than the offsets required to detect the resistive layer. Second, we consider the experimentally determined model of the offshore Vancouver Island hydrate zone, consisting of a 5.5 Ωm, 36 m thick hydrate layer overlying a 0.7 Ωm sedimentary half-space, with the addition of two borehole casings extending 300 m into the seafloor. In this case, results show that the distortion produced by casings located within a 100 m safety zone of the CSEM system will be measured at 4 of the 5 receivers. We conclude that the boreholes must be positioned at least 200 m away from the CSEM array so as to minimize the effects of the casings.

Many geophysicists perform reverse-time migration using a variety of artificial sources to obtain the source wavefield. Upon processing the seismic data, however, it is difficult to recover the original phase and amplitude of the source wavelet used for seismic exploration, regardless of the source. We have therefore used several artificial source wavelets such as Ricker or the first derivative Gauss wavelets expressed by well-known functions. There are some differences between these artificial source wavelets and the original source wavelets, resulting in imperfect migration images. Artificial source wavelets tend to distort the exact location of subsurface reflectors and they create noise around the boundary of the stratum. To solve this problem, we applied the source estimation technique to the reverse-time migration algorithm. The source estimation technique approximates the source wavelet to the original exploration source wavelet by a deconvolution method. This technique is used in full waveform inversion and provides better inversion results as demonstrated by other studies. To prove the effect of reverse-time migration with source estimation, we tested this algorithm on the Sigsbee2a model, SEG/EAGE 3D salt model and 3D real field land data. Using the resulting images of these three models, we found that the source estimation technique can yield better migration images. To suppress the artefacts produced in the migration image, we used a wavenumber filter and Laplacian filter on 2D and 3D examples, respectively. Furthermore, we used the pseudo-Hessian similar to the source illumination to scale the migration image because the virtual source imaging condition was used for reverse-time migration.

We investigate a pseudo-seismic approach based on the so-called inverse Q-transform as an alternative way of processing transient electromagnetic (TEM) data. This technique transforms the diffusive TEM response into that of propagating waves obeying the standard wave-equation. These transformed data can be input into standard seismic migration schemes with the potential of giving higher resolution subsurface images. Such images contain geometrical and qualitative information about the medium but no quantitative results are obtained as in model-based inversion techniques. These reconstructed images can be used directly for geological interpretation or in further constraining possible inversions. We extend the original Q-transform based on an electrical-source formulation to the case of a large-loop TEM source. Moreover, an efficient discrete version of the inverse of this modified Q-transform is presented using a regularization method. Application of this inverse transform to the measured TEM responses gives the corresponding pseudo-seismic data, which are input into a 3D migration scheme. We then use a 3D boundary element type of Kirchhoff migration to ensure high computational efficiency. This proposed method was applied to both synthetic data as well as field measurements taken from an engineering geology survey. The results indicate that the resolution of the TEM data is significantly improved when compared with standard apparent-resistivity plots, demonstrating that higher resolution 3D transient electromagnetic imaging is feasible using this method.

Wave-induced fluid flow at microscopic and mesoscopic scales arguably constitutes the major cause of intrinsic seismic attenuation throughout the exploration seismic and sonic frequency ranges. The quantitative analysis of these phenomena is, however, complicated by the fact that the governing physical processes may be dependent. The reason for this is that the presence of microscopic heterogeneities, such as micro-cracks or broken grain contacts, causes the stiffness of the so-called modified dry frame to be complex-valued and frequency-dependent, which in turn may affect the viscoelastic behaviour in response to fluid flow at mesoscopic scales. In this work, we propose a simple but effective procedure to estimate the seismic attenuation and velocity dispersion behaviour associated with wave-induced fluid flow due to both microscopic and mesoscopic heterogeneities and discuss the results obtained for a range of pertinent scenarios.

We propose here a new, robust, methodology to estimate the errors on a magnetotelluric (MT) impedance tensor. This method is developed with the bounded influence remote-reference processing (BIRRP) code in a single site configuration. The error is estimated by reinjecting an electric field residual obtained after the calculation of an impedance tensor into a tensor function calculation procedure. We show using synthetic examples that the error tensor calculated with our method yields a more reliable error estimate than the one calculated from Jackknife statistics. The modulus of realistic error estimates can be used as a quality control and an accurate inversion constraint of MT surveys. Moreover, reliable error estimates are necessary for new applications of MT to dynamic subsurface processes such as reservoir monitoring.

Determining the focal mechanism of earthquakes helps us to better define faults and understand the stress regime. This technique can be helpful in the oil and gas industry where it can be applied to microseismic events. The objective of this paper is to find double couple focal mechanisms, excluding scalar seismic moments, and the depths of small earthquakes using data from relatively few local stations. This objective is met by generating three-component synthetic seismograms to match the observed normalized velocity seismograms. We first calculate Green's functions given an initial estimate of the earthquake's hypocentre, the locations of the seismic recording stations and a 1D velocity model of the region for a series of depths. Then, we calculate the moment tensor for different combinations of strikes, dips and rakes for each depth. These moment tensors are combined with the Green's functions and then convolved with a source time function to produce synthetic seismograms. We use a grid search to find the synthetic seismogram with the largest objective function that best fits all three components of the observed velocity seismogram. These parameters define the focal mechanism solution of an earthquake. We tested the method using three earthquakes in Southern California with moment magnitudes of 5.0, 5.1 and 4.4 using the frequency range 0.1–2.0 Hz. The source mechanisms of the events were determined independently using data from a multitude of stations. Our results obtained, from as few as three stations, generally match those obtained by the Southern California Earthquake Data Center. The main advantage of this method is that we use relatively high-frequency full-waveforms, including those from short-period instruments, which makes it possible to find the focal mechanism and depth of earthquakes using as few as three stations when the velocity structure is known.

Improved reservoir characterization and monitoring can be achieved by combining seismic and controlled-source electromagnetic techniques. This requires developing coherent rock physics descriptions. In this paper we demonstrate consistent joint elastic-electrical modelling according to the differential effective-medium theory. We test our modelling against data from a compaction experiment on a set of 11 sandstone core samples from the same quarry location. The presented approach is analogous to calibrating a rock physics model to a particular reservoir based on data from possible well logs and core samples. For simplicity we choose to use multivariable non-linear regression in the inversion. It shows that this technique is able to identify solutions that are physically sound. However, a more rigorous inversion method might be considered in future implementations. To identify the critical parameters we test the elastic-electrical sensitivity of the various unknown variables involved. The most sensitive parameters identified are then perturbed during the modelling. The mineralogy consists mainly of quartz, which we assume to be spherical and kaolinite. We use the resistivity to calibrate the aspect ratio of the clay grains and estimate the porosity reduction due to compaction. These values are in turn used in inverse modelling of the bulk and shear moduli. The solid minerals make up the inclusion material in the differential effective- medium modelling for both the elastic and electrical properties. Hence, this formulation constitutes a consistent joint elastic-electrical modelling scheme. We achieve good fits between the model results and the laboratory measurements for most of the samples. The reason for the less good fit with some of the samples might be due to measurement errors in the laboratory. This is supported by the observed abnormal stiffness compaction trends associated with those samples.

Projection filtering has been used for many years in seismic processing as a tool to extract a signal out of noisy data. The effectiveness of projection filtering reaches a limit when seismic events are affected by static shifts. Such shifts degrade the lateral coherency of the data, which is the strongest assumption made by projection filtering. We propose an algorithm to estimate projection filters and static shifts simultaneously in order to perform noise attenuation in the presence of static shifts in the data. We then show results on synthetic and real data to demonstrate the denoising capabilities of our algorithm.

In this paper, we examine the influence of a velocity model and microseismic source frequency on microseismic waveforms and event locations. Finite-difference waveform synthetics are generated based on the Cotton Valley hydraulic fracture experiment, where we vary the vertical heterogeneity of the velocity models as well as the microseismic source frequencies. We find that differences between plausible velocity models lead to changes in arrival times of approximately 0.0035 seconds for P-waves and 0.0085 seconds for S-waves. Based on the average P- and S-wave velocities, the difference in the P- and S-wave traveltimes is equivalent to approximately 20 m in location difference. Significant increases in the waveform coda develop with increasing model heterogeneity and increasing source frequency. The presence of signal noise as well as other sources of error (e.g., uncertainty in geophone location) will likely lead to further increase in uncertainty in location error estimates. Thus we note that location error due to incorrect velocity models cannot be ignored.

Hydrocarbon reservoirs are generally located beneath complex geological structures. Frequently, such areas contain seismic diffractors that carry detailed structure information in the order of the seismic wavelength. Therefore, the development of computational facilities capable of detecting diffractor points with a good resolution is desirable but has been a challenge in the area of seismic processing. In this work, we present a method for the detection of diffraction points in the common-offset-gather domain. The method applies a two-class k nearest neighbours (kNN) pattern recognition technique to amplitudes along diffraction traveltime curves to distinguish between diffractions and reflections or noise. While the method, in principle, requires knowledge of the migration velocity field, it is very robust with respect to an erroneous model. Numerical examples using synthetic seismic and field ground-penetrating-radar (GPR) data demonstrate the feasibility of the technique and show its usefulness for automatically mapping diffraction points in a seismic section. In our applications, the method was able to detect all diffractions present in the data and did not produce any false positives.

A sea-bed reflection is used to estimate changes in water layer velocities between time-lapse seismic surveys. Such corrections are crucial in order to obtain high-quality 4D seismic data. This might be a challenge in areas where rough sea-bed topography creates sea-bed diffractions that interfere with the sea-bed reflection, as in several of the northern fields in the Norwegian Sea. These diffractions and diffracted multiples are difficult to attenuate during data processing and become a source of noise in time-lapse data.

In this work we study how cross-correlation analysis of time-lapse seismic data at a sea-bed reflection may be perturbed by the presence of diffractions. The sea-bed topography from the Norne field is used in 2D finite difference modelling to explain some of the observed variation in a water layer time-shift in field data. We find that a rough sea-bed and the diffracted energy it induces cause residual noise on the 4D data. The variation to the water layer time-shift increases with sea-bed complexity and is amplified by interaction with other sources of non-repeatability like water column variations, mis-positioning and strength of the ice scours creating the diffracted energy. Time-shift variations with mis-positioning and velocity changes between the surveys seem to best explain the observed variation in the time-shift for time-lapse seismic field data from Norne.

Curvature of a surface is typically applied in seismic data interpretation; however this work outlines its application to a potential field, specifically aeromagnetic data. The curvature of a magnetic grid (from point data) is calculated by fitting a quadratic surface within a moving window at each grid node. The overall and directional curvatures calculated within this window provide insight into the geometry of the magnetic grid surface and causative sources. Curvature analysis is an in-depth study of both qualitative (graphically) and quantitative (statistically) approaches. This analysis involved the calculation of full, profile and plan curvatures. The magnitude, sign and relative ratios enable the user to define source location and geometry and also discriminate source type; for example, differentiation between a fault and normal polarity dyke. The reliability of the analysis is refined when a priori geological knowledge is available and basic statistics are considered. By allotting a weighting scheme to various statistical populations (e.g., standard deviation), increased detail is extracted on the different lithologies and structures represented by the data set. Furthermore, the curvature's behaviour is analogous to derivative calculation (vertical, horizontal and tilt) by producing a zero value at the source edge and either a local maxima or minima over the source. Application prior to semi-automated methods may help identify correct indices necessary for identification of magnetic sources. Curvature analysis is successfully applied to an aeromagnetic data set over the 2.6–1.85 Ga Paleoproterozoic Wopmay orogen, Northwest Territories, Canada. This area has undergone regional and local-scale faulting and is host to multiple generations of dyke swarms. As the area has been extensively mapped, this data set proved to be an ideal test site.

We conducted a detailed experimental investigation of the effect of CO₂ injection on the electrical conductivity of water bearing porous media, needed for an improved geophysical monitoring of CO₂ storage reservoirs. Therefore, we developed an experimental set-up that allows to investigate electrical characteristics of the injection process as well as the impact of dissolved CO₂ on pore water conductivity. We found that a gaseous, fluid and supercritical pure CO₂ phase bears no relevant conductivity at pressures up to 13 MPa and temperatures up to 50° C. When CO₂ dissolves in pore water, pressure-dependent dissociation processes can double the pore water conductivity, that can be used in leakage detection. This is quantified by an adaptation of Archie’s law. The empirical adaptation and the experimental data are confirmed by combined geochemical-geoelectrical modelling. Furthermore, water-saturated sand samples were investigated while CO₂ displaced the pore water at pressures up to 13 MPa and temperatures up to 40° C. A decrease in electrical conductivity by a factor of up to 33 was measured, corresponding to a residual water saturation of 14–19%. Qualitatively, a decrease was also demonstrated under supercritical conditions. As an integrative interpretation, a conceptual model of electrical rock properties during CO₂ sequestration is presented.

We used a laboratory scale model to study the effects aligned fractures might have on seismic wave propagation at a larger scale in real Earth imaging. Our main objective was to investigate the effect of aligned fractures on seismic P-wave amplitude through the estimation of the induced attenuation. The physical model was constructed from a mixture of epoxy resin and silicon rubber, with inclusions designed to simulate two sets of inclined fractures at an angle of 29.2° with each other. Two-dimensional reflection data were acquired using the pulse and transmission method in three principal directions relative to the fracture strike azimuth with the model submerged in a water tank. We used the Quality Versus Offset (QVO) method, an extension of the classical spectral ratio method for determining attenuation to estimate the induced attenuation (inverse of the seismic quality factor) from the Common Mid Point (CMP) pre-processed gathers. The results of our analysis show that the induced P-wave attenuation is anisotropic, with elliptical (cos2θ) variations with respect to the survey azimuth angle θ. The minor axis of the Q ellipse corresponds to the fracture normal. In this direction, i.e. across the material grain, the attenuation is a maximum. The major axis corresponds to the fracture strike direction (parallel to the material grain) where minimum attenuation occurs. These attenuation results show consistency with the azimuthal anisotropy observed in the stacking velocities in the fractured-layer and are all consistent with the physical model, and thus provide a physical basis for using attenuation anisotropy to derive fracture properties from seismic data.

Velocity dispersion is not usually a problem in surface seismic data processing, as the seismic bandwidth is relatively narrow and thus for most Q values, dispersive effects are not noticeable. However, for highly absorptive bodies, such as the overpressured free gas accumulations associated with some gas hydrates or high-porosity normally pressured gas sands, dispersive effects may be seen. In this work I analyse one such data set from the offshore north-east coast of India. I demonstrate that the effect is measurable and that compensating for it in either data processing or migration can improve the wavelet character, as well as delivering an estimate of the effective Q values in the associated geobody. I also raise the question as to whether velocities derived using low-frequency waveform inversion over such dispersive geobodies are wholly appropriate for migration of full seismic-bandwidth data.

With seismic interferometry or the virtual source method, controlled sources can be redatumed from the Earth’s surface to generate so-called virtual sources at downhole receiver locations. Generally this is done by cross-correlation of the recorded downhole data and stacking over source locations. By studying the retrieved data at zero time lag, downhole illumination conditions that determine the virtual source radiation pattern can be analysed without a velocity model. This can be beneficial for survey planning in time-lapse experiments. Moreover, the virtual source radiation pattern can be corrected by multi-dimensional deconvolution or directional balancing. Such an approach can help to improve virtual source repeatability, posing major advantages for reservoir monitoring. An algorithm is proposed for so-called illumination balancing (being closely related to directional balancing). It can be applied to single-component receiver arrays with limited aperture below a strongly heterogeneous overburden. The algorithm is demonstrated on synthetic 3D elastic data to retrieve time-lapse amplitude attributes.

Most ray-based migration and tomography methods require a certain degree of smoothness of the depth velocity model. Since smoothing changes the velocity model, it is generally impossible to preserve the traveltime between all pairs of points in the model. Using conventional smoothing, the traveltime errors are particularly large at discontinuities in the velocity model. These errors are offset-dependent and they cause errors in both the depth and residual moveout (RMO) of depth migrated images. Here we propose a new method, Preserved-Traveltime Smoothing (PTS) with an objective of preserving traveltimes (and hence depths) at these discontinuities. This is accomplished by smoothing of velocity moments for anisotropic models using a specific cross-correlation filter with the desired smoothness properties. The method is valid for isotropic, transversely isotropic with vertical symmetry axis (VTI) and structural transverse isotropic (STI) models. The variations of the model parameters perpendicular to the symmetry axis of the anisotropy are assumed to be small.

Microzonation studies using ambient noise measurements constitute a promising way for seismic hazard evaluation in urban areas. Among the existing techniques, seismic noise array measurements have become a valuable tool for estimating Vs profiles and thus, the characteristics of a soil structure. Although methods based on analysis of seismic noise are simpler, cheaper and faster than borehole drilling and down-hole or cross-hole logs to derive shear-wave velocity profiles, array deployment requires the use of several stations (broadband or short-period sensors) that are not always available. In this paper, we have compared the results obtained by 10 Hz-vertical-geophone arrays with the results provided by 1 Hz-sensor arrays. Two sites in the Bajo Segura Basin (SE Spain), with different soil characteristics, were chosen for array deployment. The comparison is carried out in terms of dispersion curves by using frequency-wavenumber (f-k) and extended spatial autocorrelation (ESAC) techniques. Both analyses show a good agreement using either 1 Hz sensors or 10 Hz geophones; moreover, they demonstrate that it is possible to extend the analysis in a frequency range much below the natural frequency of the geophones. The results of our study confirm the suitability of standard seismic refraction/reflection equipment also for ambient noise array measurements, which constitutes a cheaper and faster way for investigating soil characteristics.

We propose a full-waveform inversion algorithm using the Gauss-Newton inversion method with active constraint balancing that uses the spatially variant damping factor and source normalized wavefield approach for surface seismic data in the frequency domain. The active constraint balancing technique automatically determines the optimum distribution of damping factors that control the stability and resolution in Gauss-Newton inversion by using a parameter resolution matrix and spread function analysis. Through numerical experiments, we present that the active constraint balancing scheme provides stable inversion results without a severe loss of resolution compared with the conventional Gauss-Newton method. The reconstructed image using the active constraint balancing method more closely resembles the true image for the region with low sensitivity. Also, the estimated value converges faster to the smaller RMS error level than those estimated by the conventional Gauss-Newton method. We also implement the normalized wavefield method to overcome the lack of precise knowledge on the source. The source normalized wavefield approach effectively removes the potential inversion errors from source estimation because the source spectrum is eliminated during the normalization procedure. Our inversion algorithm, using the source normalization scheme, provides excellent inversion results even though the data are generated by two slightly different source wavelets. We present that the frequency selection scheme proposed by Sirgue and Pratt, which is based on the average amplitude of the whole received data, provides a useful guideline for selecting the proper frequencies for our inversion. Our novel inversion algorithm successfully reconstructs the velocity model within 10–30 iterations despite its starting from a homogeneous or linearly increasing velocity model. In addition, for testing the performance of our inversion algorithm on a more complicated structure, we apply the algorithm to the SEG/EAGE overthrust model. Successful inversion is achieved as the reconstructed image approaches the true model with the consistently converging RMS error even though insufficient data are used.

The orientation of three-component borehole geophones used for recording during a microseismic monitoring experiment is estimated. The standard technology for deploying multi-component geophones in a deep borehole is wireline-based, in which the azimuthal rotation of the geophone string cannot be controlled. Each receiver can have a different rotation angle that is compensated by the particle motion analysis of the direct P-wave arrivals, picked from a walk-around VSP carried out in the proximity of the well. Knowing the orientation of borehole receivers is critical, as inaccuracies lead to systematic errors in determining the hypocentral coordinates of microseismic events. Additional errors arise from over-simplifications of P- and S-wave velocity Earth models.

In this paper, we propose a tomographic approach for improving the orientation estimates of borehole receivers based on hodogram analysis. The initial velocity model built from well logs and upholes is refined by 3D tomographic inversion of walk-around VSP data and some string shots fired in a nearby borehole. Taking into account ray bending, the estimated errors due to local velocity anomalies can be reduced. This makes our estimates of fracture orientation and microseismic hypocentres more reliable when borehole receivers are used in passive seismic surveys.

Building an accurate initial velocity model for full waveform inversion (FWI) is a key issue to guarantee convergence of full waveform inversion towards the global minimum of a misfit function. In this study, we assess joint refraction and reflection stereotomography as a tool to build a reliable starting model for frequency-domain full waveform inversion from long-offset (i.e., wide-aperture) data. Stereotomography is a slope tomographic method that is based on the inversion of traveltimes and slopes of locally-coherent events in a data cube. One advantage of stereotomography compared to conventional traveltime reflection tomography is the semi-automatic picking procedure of locally-coherent events, which is easier than the picking of continuous events, and can lead to a higher density of picks. While conventional applications of stereotomography only consider short-offset reflected waves, we assess the benefits provided by the joint inversion of reflected and refracted arrivals. Introduction of the refracted waves allows the construction of a starting model that kinematically fits the first arrivals, a necessary requirement for full waveform inversion. In a similar way to frequency-domain full waveform inversion, we design a multiscale approach of stereotomography, which proceeds hierarchically from the wide-aperture to the short-aperture components of the data, to reduce the non-linearity of the stereotomographic inversion of long-offset data. This workflow which combines stereotomography and full waveform inversion, is applied to synthetic and real data case studies for the Valhall oil-field target. The synthetic results show that the joint refraction and reflection stereotomography for a 24-km maximum offset data set provides a more reliable initial model for full waveform inversion than reflection stereotomography performed for a 4-km maximum offset data set, in particular in low-velocity gas layers and in the deep part of a structure below a reservoir. Application of joint stereotomography, full waveform inversion and reverse-time migration to real data reveals that the FWI models and the reverse-time migration images computed from the stereotomography model shares several features with FWI velocity models and migrated images computed from an anisotropic reflection-traveltime tomography model, although stereotomography was performed in the isotropic approximation. Implementation of anisotropy in joint refraction and reflection stereotomography of long-offset data is a key issue to further improve the accuracy of the method.

A reconstruction method known as Projection Onto Convex Sets (POCS) is an effective, uncomplicated and robust method for the recovery of irregularly missing seismic traces. However, slow convergence of the POCS reconstruction method could jeopardize its computational appeal. For this reason, we investigate the performance of the POCS reconstruction method in terms of different threshold schedules and present a new data driven threshold that leads to an efficient implementation of the POCS method. In particular, we show that high quality solutions can be obtained in a few iterations. In addition, we address an important issue with the classical implementations of POCS reconstruction in that they cannot interpolate regularly missing data. To solve this problem, we introduce a masking operator that is based on a dominant dip scanning method into the POCS iteration. At the end, we present a variant of the POCS method that permits de-noising seismic volumes during the reconstruction stage. This is achieved by defining a weighted trace re-insertion strategy that alleviates the influence of noisy traces in the final reconstruction of the seismic volume. We show the effectiveness of the proposed method using synthetic and field data.

The Amer Lake area is located within the Churchill Structural Province in the Kivalliq Region of Nunavut, approximately 160 km north-west of Baker Lake. Two distinct geophysical-geological entities are structurally intercalated: an Archean mixed granitoid gneiss – metasedimentary-metavolcanic basement and the unconformably overlying Paleoproterozoic Amer Group metasediments. From east of Amer Lake stretching toward the south-west, these two entities form the Amer fold and thrust belt. At the north-east end of this belt, high-resolution aeromagnetic data define a distinctive oval shape that has been interpreted as a south-west trending doubly plunging synform. The outcrop within the interior of this structure is sparse resulting in limited structural data and speculative geological interpretations with multiple geometries possible. The high-resolution aeromagnetic data compiled through an industry-government consortium and newly acquired detailed gravity profiles were modelled to provide constraints on the geometry of this synform.

We document a geophysical-geological feedback process whereby the available geological and geophysical data were used to derive constraints on inversion models for the synform. Starting with available limited litho-structural data the presence of a double plunging synform was directly inferred from the aeromagnetic data. Segments of the aeromagnetic data have 2D morphology and so can be modelled using a simple parametric 2D dipping slab inversion approach. Models of profiles extracted from the aeromagnetic data were used to provide preliminary dip and magnetic susceptibility constraints for the Three Lakes mudstone with iron formation and the Five Mile Lake basalt. Landsat imagery outlined the spatial limits of the stratigraphically underlying, non-magnetic Ayagaq quartzite. Incorporating these outputs as bounds in the input / reference model for a UBC-GIF 3D magnetic inversion helped to accentuate the geological structure in the output mesh: an enhanced inversion that incorporates both geological and geophysical constraints. The validity of the resulting inversion model was tested by computing 2D forward models of the gravity profile data. The inversion model generated by this study emphasizes the importance of integrating information from as many knowledge sources as one can find. More trust can be placed on forward and inversion models where there is agreement among all data sets and a coherency of structural style.

For an accurate interpretation of seismic data, multiple-free data are of great value. Removing surface multiples and interbed multiples proves to be challenging in many cases. The nowadays widely used method of Surface-Related Multiple Elimination (SRME) has lately been redefined as a full-waveform inversion process, resulting in the method of Estimation of Primaries by Sparse Inversion (EPSI). The new method is shown to be more accurate than the former method in several situations, because it estimates primaries such that they, together with their multiples, explain the input data. Its main advantage is that the minimum energy assumption in traditional multiple subtraction is avoided. The SRME methodology has been extended to the case of internal multiples by several authors, however, the involved subtraction of predicted multiples is probably even more challenging than for the surface-multiple case. Therefore, in this paper the EPSI method is generalized to remove both surface and interbed multiples. As in previous implementations of internal multiple removal based on data-driven convolution, the newly proposed scheme requires some knowledge about the subsurface: the data should be divided into (macro) layers and appropriate time windows must be selected. The method is tested on two 2D synthetic datasets to prove its viability. Furthermore, application to a 2D field dataset showed improved accuracy compared to conventional prediction and subtraction.

The attenuation of coherent and random noise still poses technical challenges in seismic data processing, especially in onshore environments. Multichannel Singular Spectrum Analysis (MSSA) is an existing and effective technique for random-noise reduction. By incorporating a randomizing operator into MSSA, this modification creates a new and powerful filtering method that can attenuate both coherent and random noise simultaneously. The key of the randomizing operator exploits the fact that primary events after NMO are relatively horizontal. The randomizing operator randomly rearranges the order of input data and reorganizes coherent noise into incoherent noise but has a minimal effect on nearly horizontal primary reflections. The randomizing process enables MSSA to suppress both coherent and random noise simultaneously. This new filter, MSSARD (MSSA in the randomized domain) also resembles a combination of eigenimage and Cadzow filters. I start with a synthetic data set to illustrate the basic concept and apply MSSARD filtering on a 3D cross-spread data set that was severely contaminated with ground roll and scattered noise. MSSARD filtering gives superior results when compared with a conventional 3D f-k filter. For a random-noise example, the application of MSSARD filtering on time-migrated offset-vector-tile (OVT) gathers also produces images with higher signal-to-noise ratios than a conventional f-xy deconvolution filter.

Microseismic monitoring, particularly the monitoring of hydraulic fracturing in gas- and oil-bearing shales, has developed significantly over the last ten years. Early work focused on the location of microseismic events but more recently there have been attempts to extract more of the information afforded by this rich data source. In particular, the recovery of the frequency-magnitude distribution, which is expected to follow a Gutenberg-Richter distribution, may provide insights into the prevailing effective stress regime in the vicinity of the events. This stress regime varies with distance from the hydraulic fracturing: at the propagating fracture one expects conditions for tensile or shear failure, away from the fracture one may broadly expect microseismicity associated with pre-existing weakness in the rock, occurring at effective stress conditions close to the conditions existing prior to the treatment.

All geophysical experiments are detection limited and the microseismic monitoring case does not differ in this regard. In constructing a statistical indicator such as the distribution of moment magnitudes we would like the estimate to be robust and use as much of the data as possible. In analysing earthquake catalogues the predominant practise is to determine a magnitude of completeness denoting the detection limit of the catalogue. This approach defines a minimum magnitude above which all events are thought to have been reliably recorded. In effect, this imposes an artificial, conservative detection limit to replace the unknown detection limit of the catalogue. We present the case of an arbitrary detection limit and introduce an approach from astronomy that is particularly suited to the single-well observing geometry most prevalent in hydraulic fracture monitoring.

We calculate b-values for a set of event magnitudes from the Barnett Shale formation, where multiple stimulation treatments were applied in a pair of wells (‘zipper frac’) followed by a four-stage treatment in a third well and find significant variations in the b-value between the pumped stages.

Randomized source-encoding has recently been proposed as a way to dramatically reduce the costs of full waveform inversion. The main idea is to replace all sequential sources by a small number of simultaneous sources. This introduces random cross-talk in model updates and special stochastic optimization strategies are required to deal with this. Two problems arise with this approach: i) source-encoding can only be applied to fixed-spread acquisition setups and ii) stochastic optimization methods tend to converge very slowly, relying on averaging to suppress the cross-talk. Although the slow convergence is partly off-set by a low iteration cost, we show that conventional optimization strategies are bound to outperform stochastic methods in the long run. In this paper we argue that we do not need randomized source-encoding to reap the benefits of stochastic optimization and we review an optimization strategy that combines the benefits of both conventional and stochastic optimization. The method uses a gradually increasing batch of sources. Thus, iterations are initially very cheap and this allows the method to make fast progress in the beginning. As the batch-size grows, the method behaves like conventional optimization, allowing for fast convergence. Stylized numerical examples suggest that the stochastic and hybrid methods perform equally well with and without source-encoding and that the hybrid method outperforms both conventional and stochastic optimization. The method does not rely on source-encoding techniques and can thus be applied to marine data. We illustrate this on a realistic synthetic model.

The fast generalized Fourier transform algorithm is extended to two-dimensional data cases. The algorithm provides a fast and non-redundant alternative for the simultaneous time-frequency and space-wavenumber analysis of data with time-space dependencies. The transform decomposes data based on local slope information and therefore making it possible to extract the weight function based on dominant dips from alias-free low frequencies. By projecting the extracted weight function to alias-contaminated high frequencies and utilizing a least-squares fitting algorithm, a beyond-alias interpolation method is accomplished. Synthetic and real data examples are provided to examine the performance of the proposed interpolation method.

A passive seismic experiment was conducted in April/May 2010 in the Albertine Graben region in Uganda to record low-frequency seismic signals and explore the possibility of their exploitation in this area as a direct hydrocarbon indicator (DHI). Recordings were made at locations directly overlying both hydrocarbon and water-bearing strata within the sedimentary basin as well as reference sites external to the basin, directly on the basement. Contrary to findings published in some literature to date, we found that spatial variations in the analysed wavefield parameters correlate with the underlying geology rather than the presence or absence of hydrocarbons. Inversion of the surface-wave (fundamental mode) dispersion curve as well as the observed horizontal-to-vertical spectral ratio of both surface and body waves provide evidence that the observed spectral variations can be explained solely by a simple layered/gradient velocity model, without the presence of any kind of anomaly that could be attributed exclusively to a hydrocarbon reservoir.

Consequently, it is recommended that knowledge of the geological and velocity structure is sought when analysing passive low-frequency seismic data sets. This is a fundamental prerequisite in order to guard against misinterpretation of the spatial variation of seismic derived attributes as DHIs.

We present a joint inversion scheme that couples P-wave refraction and seismic surface-wave data for a layered subsurface. An algorithm is implemented with a damped least-squares approach. The estimated parameters are S- and P-wave velocities and layer thicknesses, while densities are assumed constant during inversion. The coupling is both geometric and physical: layer thicknesses are the same for S- and P-wave velocity profiles and P-wave velocities enter in both forward algorithms. Sensitivity analysis, performed on synthetic data, reveals that surface-wave dispersion curves can be sensitive also to P-wave velocity of some layers (especially for Poisson's ratio values smaller than about 0.35), allowing synergic resolution of this parameter. Applications on both synthetic and field data show that the proposed approach mitigates the hidden layer problem of seismic refraction and leads to more accurate results than individual inversions also for surface waves. Additional constraints on the objective function on a priori Poisson's ratio values allow unrealistic and not admissible V_P and V_S values to be avoided; such constraints were applied in one field case considering the a priori information available about water-table depth. It is also shown that estimation of porosity can help the selection of the proper constraint on a priori Poisson's ratio.

Traveltime information is crucial for parameter estimation, especially if the medium is described by a set of anisotropy parameters. We can efficiently estimate these parameters if we are able to relate them analytically to traveltimes, which is generally hard to do in inhomogeneous media. I develop traveltime approximations for transversely isotropic media with a horizontal symmetry axis (HTI) as simplified and even linear functions of the anisotropy parameters. This is accomplished by perturbing the solution of the HTI eikonal equation with respect to the anellipticity parameter, η and the azimuth of the symmetry axis (typically associated with the fracture direction) from a generally inhomogeneous, elliptically anisotropic background medium. Such a perturbation is convenient since the elliptically anisotropic information might be obtained from well velocities in HTI media. Thus, we scan for only η and the symmetry-axis azimuth. The resulting approximations can provide a reasonably accurate analytical description of the traveltime in a homogenous background compared to other published moveout equations. They also help extend the inhomogenous background isotropic or elliptically anisotropic models to an HTI one with a smoothly variable η and symmetry-axis azimuth.

The purpose of this paper is to study the possibility of performing practically stable and efficient frequency-space (f−x) wavefield extrapolation for the application of seismic imaging and datuming via infinite impulse response (IIR) filters. The model reduction control theory was adopted to design such IIR f−x extrapolation filters. The model reduction theory reduces the order of a given order system which, in this case, involves reducing a finite impulse response (FIR) f−x extrapolation filter system into an IIR f−x extrapolation filter system. This theory relies on decomposing the states of the given filter system into strong and weakly coupled sub-systems, and then eliminating the weakly coupled states via singular value decomposition of the Hankel and the impulse response Gramian matrices. Simulation results indicate that IIR f−x filters can be obtained, which are stable from an IIR filter design point of view. Simulations also indicate that stable seismic impulse responses and synthetics can be obtained with a reduced system model order and, hence, less computational efforts with respect to the number of complex multiplications and additions per output sample. It is hoped that this study will open new possibilities for researchers to reconsider designing IIR f−x explicit depth extrapolation filters due to their expected computational savings and wavenumber response accuracy, when compared to the FIR f−x explicit depth extrapolation filters.

Many natural phenomena, including geologic events and geophysical data, are fundamentally nonstationary - exhibiting statistical variation that changes in space and time. Time-frequency characterization is useful for analysing such data, seismic traces in particular.

We present a novel time-frequency decomposition, which aims at depicting the nonstationary character of seismic data. The proposed decomposition uses a Fourier basis to match the target signal using regularized least-squares inversion. The decomposition is invertible, which makes it suitable for analysing nonstationary data. The proposed method can provide more flexible time-frequency representation than the classical S transform. Results of applying the method to both synthetic and field data examples demonstrate that the local time-frequency decomposition can characterize nonstationary variation of seismic data and be used in practical applications, such as seismic ground-roll noise attenuation and multicomponent data registration.

We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media.

Carbon capture and storage is a viable greenhouse gas mitigation technology and the Sleipner CO₂ sequestration site in the North Sea is an excellent example. Storage of CO₂ at the Sleipner site requires monitoring over large areas, which can successfully be accomplished with time lapse seismic imaging. One of the main goals of CO₂ storage monitoring is to be able to estimate the volume of the stored CO₂ in the reservoir. This requires a parametrization of the subsurface as exact as possible. Here we use elastic 2D time-domain full waveform inversion in a time lapse manner to obtain a P-wave velocity constrain directly in the depth domain for a base line survey in 1994 and two post-injection surveys in 1999 and 2006. By relating velocity change to free CO₂ saturation, using a rock physics model, we find that at the considered location the aquifer may have been fully saturated in some places in 1999 and 2006.

Seismic wave propagation in transversely isotropic (TI) media is commonly described by a set of coupled partial differential equations, derived from the acoustic approximation. These equations produce pure P-wave responses in elliptically anisotropic media but generate undesired shear-wave components for more general TI anisotropy. Furthermore, these equations suffer from instabilities when the anisotropy parameter ε is less than δ. One solution to both problems is to use pure acoustic anisotropic wave equations, which can produce pure P-waves without any shear-wave contaminations in both elliptical and anelliptical TI media. In this paper, we propose a new pure acoustic transversely isotropic wave equation, which can be conveniently solved using the pseudospectral method. Like most other pure acoustic anisotropic wave equations, our equation involves complicated pseudo-differential operators in space which are difficult to handle using the finite difference method. The advantage of our equation is that all of its model parameters are separable from the spatial differential and pseudo-differential operators; therefore, the pseudospectral method can be directly applied. We use phase velocity analysis to show that our equation, expressed in a summation form, can be properly truncated to achieve the desired accuracy according to anisotropy strength. This flexibility allows us to save computational time by choosing the right number of summation terms for a given model. We use numerical examples to demonstrate that this new pure acoustic wave equation can produce highly accurate results, completely free from shear-wave artefacts. This equation can be straightforwardly generalized to tilted TI media.

The relation between vertical and horizontal slownesses, better known as the dispersion relation, for transversely isotropic media with a tilted symmetry axis (TTI) requires solving a quartic polynomial equation, which does not admit a practical explicit solution to be used, for example, in downward continuation. Using a combination of the perturbation theory with respect to the anelliptic parameter and Shanks transform to improve the accuracy of the expansion, we develop an explicit formula for the vertical slowness that is highly accurate for all practical purposes. It also reveals some insights into the anisotropy parameter dependency of the dispersion relation including the low impact that the anelliptic parameter has on the vertical placement of reflectors for a small tilt in the symmetry angle.

I introduce a new explicit form of vertical seismic profile (VSP) traveltime approximation for a 2D model with non-horizontal boundaries and anisotropic layers. The goal of the new approximation is to dramatically decrease the cost of time calculations by reducing the number of calculated rays in a complex multi-layered anisotropic model for VSP walkaway data with many sources. This traveltime approximation extends the generalized moveout approximation proposed by Fomel and Stovas. The new equation is designed for borehole seismic geometry where the receivers are placed in a well while the sources are on the surface. For this, the time-offset function is presented as a sum of odd and even functions. Coefficients in this approximation are determined by calculating the traveltime and its first- and second-order derivatives at five specific rays. Once these coefficients are determined, the traveltimes at other rays are calculated by this approximation. Testing this new approximation on a 2D anisotropic model with dipping boundaries shows its very high accuracy for offsets three times the reflector depths. The new approximation can be used for 2D anisotropic models with tilted symmetry axes for practical VSP geometry calculations. The new explicit approximation eliminates the need of massive ray tracing in a complicated velocity model for multi-source VSP surveys. This method is designed not for NMO correction but for replacing conventional ray tracing for time calculations.

Reservoir characterization involves describing different reservoir properties quantitatively using various techniques in spatial variability. Nevertheless, the entire reservoir cannot be examined directly and there still exist uncertainties associated with the nature of geological data. Such uncertainties can lead to errors in the estimation of the ultimate recoverable oil. To cope with uncertainties, intelligent mathematical techniques to predict the spatial distribution of reservoir properties appear as strong tools. The goal here is to construct a reservoir model with lower uncertainties and realistic assumptions. Permeability is a petrophysical property that relates the amount of fluids in place and their potential for displacement. This fundamental property is a key factor in selecting proper enhanced oil recovery schemes and reservoir management. In this paper, a soft sensor on the basis of a feed-forward artificial neural network was implemented to forecast permeability of a reservoir. Then, optimization of the neural network-based soft sensor was performed using a hybrid genetic algorithm and particle swarm optimization method. The proposed genetic method was used for initial weighting of the parameters in the neural network. The developed methodology was examined using real field data. Results from the hybrid method-based soft sensor were compared with the results obtained from the conventional artificial neural network. A good agreement between the results was observed, which demonstrates the usefulness of the developed hybrid genetic algorithm and particle swarm optimization in prediction of reservoir permeability.

We generalize the classical theory of acoustoelasticity to the porous case (one fluid and a solid frame) and finite deformations. A unified treatment of non-linear acoustoelasticity of finite strains in fluid-saturated porous rocks is developed on the basis of Biot’s theory. A strain-energy function, formed with eleven terms, combined with Biot’s kinetic and dissipation energies, yields Lagrange’s equations and consequently the wave equation of the medium. The velocities and dissipation factors of the P- and S-waves are obtained as a function of the 2nd- and 3rd-order elastic constants for hydrostatic and uniaxial loading. The theory yields the limit to the classical theory if the fluid is replaced with a solid with the same properties of the frame. We consider sandstone and obtain results for open-pore jacketed and closed-pore jacketed ‘gedanken’ experiments. Finally, we compare the theoretical results with experimental data.

In this paper we present a case history of seismic reservoir characterization where we estimate the probability of facies from seismic data and simulate a set of reservoir models honouring seismically-derived probabilistic information. In appraisal and development phases, seismic data have a key role in reservoir characterization and static reservoir modelling, as in most of the cases seismic data are the only information available far away from the wells. However seismic data do not provide any direct measurements of reservoir properties, which have then to be estimated as a solution of a joint inverse problem. For this reason, we show the application of a complete workflow for static reservoir modelling where seismic data are integrated to derive probability volumes of facies and reservoir properties to condition reservoir geostatistical simulations. The studied case is a clastic reservoir in the Barents Sea, where a complete data set of well logs from five wells and a set of partial-stacked seismic data are available. The multi-property workflow is based on seismic inversion, petrophysics and rock physics modelling. In particular, log-facies are defined on the basis of sedimentological information, petrophysical properties and also their elastic response. The link between petrophysical and elastic attributes is preserved by introducing a rock-physics model in the inversion methodology. Finally, the uncertainty in the reservoir model is represented by multiple geostatistical realizations. The main result of this workflow is a set of facies realizations and associated rock properties that honour, within a fixed tolerance, seismic and well log data and assess the uncertainty associated with reservoir modelling.

Understanding petrographical, geochemical and electrical properties of rocks is essential for investigating minerals. This paper presents a study of the petrographical, geochemical and A.C. electrical properties of carbonate rock samples. The samples collected show six lithostratigraphic rock units.

Electrical properties were measured using a non-polarizing electrode at room temperature (∼20°C) and a relative atmospheric humidity of ∼50% by weight in the frequency range from 42 Hz to 5 MHz. The difference in electrical properties between the samples was attributed to the change in composition and texture between the samples. Electrical properties generally change with many factors (grain size, chemical composition, grain shape and facies). The dielectric constant decreases with frequency and increases with conductor composition. The conductivity increases with the increase of conductor paths between electrodes. Many parameters can contribute to the same result of the electrical properties.

The main objective of the present study is to shed more light on the relation between the texture and geochemical composition of measured samples (carbonates that contain clays and quartz grains) through electrical laboratory measurements (conductivity and dielectric constant as a function of frequency).

Simulation of induction logging responses in formations with large conductivity contrasts is an important but challenging problem due to the singularity of a linear system caused by large contrasts. Also, three-dimensional (3D) analysis of complex geophysical structures usually encounters high computational demands. In this paper, a pre-corrected fast Fourier transform (pFFT)-accelerated integral equation method is applied to overcome these difficulties. In the approach, the entire formation is included in the solution domain. The volume integral equation is set up in the region based on the fact that the total field is the summation of the excitation field and the secondary field. The emitted field by the transmitter coil (treated as a magnetic dipole) is regarded as the excitation of the system. Then the method of moments (MoM) is used to solve the integral equation. To reduce the high computational requirements of the MoM, the pFFT method is used to speed up the solution of the matrix equation and reduce the memory requirement as well. The resultant method is capable of computing induction logging problems involving large and complex formations. For problems with high conductivity contrasts, the solution of the matrix equation usually converges very slow or even fails to converge due to the large condition number of the coefficient matrix. To overcome this difficulty, an incomplete LU pre-conditioner is used to significantly speed up the convergence of the matrix equation, thus further reducing the computation time. Numerical results show that the present method is efficient and flexible for 3D simulation of induction logging and is specifically superior for problems with high conductivity contrasts.

Although metal detectors remain the workhorses of humanitarian demining, it is well established that the performance of both continuous wave (frequency domain) and pulsed induction (time domain) detectors can be severely compromised by so-called ‘soil-effects’. Generally, problem soils reduce the signal-to-noise ratio and increase the false-detection rate. In certain locations, the soil-effect is so severe as to render the detector practically inoperable. The current study is part of an ongoing international effort to establish and quantify the influence of soil electromagnetic properties on the operation of metal detectors and related sensor technologies. In particular, we examine the relative influence of soil electrical conductivity, magnetic susceptibility and associated frequency dependence on the time domain electromagnetic (TDEM) response of pulsed induction metal detectors and related small-scale TDEM sensors.

Electromagnetic signals from distant radio transmitters in the frequency range 15–250 kHz were measured to model an electrical resistivity structure beneath 7 profiles in the vicinity of the Karinu limestone quarry in Estonia with the aim to map the extent of the economically exploitable limestone. The resistivity models from a 2D inversion of determinant resistivity and phase values using an Occam type of regularization contained reasonably accurate information about the geometry, namely depth to the top and the bottom of the target high-resistivity limestone. The resistivity models correlated well with existing geological evidences as well as information from closely located boreholes. However, the sharp lithological boundaries seen in the boreholes were not resolved exactly in the resistivity models. This is probably because of the smoothing regularization used in the inversion process. Combined use of borehole data together with resistivity models resulted in two major geological interpretations; a) towards the western part of the existing limestone quarry there is a NNW to NS striking fault, covered by post-glacial sediments, b) a potential cost-effective exploitable area containing high quality highly resistive limestone is located south of the existing quarry. This case study shows the applicability of the reasonably fast radio magnetotelluric (RMT) method for the exploration of near-surface resources.

The streaming potential across a porous medium is induced by a fluid flow due to an electric double layer between a solid and a fluid. When an acoustic wave propagates through a porous medium, the wave pressure generates a relative movement between the solid and the fluid. The moving charge in the fluid induces an electric field and seismoelectric conversion. In order to investigate the streaming potential and the seismoelectric conversion in the same rock sample, we conduct measurements with Berea sandstone saturated by NaCl solutions with different conductivities. We measure the electric voltage (streaming potential) across a cylindrical sample in NaCl solutions with different conductivities and under different pressures to determine the DC coupling coefficients. We also measure the seismoelectric signals induced by acoustic waves with a Berea sandstone plate at different frequencies and solution conductivities. The pressures of the acoustic waves are calibrated with a standard hydrophone (Brüel & 8103) at different frequencies (15–120 kHz). We calculate the quantitative coupling coefficients of the seismoelectric conversion at DC and at high frequencies with samples saturated by solutions with different conductivities. When the Berea sandstone sample is saturated by the NaCl solution with 0.32 mS/m in conductivity, for example, the DC and seismoelectric coupling coefficients at 15 kHz are 0.024 μV/Pa and 0.019 μV/Pa, respectively. The seismoelectric coupling coefficient is an important and helpful parameter for designing a seismoelectric tool. More experimental measurements of seismoelectric coupling coefficients in the frequency range of 100 Hz to 15 kHz are needed in the future.