Time‐lapse pre‐stack seismic data registration and inversion for CO2 sequestration study at Cranfield

Pre‐stack seismic data are indicative of subsurface elastic properties within the amplitude versus offset characteristic and can be used to detect elastic rock property changes caused by injection. We perform time‐lapse pre‐stack 3‐D seismic data analysis for monitoring sequestration at Cranfield. The time‐lapse amplitude differences of Cranfield datasets are found entangled with time‐shifts. To disentangle these two characters, we apply a local‐correlation‐based warping method to register the time‐lapse pre‐stack datasets, which can effectively separate the time‐shift from the time‐lapse seismic amplitude difference without changing the original amplitudes. We demonstrate the effectiveness of our registration method by evaluating the inverted elastic properties. These inverted time‐lapse elastic properties can be reliably used for monitoring plumes.     

Effects of variations in fluid properties and fracture geometry on dispersion,anisotropy, and reflection in media with planar fractures

Our objective was to discover the effect of variations in fluid properties and fracture geometry on the velocity of seismic wave propagation in fluid‐saturated media with parallel planar fractures. We used numerical models calculated by analytical solutions to examine the behaviour of P‐wave phase velocity dispersion in the normal direction to layering, in non‐porous and porous media with planar fractures. We also examined the anisotropy of low frequency phase and group velocities of fast and slow P‐waves and angular‐dependent reflection coefficients in media with planar fractures, under conditions of saturation by fluids with varying bulk moduli, densities, and fracture apertures. We defined several parametre , , and characterising dispersion, characterising anisotropy, characterising the difference between fast and slow modes, and R₀ and characterising reflection. Our results show that the behaviour of dispersion shows wider stopbands in the case of gas saturation. Concavity indicator of dispersion for gas saturation was greater than that for liquid saturation and is usually greater than one. Anisotropy is more sensitive to bulk modulus contrast than to density contrast between the solid and the fluid, and is more sensitive to density contrast than to bulk modulus contrast. The case of gas saturation usually had a greater negative R₀ and a greater value of compared with those of brine and heavy and light oil saturations. Our results are helpful in distinguishing fluid types saturating geophysical fractures and estimating the aperture and spacing of planar fractures. In seismic exploration, bulk modulus and fluid density can provide useful information in distinguishing among brine, oil, and gas; fracture geometry is important to estimate the permeability of reservoirs.     

A fast algorithm for 3D azimuthally anisotropic velocity scan

The conventional velocity scan can be computationally expensive for large‐scale seismic data sets, particularly when the presence of anisotropy requires multiparameter scanning. We introduce a fast algorithm for 3D azimuthally anisotropic velocity scan by generalizing the previously proposed 2D butterfly algorithm for hyperbolic Radon transforms. To compute semblance in a two‐parameter residual moveout domain, the numerical complexity of our algorithm is roughly as opposed to of the straightforward velocity scan, with N being the representative of the number of points in a particular dimension of either data space or parameter space. Synthetic and field data examples demonstrate the superior efficiency of the proposed algorithm.     

Non‐convex compressed sensing with frequency mask for seismic data reconstruction and denoising

Compressed Sensing has recently proved itself as a successful tool to help address the challenges of acquisition and processing seismic data sets. Compressed sensing shows that the information contained in sparse signals can be recovered accurately from a small number of linear measurements using a sparsity‐promoting regularization. This paper investigates two aspects of compressed sensing in seismic exploration: (i) using a general non‐convex regularizer instead of the conventional one‐norm minimization for sparsity promotion and (ii) using a frequency mask to additionally subsample the acquired traces in the frequency‐space () domain. The proposed non‐convex regularizer has better sparse recovery performance compared with one‐norm minimization and the additional frequency mask allows us to incorporate a priori information about the events contained in the wavefields into the reconstruction. For example, (i) seismic data are band‐limited; therefore one can use only a partial set of frequency coefficients in the range of reflections band, where the signal‐to‐noise ratio is high and spatial aliasing is low, to reconstruct the original wavefield, and (ii) low‐frequency characteristics of the coherent ground rolls allow direct elimination of them during reconstruction by disregarding the corresponding frequency coefficients (usually bellow 10 Hz) via a frequency mask. The results of this paper show that some challenges of reconstruction and denoising in seismic exploration can be addressed under a unified formulation. It is illustrated numerically that the compressed sensing performance for seismic data interpolation is improved significantly when an additional coherent subsampling is performed in the domain compared with the domain case. Numerical experiments from both simulated and real field data are included to illustrate the effectiveness of the presented method.     

Experimental quantification of the seismoelectric transfer function and its dependence on conductivity and saturation in loose sand

Under certain circumstances, seismic propagation within porous media may be associated to the conversion of mechanical energy to electromagnetic energy, which is known as a seismo‐electromagnetic phenomenon. The propagation of fast compressional P‐waves is more specifically associated to the manifestations of a seismoelectric field linked to the fluid flows within the pores. The analysis of seismoelectric phenomena, which requires the combination of the theory of electrokinetics and Biot's theory of poroelasticity, provides us with transfer function that links the coseismic seismoelectric field E to the seismic acceleration . To measure the transfer function, we have developed an experimental setup enabling seismoelectric laboratory observation in unconsolidated quartz sand within the kilohertz range. The investigation focused on the impact of fluid conductivity and water saturation over the coseismic seismoelectric field. During the experiment, special attention was given to the accuracy of electric field measurements. We concluded that, to obtain a reliable estimate of the electric field amplitude, the dipole from which the potential differences are measured should be of much smaller length than the wavelength of the propagating seismic field. Time‐lapse monitoring of the seismic velocities and seismoelectric transfer functions were performed during imbibition and drainage experiments. In all cases, the quantitative analysis of the seismoelectric transfer function was in good agreement with theoretical predictions. While investigating saturation variations from full to residual water saturation, we showed that the ratio undergoes a switch in polarity at a particular saturation , which also implies a sign change of the filtration, traducing a reversal of the relative fluid displacement with respect to the frame. This sign change at critical saturation stresses a particular behaviour of the poroelastic medium: the dropping of the coseismic electric field to zero traduces the absence of relative pore/fluid displacements representative of a Biot dynamically compatible medium. We concluded from our experimental study in loose sand that the measurements of the coseismic seismoelectric coupling may provide information on fluid distribution within the pores and that the reversal of the seismoelectric field may be used as an indicator of the dynamically compatible state of the medium.     

Identifying gravity anomalies caused by granitic intrusions in Nanling mineral district,China: a multifractal perspective

Several power‐law relationships of geophysical potential fields have been discussed recently with renewed interests, including field value–distance () and power spectrum–wavenumber () models. The singularity mapping technique based on the density/concentration–area (C–A) power‐law model is applied to act as a high‐pass filter for extracting gravity and magnetic anomalies regardless of the background value and to detect the edges of gravity or magnetic sources with the advantage of scale invariance. This is demonstrated on a synthetic example and a case study from the Nanling mineral district, Southern China. Compared with the analytic signal amplitude and total horizontal gradient methods, the singularity mapping technique provides more distinct and less noisy boundaries of granites than traditional methods. Additionally, it is efficient for enhancing and outlining weak anomalies caused by concealed granitic intrusions, indicating that the singularity method based on multifractal analysis is a potential tool to process gravity and magnetic data.     

Suppression of near‐surface scattered body‐to‐surface waves: a steerable and nonlinear filtering approach

We present an approach based on local‐slope estimation for the separation of scattered surface waves from reflected body waves. The direct and scattered surface waves contain a significant amount of seismic energy. They present great challenges in land seismic data acquisition and processing, particularly in arid regions with complex near‐surface heterogeneities (e.g., dry river beds, wadis/large escarpments, and karst features). The near‐surface scattered body‐to‐surface waves, which have comparable amplitudes to reflections, can mask the seismic reflections. These difficulties, added to large amplitude direct and back‐scattered surface (Rayleigh) waves, create a major reduction in signal‐to‐noise ratio and degrade the final sub‐surface image quality. Removal of these waves can be difficult using conventional filtering methods, such as an filter, without distorting the reflected signal. The filtering algorithm we present is based on predicting the spatially varying slope of the noise, using steerable filters, and separating the signal and noise components by applying a directional nonlinear filter oriented toward the noise direction to predict the noise and then subtract it from the data. The slope estimation step using steerable filters is very efficient. It requires only a linear combination of a set of basis filters at fixed orientation to synthesize an image filtered at an arbitrary orientation. We apply our filtering approach to simulated data as well as to seismic data recorded in the field to suppress the scattered surface waves from reflected body waves, and we demonstrate its superiority over conventional techniques in signal preservation and noise suppression.     

Spectral decomposition and de‐noising via time‐frequency and space‐wavenumber reassignment

The reassignment method remaps the energy of each point in a time‐frequency spectrum to a new coordinate that is closer to the actual time‐frequency location. Two applications of the reassignment method are developed in this paper. We first describe time‐frequency reassignment as a tool for spectral decomposition. The reassignment method helps to generate more clear frequency slices of layers and therefore, it facilitates the interpretation of thin layers. The second application is to seismic data de‐noising. Through thresholding in the reassigned domain rather than in the Gabor domain, random noise is more easily attenuated since seismic events are more compactly represented with a relatively larger energy than the noise. A reconstruction process that permits the recovery of seismic data from a reassigned time‐frequency spectrum is developed. Two approaches of the reassignment method are used in this paper, one of which is referred to as the trace by trace time reassignment that is mainly used for seismic spectral decomposition and another that is the spatial reassignment that is mainly used for seismic de‐noising. Synthetic examples and two field data examples are used to test the proposed method. For comparison, the Gabor transform method, inversion‐based method and common deconvolution method are also used in the examples.     

Research Note: Experimental measurements of Q‐contrast reflections

While seismic reflection amplitudes are generally determined by real acoustical impedance contrasts, there has been recent interest in reflections due to contrasts in seismic‐Q. Herein we compare theoretical and modelled seismic reflection amplitudes for two different cases of material contrasts. In case A, we examine reflections from material interfaces that have a large contrast in real‐valued impedance () with virtually no contrast in seismic‐Q. In case B, we examine reflections from material interfaces that have virtually no contrast in but that have very large seismic‐Q contrasts. The complex‐valued reflection coefficient formula predicts non‐zero seismic reflection amplitudes for both cases. We choose physical materials that typify the physics of both case A and case B. Physical modelling experiments show significantly large reflections for both cases – with the reflections in the two cases being phase shifted with respect to each other, as predicted theoretically. While these modelling experiments show the existence of reflections that are predicted by theory, there are still intriguing questions regarding the size of the Q‐contrast reflections, the existence of large Q‐contrast reflections in reservoir rocks and the possible application of Q‐reflection analysis to viscosity estimation in heavy oilfields.     

Diel patterns in coastal‐stream nitrate concentrations linked to evapotranspiration in the riparian zone of a low‐relief,agricultural catchment

Evapotranspiration (ET) can cause diel fluctuations in the elevation of the water table and the stage in adjacent streams. The diel fluctuations of water levels change head gradients throughout the day, causing specific discharge through near‐stream sediment to fluctuate at the same time scale. In a previous study, we showed that specific discharge controls the residence time of groundwater in streambed sediment that, in turn, exerted the primary control on removal from groundwater passing through the streambed. In this study, we examine the magnitude of diel specific discharge patterns through the streambed driven by ET in the riparian zone with a transient numerical saturated–unsaturated groundwater flow model. On the basis of a first‐order kinetic model for removal, we predicted diel fluctuations in stream concentrations. Model results indicated that ET drove a diel pattern in specific discharge through the streambed and riparian zone (the removal zones). Because specific discharge is inversely proportional to groundwater travel time through the removal zones and travel time determines the extent of removal, diel changes in ET can result in a diel pattern in concentration in the stream. The model predictions generally matched observations made during summertime base‐flow conditions in a small coastal plain stream in Virginia. A more complicated pattern was observed following a seasonal drawdown period, where source components to the stream changed during the receding limb of the hydrograph and resulted in diel fluctuations being superimposed over a multi‐day trend in concentrations. Copyright © 2013 John Wiley & Sons, Ltd.     

Surface‐wave inversion for a P‐velocity profile with a constant depth gradient of the squared slowness

Surface waves are often used to estimate a near‐surface shear‐velocity profile. The inverse problem is solved for the locally one‐dimensional problem of a set of homogeneous horizontal elastic layers. The result is a set of shear velocities, one for each layer. To obtain a P‐wave velocity profile, the P‐guided waves should be included in the inversion scheme. As an alternative to a multi‐layered model, we consider a simple smooth acoustic constant‐density velocity model, which has a negative constant vertical depth gradient of the squared P‐wave slowness and is bounded by a free surface at the top and a homogeneous half‐space at the bottom. The exact solution involves Airy functions and provides an analytical expression for the dispersion equation. If the ratio is sufficiently small, the dispersion curves can be picked from the seismic data and inverted for the continuous P‐wave velocity profile. The potential advantages of our model are its low computational cost and the fact that the result can serve as a smooth starting model for full‐waveform inversion. For the latter, a smooth initial model is often preferred over a rough one. We test the inversion approach on synthetic elastic data computed for a single‐layer P‐wave model and on field data, both with a small ratio. We find that a single‐layer model can recover either the shallow or deeper part of the profile but not both, when compared with the result of a multi‐layer inversion that we use as a reference. An extension of our analytic model to two layers above a homogeneous half‐space, each with a constant vertical gradient of the squared P‐wave slowness and connected in a continuous manner, improves the fit of the picked dispersion curves. The resulting profile resembles a smooth approximation of the multi‐layered one but contains, of course, less detail. As it turns out, our method does not degrade as gracefully as, for instance, diving‐wave tomography, and we can only hope to fit a subset of the dispersion curves. Therefore, the applicability of the method is limited to cases where the ratio is small and the profile is sufficiently simple. A further extension of the two‐layer model to more layers, each with a constant depth gradient of the squared slowness, might improve the fit of the modal structure but at an increased cost.     

The rotated Cartesian coordinate method to remove the axial singularity of cylindrical coordinates in finite‐difference schemes for elastic and viscoelastic waves

When modelling the propagation of 3D non‐axisymmetric elastic and viscoelastic waves in cylindrical coordinates using the finite‐difference time‐domain method, a mathematical singularity occurs due to the presence of terms in the elastic and viscoelastic wave equations. For many years, this issue has been impeding the accurate numerical solution near the axis. In this work, we propose a simple but effective method for the treatment of this numerical singularity problem. By rotating the Cartesian coordinate system around the z‐axis in cylindrical coordinates, the numerical singularity problems in both 2D and 3D cylindrical coordinates can be removed. This algorithm has three advantages over the conventional treatment techniques: (i) the excitation source can be directly loaded at , (ii) the central difference scheme with second‐order accuracy is maintained, and (iii) the stability condition at the axis is consistent with the finite‐difference time‐domain in Cartesian coordinates. This method is verified by several 3D numerical examples. Results show that the rotating the Cartesian coordinate method is accurate and stable at the singularity axis. The improved finite‐difference time‐domain algorithm is also applied to sonic logging simulations in non‐axisymmetric formations and sources.     

Stream response to precipitation variability: a spectral view based on analysis and modelling of hydrological cycle components

Hydrological processes commonly exhibit long‐term persistence, also known as the ‘Hurst phenomenon’. Here, we examine long‐term precipitation and streamflow time series from the Elbe River Basin to quantify differences in the spectral properties and in the Hurst parameter estimates () of the individual hydrological cycle components. Precipitation‐runoff modelling is performed for the Elbe River sub‐catchment Striegis using the Soil and Water Assessment Tool (SWAT). For 38 daily 50 years long streamflow time series from the Elbe River Basin, baseflow separation and spectral analysis is performed. The results show a spectral shift towards low‐frequency scales (>2 years) from precipitation to baseflow, with a parallel increase of from 0.52 (precipitation) to 0.65 (baseflow). The SWAT model is able to reproduce both, the main low‐frequency mode (≈7 yr.) and the (0.62) of the observed Striegis River flow time series. The baseflow appears to be the main component which shapes the low‐frequency response and of streamflow in the Elbe River Basin to the input precipitation. This conclusion is further confirmed through PMWIN‐MODFLOW groundwater modelling of a hypothetic phreatic stream‐connected aquifer system that consists of various soils (sand, loamy sand and silt). A power shift towards lower frequencies and an increase of for the hydraulic heads is obtained, as the aquifer's lateral dimensions increase and its hydraulic conductivity decreases. The average of the groundwater heads is 0.80, 0.90 and 1.0 for sand, loamy sand and silt aquifers, respectively. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluating equilibrium and non‐equilibrium transport of ammonium in a loam soil column

Release of nitrogen compounds into groundwater, particularly those compounds from excessive agricultural fertilization, is a major concern in an aquifer recharge. Among the nitrogen compounds, ammonium ( ) is a common one. In order to assess the risk of agricultural fertilizer contamination to an aquifer through infiltration, adsorption onto a loamy agricultural soil profile (0–0.60 m depth) was studied using a soil column experiment and modelling simulation. The soil used in the experiment was drawn from an agricultural field in Xinzhen, Fangshan district, Beijing, China, and reconstituted in laboratory soil columns. Column experiments were conducted using bromide (conservative tracer) and ‐bearing aqueous solutions. The ammonium concentrations in the soil water samples were measured, and their values were plotted as the breakthrough curves. The chemical's soil–water distribution coefficients (K_d) were calculated using breakthrough curves. Then the retardation factor (R) in saturated soil was calculated. For the ‐bearing aqueous solutions, the strongest adsorption occurred at the soil depth of 0.30–0.45 m. The convection–dispersion equation model and chemical non‐equilibrium model in Hydrus‐1D were used to simulate transport in the loamy soil. The two‐site chemical non‐equilibrium model in Hydrus‐1D was best to simulate transport through the soil column. Parameter sensitivity study was conducted to investigate the influences of solute transport by K_d, the fraction of exchange sites assuming to be in equilibrium with the solution phase (f), the longitudinal dispersivity (λ), and the first‐order rate coefficients (ω). The sensitivity analysis results indicate K_d is the most critical parameter.     

Development of duration‐dependent damage‐based inelastic response spectra

A simple relationship is proposed in this paper to construct damage‐based inelastic response spectra including the effect of ground motion duration that it can be used for damage control in seismic design of structures. This relation is established for three groups of ground motions with short‐duration, moderate‐duration, and long‐duration ranges. To develop the model, the duration effect is included in the cyclic ductility of structures by an energy‐based method, and then strength reduction factors are computed based on this modified ductility (named ). The strength reduction factors were calculated for 44 stiffness‐degrading oscillators having vibration periods between 0.05 and 4.0 s, four ultimate ductility capacities, and five damage levels subjected to 296 earthquake records. The results showed that ductility capacity, damage level, and ground motion duration are effective parameters in the energy dissipation of structures, which affect the spectra. The values of short‐period oscillators (e.g., low‐rise structures) under short‐duration records are generally greater than those under moderate‐duration and long‐duration records. Residual analysis has been made in terms of magnitude and distance to examine the validity of the proposed simple expression. Finally, the introduced spectra were compared with three previously published proposals. Copyright © 2016 John Wiley & Sons, Ltd.     

Measuring changes in fracture properties from temporal variations in anisotropic attenuation of microseismic waveforms

We investigate fracture‐induced attenuation anisotropy in a cluster of events from a microseismic dataset acquired during hydraulic fracture stimulation. The dataset contains 888 events of magnitude ?3.0 to 0.0. We use a log‐spectral‐amplitude‐ratio method to estimate change in over a half‐hour time period where fluid is being injected and an increase in fracturing from S‐wave splitting analysis has been previously inferred. A Pearson's correlation analysis is used to assess whether or not changes in attenuation with time are statistically significant. P‐waves show no systematic change in during this time. In contrast, S‐waves polarised perpendicular to the fractures show a clear and statistically significant increase with time, whereas S‐waves polarised parallel to the fractures show a weak negative trend. We also compare between the two S‐waves, finding an increase in with time. A poroelastic rock physics model of fracture‐induced attenuation anisotropy is used to interpret the results. This model suggests that the observed changes in t* are related to an increase in fracture density of up to 0.04. This is much higher than previous estimates of 0.025 ± 0.002 based on S‐wave velocity anisotropy, but there is considerably more scatter in the attenuation measurements. This could be due to the added sensitivity of attenuation measurement to non‐aligned fractures, fracture shape, and fluid properties. Nevertheless, this pilot study shows that attenuation measurements are sensitive to fracture properties such as fracture density and aspect ratio.     

Spatial and temporal variations in rainfall characteristics in mountainous and lowland areas in Taiwan

Although changes in rainfall characteristics have been noted across the world, few studies have reported those in mountainous areas. This study was undertaken to clarify spatial and temporal variations in rainfall characteristics such as annual rainfall amount (Pr), mean daily rainfall intensity (η), and ratio of rain days (λ) in mountainous and lowland areas in Taiwan. To this aim, we examined spatial and year‐to‐year variations and marginal long‐term trends in Pr, η, and λ, based on rainfall data from 120 stations during the period 1978–2008. The period mean rainfall () at the lowland stations had strong relationships with the period mean daily rainfall intensity () and the period mean ratio of rain days () during those 31 years. Meanwhile, was only strongly related to at mountainous stations, indicating that influences on spatial variations in were different between lowland and mountainous stations. Year‐to‐year variations in Pr at each station were primarily determined from the variation in η at most stations for both lowland and mountainous stations. Long‐term trend analysis showed that Pr and η increased significantly at 10% and 31% of the total 120 stations, respectively, and λ decreased significantly at 6% of the total. The increases in Pr were mostly accompanied by increases in η. Although stations with significant η increases were slightly biased toward the western lowland area, increases or decreases in Pr and λ were not common. These results contribute to understanding the impacts of possible climate changes on terrestrial hydrological cycles. Copyright © 2012 John Wiley & Sons, Ltd.     

Parsimonious wave‐equation travel‐time inversion for refraction waves

We present a parsimonious wave‐equation travel‐time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N geophones evenly deployed along the line. These two reciprocal shots contain approximately 2N refraction travel times, which can be spawned into refraction travel times by an interferometric transformation. Then, these virtual refraction travel times are used with a source wavelet to create N virtual refraction shot gathers, which are the input data for wave‐equation travel‐time inversion. Numerical results show that the parsimonious wave‐equation travel‐time tomogram has about the same accuracy as the tomogram computed by standard wave‐equation travel‐time inversion. The most significant benefit is that a reciprocal survey is far less time consuming than the standard refraction survey where a source is excited at each geophone location.     

Regulating Environmental Factors of Nutrients Release from Wheat Straw Biochar for Sustainable Agriculture

One mechanism by which biochar application enhances soil nutrient availability is through direct nutrients release from biochar. However, factors controlling the release processes are poorly understood. In this study, the effects of pH, biochar to water ratio, temperature, ionic strength, and equilibration time on the release of PO, NO, NH, K⁺, Na⁺, Ca²⁺, and Mg²⁺ from biochar were evaluated in simulated experiments. The release of PO, K⁺, Ca²⁺, and Mg²⁺ was significantly affected by extraction pH, suggesting that their release from biochar was pH dependent or an H⁺‐consuming process. Correlation analysis indicated that PO and Ca²⁺, PO and Mg²⁺, and Ca²⁺ and Mg²⁺ were co‐solubilized with increasing soil acidity. To a lesser extent, the recovery of the nutrients was also affected by the ratio of biochar to water: more nutrients were soluble with more water supply. In contrast, the release of Na was not affected by pH while the concentration increased with decreasing biochar to water ratio. Meanwhile, other factors (temperature, ionic strength, and equilibration time) had less effect on nutrient release from biochar. Under the influence of pH, the patterns of NO and PO release from biochar were different: extractable NO concentration was not affected by the pH but more PO was released in strongly acidic conditions. Our data suggested that P was mainly retained in inorganic forms while N was in organic forms in biochar. We conclude that environmental factors have marked influences on nutrients release from biochar.