Multi-parameter reflection waveform inversion for acoustic transversely isotropic media with a vertical symmetry axis

Full waveform inversion in transversely isotropic media with a vertical symmetry axis provides an opportunity to better match the data at the near and far offsets. However, multi-parameter full waveform inversion, in general, suffers from serious cycle-skipping and trade-off problems. Reflection waveform inversion can help us recover a background model by projecting the residuals of the reflected wavefield along the reflection wavepath. Thus, we extend reflection waveform inversion to acoustic transversely isotropic media with a vertical symmetry axis utilizing the proper parameterization for reduced parameter trade-off. From a radiation patterns analysis, an acoustic transversely isotropic media with a vertical symmetry axis is better described by a combination of the normal-moveout velocity and the anisotropic parameters η and δ for reflection waveform inversion applications. We design a three-stage inversion strategy to construct the optimal resulting model. In the first stage, we only invert for the background by matching the simulated reflected wavefield from the perturbations of and δ with the observed reflected wavefield. In the second stage, the background and η are optimized simultaneously and the far-offset reflected wavefield mainly contribute to their updates. We perform Born modelling to compute the reflected wavefield for the two stages of reflection waveform inversion. In the third stage, we perform full waveform inversion for the acoustic transversely isotropic media with a vertical symmetry axis to delineate the high-wavenumber structures. For this stage, the medium is described by a combination of the horizontal velocity , η and ε instead of , η and δ. The acoustic multi-parameter full waveform inversion utilizes the diving waves to improve the background as well as utilizes reflection for high-resolution information. Finally, we test our inversion algorithm on the modified Sigsbee 2A model (a salt free part) and a two-dimensional line from a three-dimensional ocean bottom cable dataset. The results demonstrate that the proposed reflection waveform inversion approach can recover the background model for acoustic transversely isotropic media with a vertical symmetry axis starting from an isotropic model. This recovered background model can mitigate the cycle skipping of full waveform inversion and help the inversion recover higher resolution structures.     

Separation of multi-mode surface waves by supervised machine learning methods

Logistic regression, neural networks and support vector machines are tested for their effectiveness in isolating surface waves in seismic shot records. To distinguish surface waves from other arrivals, we train the algorithms on three distinguishing features of surface-wave dispersion curves in the domain: spectrum coherency of the trace's magnitude spectrum, local dip and the frequency range for a fixed wavenumber k in the spectrum. Numerical tests on synthetic data show that the kernel-based support vector machines algorithm gives the highest accuracy in predicting the surface-wave window in the domain compared to neural networks and logistic regression. This window is also used to automatically pick the fundamental dispersion curve. The other two methods correctly pick the low-frequency part of the dispersion curve but fail at higher frequencies where there is interference with higher-order modes.     

Spatio-temporal characteristics of small-scale wave–current ripples on the Ameland ebb-tidal delta

Ebb-tidal deltas are highly dynamic environments affected by both waves and currents that approach the coast under various angles. Among other bedforms of various scales, these hydrodynamics create small-scale bedforms (ripples), which increase the bed roughness and will therefore affect hydrodynamics and sediment transport. In morphodynamic models, sediment transport predictions depend on the roughness height, but the accuracy of these predictors has not been tested for field conditions with strongly mixed (wave–current dominated) forcing. In this study, small-scale bedforms were observed in the field with a 3D Profiling Sonar at five locations on the Ameland ebb-tidal delta, the Netherlands. Hydrodynamic conditions ranged from wave dominated to current dominated, but were mixed most of the time. Small-scale ripples were found on all studied parts of the delta, superimposed on megaripples. Even though a large range of hydrodynamic conditions was encountered, the spatio-temporal variations in small-scale ripple dimensions were relatively small (height 0.015 m, length 0.11 m). Also, the ripples were always highly three-dimensional. These small dimensions are probably caused by the fact that the bed consists of relatively fine sediment. Five bedform height predictors were tested, but they all overestimated the ripple heights, partly because they were not created for small grain sizes. Furthermore, the predictors all have a strong dependence on wave- and current-related velocities, whereas the ripple heights measured here were only related to the near-bed orbital velocity. Therefore, ripple heights and lengths in wave–current-dominated, fine-grained coastal areas ( mm) may be best estimated by constant values rather than values dependent on the hydrodynamics. In the case of the Ameland ebb-tidal delta, these values were found to be m and m. ©2019 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

Starved versus alluvial river bedforms: an experimental investigation

Laboratory experiments were conducted to investigate the formation of river bedforms under sediment supply-limited conditions, i.e. when a motionless substratum is bared by the dynamics of the mobile sediments. Three series of experiments were organized in a laboratory flume by fixing all the hydrodynamic and morphodynamic parameters but varying the thickness of the initial layer of mobile sediments which covers the rigid bottom of the flume. At the end of all the experiments, which lasted for the same amount of time, the formation of transverse sand dunes was observed. For decreasing , the rigid bottom of the flume was bared progressively earlier during the experiment and the measurements showed a clear tendency of the bedforms to lengthen, i.e. to increase their crest-to-crest distance. Moreover, under strong supply limitation, the two-dimensional transverse dunes turned into three-dimensional barchanoid forms and into isolated barchan dunes characterized by an abrupt reduction in bedform heights. A two-dimensional Fourier analysis of the bottom profile was performed, providing the amplitude of the main streamwise and spanwise harmonic components of the bottom morphology as a function of . © 2019 John Wiley & Sons, Ltd.     

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.     

Pre-stack seismic inversion based on -norm regularized logarithmic absolute misfit function

Ill-posedness is one of the most common and intractable issues that arise when solving geophysical inverse problems. Ill-posedness could be induced by various factors such as noise, band-limited intrinsic property of seismic data and inappropriate forward operators. Regularization has been proven to be an effective method widely accepted for mitigating the adverse effects of ill-posedness. Aiming to improve the stability and fidelity of the pre-stack seismic inversion process, we implement the inversion in a Bayesian framework, with a logarithmic absolute criterion taken as a likelihood function, and an -norm metric as a priori constraint. Here, we exploit the linear approximation as the forward operator, and optimize the regularized misfit function by the alternating direction method of multipliers. Applications of the method to synthetic and real data sets yielded improved inversion results in terms of accuracy and resolution, and demonstrated the robustness of the method to noise.     

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.     

Characterizing the degree of amplitude‐variation‐with‐offset nonlinearity in seismic physical modelling reflection data

The nonlinearity of the seismic amplitude‐variation‐with‐offset response is investigated with physical modelling data. Nonlinearity in amplitude‐variation‐with‐offset becomes important in the presence of large relative changes in acoustic and elastic medium properties. A procedure for pre‐processing physical modelling reflection data is enacted on the reflection from a water‐plexiglas boundary. The resulting picked and processed amplitudes are compared with the exact solutions of the plane‐wave Zoeppritz equations, as well as approximations that are first, second, and third order in , , and . In the low angle range of 0°–20°, the third‐order plane‐wave approximation is sufficient to capture the nonlinearity of the amplitude‐variation‐with‐offset response of a liquid‐solid boundary with , , and ρ contrasts of 1485–2745 m/s, 0–1380 m/s, and 1.00–1.19 gm/cc respectively, to an accuracy value of roughly 1%. This is in contrast to the linear Aki–Richards approximation, which is in error by as much as 25% in the same angle range. Even‐order nonlinear corrective terms are observed to be primarily involved in correcting the angle dependence of , whereas the odd‐order nonlinear terms are involved in determining the absolute amplitude‐variation‐with‐offset magnitudes.     

Experiment and Simulation of Non-Reactive Solute Transport in Porous Media

To more accurately predict the migration behavior of pollutants in porous media, we conduct laboratory scale experiments and model simulation. Aniline (AN) is used in one-dimensional soil column experiments designed under various media and hydrodynamic conditions. The advection-dispersion equation (ADE) and the continuous-time random walk (CTRW) were used to simulate the breakthrough curves (BTCs) of the solute transport. The results show that the media and hydrodynamic conditions are two important factors affecting solute transport and are related to the degree of non-Fickian transport. The simulation results show that CTRW can more effectively describe the non-Fickian phenomenon in the solute transport process than ADE. The sensitive parameter in the CTRW simulation process is , which can reflect the degree of non-Fickian diffusion in the solute transport. Understanding the relationship of with velocity and media particle size is conducive to improving the reactive solute transport model. The results of this study provide a theoretical basis for better prediction of pollutant transport in groundwater.     

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.     

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.     

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.     

Random noise attenuation via the randomized canonical polyadic decomposition

Tensor algebra provides a robust framework for multi-dimensional seismic data processing. A low-rank tensor can represent a noise-free seismic data volume. Additive random noise will increase the rank of the tensor. Hence, tensor rank-reduction techniques can be used to filter random noise. Our filtering method adopts the Candecomp/Parafac decomposition to approximates a N-dimensional seismic data volume via the superposition of rank-one tensors. Similar to the singular value decomposition for matrices, a low-rank Candecomp/Parafac decomposition can capture the signal and exclude random noise in situations where a low-rank tensor can represent the ideal noise-free seismic volume. The alternating least squares method is adopted to compute the Candecomp/Parafac decomposition with a provided target rank. This method involves solving a series of highly over-determined linear least-squares subproblems. To improve the efficiency of the alternating least squares algorithm, we uniformly randomly sample equations of the linear least-squares subproblems to reduce the size of the problem significantly. The computational overhead is further reduced by avoiding unfolding and folding large dense tensors. We investigate the applicability of the randomized Candecomp/Parafac decomposition for incoherent noise attenuation via experiments conducted on a synthetic dataset and field data seismic volumes. We also compare the proposed algorithm (randomized Candecomp/Parafac decomposition) against multi-dimensional singular spectrum analysis and classical prediction filtering. We conclude the proposed approach can achieve slightly better denoising performance in terms of signal-to-noise ratio enhancement than traditional methods, but with a less computational cost.     

Deterministic ground motion simulations with shallow crust nonlinearity at Garner Valley in Southern California

We present deterministic ground motion simulations that account for the cyclic multiaxial response of sediments in the shallow crust. We use the Garner Valley in Southern California as a test case. The multiaxial constitutive model is based on the bounding surface plasticity theory in terms of total stress and is implemented in a high‐performance computing finite‐element parallel code. A major advantage of this model is the small number of free parameters that need to be calibrated given a shear modulus reduction curve and the ultimate soil strength. This, in turn, makes the model suitable for regional‐scale simulations, where geotechnical data in the shallow crust are scarce. In this paper, we first describe a series of numerical experiments designed to verify the model implementation. This is followed by a series of idealized large‐scale simulations in a 35 26 4.5 km domain that encompasses the Garner Valley downhole array site, which is an instrumented and well‐characterized site in Southern California. Material properties were extracted from the Southern California Earthquake Center Community velocity model, CVM‐S4.26, considering its optional geotechnical layer, while the modulus reduction curves and soil strength were selected empirically to constrain the nonlinear soil model parameters. Our nonlinear simulations suggest that peak ground displacements within the valley increase relative to the linear case, while peak ground accelerations can increase or decrease, depending on the frequency content of the excitation. The comparisons of our simulations against hybrid three‐dimensional–one‐dimensional site response analyses suggest the inadequacy of the latter to capture the complexity of fully three‐dimensional simulations.     

Investigating young water fractions in a small Mediterranean mountain catchment: Both precipitation forcing and sampling frequency matter

The proportion of water younger than 2–3 months (young water fraction, F_yw) has become increasingly investigated in catchment hydrology. F_yw is typically estimated by comparing seasonal tracer cycles in precipitation and streamflow, through water sampling. However, some open research questions remain, such as: (i) whether part of the summer precipitation should be discarded because the high evapotranspiration demand, (ii) how well F_yw serves as a metric to compare catchments, and (iii) how sampling frequency affects F_yw estimates. To address these questions, we investigated F_yw in soil-, ground- and stream waters for the small Mediterranean Can Vila catchment. Rainfall was sampled at 5-mm intervals. Mobile soil water and groundwater were sampled fortnightly. Stream water was sampled depending on flow at variable time intervals (30 min to 1 week). Over 58 months, this sampling provided 1,529 δ¹⁸O determinations. Isotopic analyses results led us to include summer precipitation in the input signal. We found the highest F_yw in mobile soil waters (34%), while this was almost zero for groundwater except during wet periods. For stream waters, F_yw depended on the discharge variations, so that the flow-weighted young water fraction () was 22.6%, whereas the time-weighted F_yw was just 6.2%. Both and its discharge sensitivity (S_d) varied when different 12-month sampling periods were investigated. The young water fraction that would be obtained from a virtual thorough sampling () was estimated from the S_d and the observed stream flow. This showed an underestimation of by 25% for the frequent dynamic sampling and 66% for weekly sampling, due to missing high flows. Our results confirm that F_yw and its discharge sensitivity are metrics very sensitive to meteorological forcing during the analysed period. Thus, comparisons between catchments need long-term mean annual values and their variability. Our findings also support the dependence of F_yw estimates on the sampling rate and show the advantages of flow-weighted analysis. Finally, catchment water turnover investigations should be accompanied by the analysis of flow duration curves.     

Geomorphology and climate interact to control organic carbon stock and age in mountain river valley bottoms

Organic carbon (OC) in valley bottom downed wood and soil that cycles over short to moderate timescales (10¹ to 10⁵ years) represents a large, dynamic, and poorly quantified pool of carbon whose distribution and residence time affects global climate. We sought to quantify this potentially important OC pool at the watershed scale to estimate its magnitude and age, as well as determine the controls on its variability within watersheds. To do this, we compared four disparate mountain river basins to show that mountain river valley bottoms store substantial estimated OC stocks in floodplain soil and downed wood (median OC of MgC/ha, n = 178). Although soil OC is generally young (exhibiting a median radiocarbon fraction modern value of , n = 121), geomorphic processes regulate soil burial and processes that limit microbial respiration, preserving aged OC in especially deep, unconfined, wet, and/or high-elevation floodplain soils. We statistically modeled OC stocks to show that valley bottom morphology and hydrology regulate variability in floodplain soil retention and resulting variability in OC stock and age in floodplain soil throughout river networks. Comparing the distribution of OC stocks between wood and soil, we find that where floodplain soils are present, their OC stocks are generally greater than OC stocks stored in wood. Our results suggest that although mountain rivers may accumulate large OC stocks relatively rapidly, those stocks are highly sensitive to alterations in soil and wood retention, implying that human alterations to either disturb or restore floodplain wood and soil storage may have substantial impacts on OC storage in river corridors. © 2020 John Wiley & Sons, Ltd.     

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.     

Does variable channel morphology lead to dynamic salmon habitat?

Stream channel morphology forms the template upon which hydraulic aspects of aquatic habitat are created, yet spatial and temporal variability in habitat imposed by changing morphology is not well understood. This paper presents a conceptual model linking sediment supply patterns to spatial and temporal variability in channel form and aquatic habitat. To evaluate this model, change over time in three habitat variables is quantified using a 2D hydrodynamic modeling approach. A 45-year record of topographic data from Carnation Creek, a catchment in coastal British Columbia, is used for the flow modeling. Using the Nays2DH modeling platform, water depths and velocities are simulated in eight channel segments located at different positions relative to locations of historical colluvial input using seven flow levels ranging from 3% to 400% of mean annual discharge (0.02 to 3.31 m s ). Results indicate that habitat availability changes through time as a result of sediment supply-driven changes to channel morphology and wood loads, but patterns in habitat vary as a function of dominant channel segment morphology. Spatial and temporal variability in morphology also influences the relationship between habitat availability and river discharge, leading to non-stationary habitat-discharge rating curves. When habitat areas are predicted by applying these curves to daily flow series spanning annual dry seasons, over 50% of the variance in cumulative seasonal habitat area can be explained by year-to-year changes in channel morphology and wood loading, indicating that changing morphology is an important factor for driving temporal habitat variability. This variance is related to the morphological variability of a channel segment, which in turn is associated with the segment position relative to zones of colluvial input. Collectively, these results suggest that variability in habitat is impacted by channel morphology, and can be evaluated partly on the basis of a channel's sediment supply regime. © 2019 John Wiley & Sons, Ltd.     

Robust f‐x projection filtering for simultaneous random and erratic seismic noise attenuation

Linear prediction filters are an effective tool for reducing random noise from seismic records. Unfortunately, the ability of prediction filters to enhance seismic records deteriorates when the data are contaminated by erratic noise. Erratic noise in this article designates non‐Gaussian noise that consists of large isolated events with known or unknown distribution. We propose a robust f‐x projection filtering scheme for simultaneous erratic noise and Gaussian random noise attenuation. Instead of adopting the ?₂‐norm, as commonly used in the conventional design of f‐x filters, we utilize the hybrid ‐norm to penalize the energy of the additive noise. The estimation of the prediction error filter and the additive noise sequence are performed in an alternating fashion. First, the additive noise sequence is fixed, and the prediction error filter is estimated via the least‐squares solution of a system of linear equations. Then, the prediction error filter is fixed, and the additive noise sequence is estimated through a cost function containing a hybrid ‐norm that prevents erratic noise to influence the final solution. In other words, we proposed and designed a robust M‐estimate of a special autoregressive moving‐average model in the f‐x domain. Synthetic and field data examples are used to evaluate the performance of the proposed algorithm.