Bulk-density ( ρ) of soil is an important indicator of soil compaction and type. A knowledge of the spatial variability of in situ soil density is important in geotechnical engineering, hydrology and agriculture. Surface geophysical methods have so far shown limited success in providing an accurate and high-resolution image of 3-D soil-density distribution. In this pursuit, 3-D seismic full-waveform inversion (FWI) is promising, provided the robustness and accuracy of density inversion via this approach can be established in the near-surface scale. Ho wever , simultaneous reconstruction of ρand seismic wave velocities through multiparameter FWI remains a challenging task. Near-surface seismic data are commonly dominated by dispersive surface waves whose velocities are controlled by the value and distribution of shear-wave velocity ( V S ). One major difficulty in estimating reliab ly ρfrom near -surface seismic data is due to the relati vel y low sensiti vity of the seismic w av efield to ρcompared to seismic v elocities. Additionally, the accuracy of the estimated ρdecreases due to error in V S -an issue known as parameter coupling. Parameter coupling makes it difficult to estimate accurately ρwithin the framework of conventional gradient-based FWI. More sophisticated optimization approaches (e.g. truncated Newton) can reduce the effect of parameter coupling, but these approaches are commonl y not af fordab le in near -surface applications due to heavy computational burden. In this research, w e ha v e inv estigated how choosing correctly the force direction of the seismic source can contribute to a higher accuracy of ρestimates through 3-D FWI. Using scattered wavefields, the Hessian, and inversion tests, an in-depth and systematic investigation of data sets corresponding to different force directions has been carried out. A comparison of the scattered wavefields due to a point-localized ρperturbation for different force directions shows the robustness of the horizontal-force data set to noise compared to the vertical-force data set. Fur ther more, for a point-scatterer model, an analysis of the gradients of the misfit function using the Hessian shows that utilizing a horizontal-force source enables one to reconstruct the high-resolution gradient with relati vel y small parameter coupling. Finally, inversion tests for two different subsoil models demonstrate that 3-D FWI on a horizontal-force-source seismic data set is capable of providing a more accurate 3-D ρdistribution in soil compared to a vertical-force-source data set. Our results show that the use of a horizontal-force source might allow avoiding computationally demanding, costly optimization approaches in 3-D FWI.

@en

When using waveform tomography to perform high-resolution imaging of a medium, it is vital to calculate the sensitivity in order to describe how well a model fits a given set of data and how the sensitivity changes with the spatial distribution of the heterogeneities. The traditional principle behind calculating the sensitivity—for detecting small changes—suffers from an inherent limitation in case other structures, not of interest, are present along the wave propagation path. We propose a novel principle that leads to enhanced localization of the sensitivity of the waveform tomography, without having to know the intermediate structures. This new principle emerges from a boundary integral representation which utilizes wave interferences observed at multiple points. When tested on geophysical acoustic wave data, this new principle leads to much better sensitivity localization and detection of small changes in seismic velocities, which were otherwise impossible. Overcoming the insensitivity to a target area, it offers new possibilities for imaging and monitoring small changes in properties, which is critical in a wide range of disciplines and scales.@en

The hydraulic and mechanical characterization of fractures is crucial for a wide range of pertinent applications, such as geothermal energy production, hydrocarbon exploration, <span classCombining double low line"inline-formula">CO2</span> sequestration, and nuclear waste disposal. Direct hydraulic and mechanical testing of individual fractures along boreholes does, however, tend to be slow and cumbersome. To alleviate this problem, we propose to estimate the effective hydraulic aperture and the mechanical compliance of isolated fractures intersecting a borehole through a Bayesian Markov chain Monte Carlo (MCMC) inversion of full-waveform tube-wave data recorded in a vertical seismic profiling (VSP) setting. The solution of the corresponding forward problem is based on a recently developed semi-Analytical solution. This inversion approach has been tested for and verified on a wide range of synthetic scenarios. Here, we present the results of its application to observed hydrophone VSP data acquired along a borehole in the underground Grimsel Test Site in the central Swiss Alps. While the results are consistent with the corresponding evidence from televiewer data and exemplarily illustrate the advantages of using a computationally expensive stochastic, instead of a deterministic inversion approach, they also reveal the inherent limitation of the underlying semi-Analytical forward solver.

.@en

To quantitatively image fractures with high resolution, we have developed an elastic least-squares migration (LSM) algorithm coupled with linear-slip theory, which accurately addresses seismic wave interaction with thin structures. We derive a linearized waveform inversion using the Born approximation to the boundary integral equation for scattered waves, including linear-slip interfaces for P-SV and SH wavefields. Numerical modeling tests assuming a laboratory-scale fracture where a 20 cm long fracture is illuminated by waves with a 50 kHz center frequency show that our LSM successfully estimates fracture compliances. Furthermore, due to the presence of coupling compliances at the fracture, the results using our LSM show better images than those using the conventional LSM estimating the Lamé constants. We also numerically illustrate that our LSM can be successfully applied to dipole acoustic borehole logging data with 3 kHz center frequency for single-well reflection imaging of a 10 m long, dipping fracture embedded in a random background. Finally, we apply LSM to laboratory experimental data, measuring PP reflections from a fluid-filled fracture. We confirm that the estimated fracture compliances correspond well to those estimated by earlier amplitude variation with offset inversion. Furthermore, the LSM resolves the spatially varying fracture compliances due to local filling of water in the fracture. Because the linear-slip theory can be applied to thin structures in a wide range of scales, high-resolution imaging results and estimated fracture compliance distributions will be crucial to further address small-scale properties at fractures, joints, and geologic faults.

@en

The hydraulic characterization of fractures is crucial for geothermal energy production, hydrocarbon exploration, CO2-sequestration, and nuclear waste disposal. We propose to estimate the effective hydraulic aperture and the mechanical compliance of isolated fractures intersecting a borehole through a Bayesian inversion of full-waveform tube-wave data recorded in a vertical seismic profiling setting. Following the successful application of the proposed inversion procedure to synthetic data, we show in this study initial results of an application to real data.

@en

Time-lapse seismics has a wide range of application in different scales, from near-surface to resource exploration. Crosshole seismics is used to characterize fluid reservoirs and to obtain highly resolved rock/soil-dynamic parameters e.g., elastic moduli and Poisson ratio. Developments in distributed acoustic sensing shows the potential of deploying permanent downhole receivers at low costs. In order to achieve an efficient and accurate time-lapse seismic measurement in such scenarios, we have developed a nonlinear waveform inversion to reconstruct velocity structure between boreholes using VSP data with source located only at the surface, and no downhole sources. The new approach formulates the forward modelling using wavefield representation theorem, which enables directly estimating the velocity structure by minimizing data residuals and calculating the gradient from the adjoint state problem. We test the approach using numerical modelling of time-lapse VSP data to detect layer-specific temporal changes. A heterogeneous shallow vadose zone represents a low-velocity layer. The results show that the new approach provides more stable and more accurate temporal velocity profiles than conventional full waveform inversion, when the initial velocity model does not include the shallow low-velocity layer. The new approach is robust and highly advantageous as it does not require downhole seismic sources.

@en

Single-well reflection imaging using sonic logging data successfully locates fine-scale structures around a borehole including fractures. In order to achieve accurate and quantitative estimation of fracture properties with high resolution, we propose to couple least-squares migration with linear slip theory. The proposed least-squares migration solves linearized waveform inversion where the wavefield is approximated using a Born operator incorporating a linear slip boundary condition. Representing a fracture as a linear slip interface is advantageous in accurate seismic wave modeling and efficient estimation of fracture properties. We derive conventional elastic least-squares migration for imaging perturbations in elastic constants, and new elastic least-squares migration for imaging fracture compliances. The two formulations are tested using numerical modeling where a dipping fracture is embedded in random background medium. The results show that least-squares migration generally produces higher resolution images for both SH and P-SV wavefields than using adjoint operators. Furthermore, it shows the potential of quantitative estimation of fracture compliances which can be further used in interpreting fracture properties, e.g., fracture infill material and surface condition. The proposed approach, therefore, will be crucial in fracture characterization around a borehole.@en

A large number of geotechnical, agricultural and environmen-tal site investigations need knowledge of the distribution of hydraulic properties of the unsaturated soils and their temporal changes. Unsaturated hydraulic properties are also important in climate modelling and in the study of biological and chemical processes in the vadose zone. The ability of the soil to retain or transmit water and its constituents is reflected by these properties. In hillslopes, the flow of water, controlled by the hydraulic properties of the soil, is crucial for water resource management and for predicting slope failure caused by heavy rainfall. One of the most important hydraulic properties is the water retention curve or the soil-water characteristic curve (SWCC), which relates volumetric water content or degree of water saturation to matric suction. Water content and matric suction are related to other important soil properties including: hydraulic conductivity function, cohesion and internal friction (e.g., Guo, 1985; Lu et al., 2012; Robinson et al., 2017). The stability of an unsaturated soil slope or a river embankment subjected to rainfall is determined to a great extent by SWCC. Recently, it has been shown that changes in seismic shear-wave velocity (VS) in unsaturated soils can be used to monitor in situ the distribution of water and the dynamic water transportation in the vadose zone (Suzaki et al., 2017). In this research, among various models for SWCC, the van Genuchten (1980) model was assumed: (1) where s is matric suction, SW is degree of water saturation, a and n are van Genuchten parameters that depend on the soil-type. These describe, respectively, the air-entry suction and the slope of SWCC. A Bishop-type model for effective stress was coupled with a well-tested form of the stress-suction-saturation-depend-ence of the small-strain shear modulus G0 (Sawangsuriya et al., 2009; Han and Vanapalli, 2016), which gave (2) where x is a sample point representing a certain spatial location in the subsurface, and A and B are fitting parameters that depend on the soil-type. More recently, it has been possible to invert the SWCC parameters a and n from G0, SW and bulk density rb obtained from geophysical measurements (Suzaki et al., 2019a, 2019b). In this article, we first illustrate the accuracy in the result of SWCC inversion that one might expect when the input data is realistically noisy. Once the in-situ SWCC is obtained by inver-sion, in the next stage, considering a projected time series for the future rainfall, the distribution of hydraulic properties, viz SW and s, within the soil embankment at different times in the future is calculated through seepage analysis. This provides an important piece of information to assess the vulnerability of a dyke in the future, given an anticipated rainfall. We analyse the prediction error and its cause. Considering Coulomb failure for a sand embankment, we examine the predicted factor of safety (FOS) and its temporal evolution in comparison with the true values.@en

Characterizing subsurface fractures is a key to developing hydrocarbon and geothermal fields, as well as providing fundamental information on fracture system relevant to regional seismotectonics. Seismic characterization of fractures has generally been based on the effective medium theory, which considers seismically invisible small fractures. Therefore, there is a considerable scale gap between the fracture properties obtained by seismic methods and those from borehole logging. Recent studies of single-well reflection imaging using acoustic borehole logging data show the potential of filling the scale gap by providing fracture properties around the borehole up to a few tens of meter away from the borehole location. In the context of reflection imaging of individual fractures, in this study, we develop least-squares migration (LSM) coupled with linear-slip model. LSM solves the linearized waveform inversion to provide high-resolution quantitative images. Linear-slip model can describe wave reflection at a fracture accurately. We show numerical modelling examples of the proposed approach considering a vertical fracture with coupling compliances, and acoustic dipole measurements of a dipping fracture embedded in a background random velocity distribution. The results show that the proposed LSM provides higher resolution images than reverse-time migration, and more accurate images than the conventional LSM without linear-slip model.@en

The soil-water characteristic curve (SWCC) is crucial in order to characterize the hydraulic and mechanical properties of unsaturated soils. To overcome the problem of error/uncertainties in laboratory estimates due to sample disturbances and to incorporate spatial heterogeneities, in-situ SWCC inversion using geophysical measurements appears to be a worthwhile, albeit challenging, goal. For SWCC inversion for a dyke under rainfall or rising water level or for a dyke containing low-permeable soils, accounting for the non-hydrostatic condition is crucial. Furthermore, the geometry of a dyke is important in determining the internal stress state. In this research, we model the shear modulus in an unsaturated dyke including the effect of the dyke geometry. This is achieved by solving the static deformation problem using FEM. Our newly developed inversion scheme assumes availability of integrated geophysical measurements to obtain saturation, bulk density and shear-wave velocity. We illustrate numerically the significance of the estimation of confining stress distribution using FEM for modelling the shear modulus and for SWCC inversion. Our inversion scheme can correctly handle the non-hydrostatic condition. This can have a large impact on diverse applications related to stability of earth-retaining structures as well as in problems involving dynamic transportation of fluids.@en

Characterizing the mechanical and hydraulic properties of fractures is crucial in hydrocarbon and geothermal field development. Contrary to passive microseismic measurements, active seismic measurements using a borehole, e.g., VSP or sonic logging, have a potential to address aseismic fractures. However, there is a considerable scale gap between the characteristic wavelength in VSP and in sonic logging, which hinders consistent interpretations of active and passive measurements. Recent developments of reflection imaging using microearthquakes and dipole acoustic data successfully image individual fractures or clusters of them around a borehole, which indicates the potential to fill the gap by addressing quantitative fracture properties around a borehole up to a few tens of meters away from the borehole. In this study, we couple the least-squares migration with the linear-slip theory in order to achieve high-resolution reflection imaging of fracture compliances around a borehole, which are then useful to characterize microscale structures at the fracture. Tests in the laboratory successfully characterize the spatially varying fracture compliance due to the partial inclusion of water in the fracture. Numerical modelling tests of the source-receiver configuration of acoustic dipole measurements and random background media shows the potential of the proposed approach for quantitatively imaging fractures around a borehole.@en

The Cocoa Grove Group is planning a housing development on approximately 5.5 acres in the area of Saphire, Diamond, St Lucia. Directly downhill of the property is a WASCO (Water and Sewage Company) Spring that has supplied drinking water to the town of Soufriere, going back to historic times. This potable water is of high purity. Concern was therefore expressed by WASCO as to the advisability of implementing any development directly above the emanation of the spring. The obvious concerns are the possible change in flow volumes and chemical and biological contamination if a housing development was completed. F.D. Morgan and the St Lucia Water Resources and personnel representing the Cocoa Grove Group discussed whether or not geophysical methods could be used to map the direction of groundwater flow into the spring. The group agreed that geophysical methods could be used in an attempt to delineate the underground flow paths into the spring. But it was made clear that the investigations could produce results that could be either favorable or unfavorable to the proposed development. Consequently, geophysical surveys were planned and executed in the area of concern, to measure resistivity and self potentials (SP). The geophysics did not indicate evidence, as expected, of substantial fluid flow into the spring. However, we were able to locate the main water supply from the top of Terre Blanche down towards the spring. The flow comes downhill via a significant geological fracture that is hidden from sight in the dense tree cover. Recommendations were made that it was relatively safe to develop the site as intended, with respect to possible water contamination. In conclusion, we also recommend that WASCO could take water from another point of a topographic step on Terre Blanche. Doing so, would reduce the contamination risk essentially to zero from the planned housing development area.@en

Crosswell seismic measurements enable obtaining high resolution, high accuracy images of the subsurface between boreholes. They are, however, generally expensive considering the need of deployment of special downhole sources. In this study, we develop a novel nonlinear waveform inversion to estimate velocity structures between two vertical boreholes using VSP data without downhole sources. Contrary to the conventional full waveform inversion (FWI), the effect of wave propagation between surface sources and one of the vertical boreholes is appropriately cancelled using representation theory. Furthermore, it enables us to calculate partial derivatives of the cost function without explicitly resolving the Green’s functions in seismic interferometry. We test numerically this new approach of time-lapse monitoring of a deeper target layer, considering also the effect of changes in the complex, shallow vadose zone. We assume that the temporal changes in velocity in the vadose zone are larger than those at the deeper target layer. Our results show that in contrast to conventional FWI, the newly developed approach has the advantages of expensive crosswell seismics involving downhole sources. The estimated velocity is robust against spatiotemporal changes in the near-surface. The approach will be very useful when accurate time-lapse seismic measurements are needed in a cost-effective manner.

@en

Seismic wave propagation across a fracture is represented by a nonwelded interface or the linear-slip boundary condition. The normal and tangential fracture compliances control the magnitude of discontinuity of elastic-wave-induced displacement across the interface. The fracture compliances are functions of aperture, roughness and elasticity of the infilling materials. Therefore, imaging and characterizing the nonwelded interfaces have the potential to characterize in situ the mechanical and hydraulic properties of the fractured reservoirs. Furthermore, the nonwelded interface is useful to represent a thin, compliant zone in rock, e.g., fractures, joints, fault branches and geological faults. We explore new approaches to model, image and characterize nonwelded interfaces using elastic waves. We discuss modelling seismic responses of nonwelded interfaces using the boundary integral representation of the wavefield. We investigate the Born approximation of the boundary integral equation and the effects of higher order terms. Furthermore, we develop a new Born inversion approach to image and characterize the nonwelded interfaces, and we discuss advantages of the new approach over the recently proposed AVO inversion. We show that while the AVO inversion accurately estimates the fracture compliances assuming that the fracture geometry is known and the primary reflections are isolated without interference of other events, the Born inversion simultaneously images and characterizes a nonwelded interface using the scattered wavefield without assuming fracture geometry. We also illustrate that the Born inversion handles correctly the multiple fractures. We discuss the effectiveness of these new methods using numerically modeled datasets and laboratory experimental datasets. We show that the Born inversion successfully images the nonwelded interfaces and characterizes the spatially varying fracture compliance, simulating heterogeneous inclusion of water/fluid in a fracture.@en

The soil-water characteristic curve (SWCC) plays an important role in determining the hydraulic and mechanical properties of the unsaturated soils. SWCC is vital to evaluating the stability of a slope or a river embankment. The sensitivity of seismic shear-wave velocity to SWCC has recently been quantified. However, the inversion of SWCC from field-observed VS is challenging. In this research, we have explored the possibility of integrating shear-wave velocity, water saturation and bulk density obtained from independent geophysical measurements and utilizing the underlying physics of shear-wave in terms of suction, saturation and stress, to invert SWCC. We derive a formulation for the shear modulus by combining van Genuchten model with stress-, suction- and saturationdependence of shear modulus. The stress is estimated using FEM, thereby taking into account the effect of geometry of the embankment. Tests on realistic synthetic data indicates that the inversion is very stable. This new scheme allows, for the first time, to estimate in-situ SWCC from integrated geophysical measurements. This can potentially have a large impact in diverse applications related to stability of earth-retaining structures, natural slopes, as well as in problems involving dynamic transportation of fluids in the vadose zone.@en

Low-frequency, axially-symmetric guided waves which propagate along a fluid-filled borehole (tube waves) are studied in order to characterize the hydraulic fractures intersecting the borehole. We formulate a new equation for the total tube wavefield, which includes simultaneous effects of (1) tube-wave scattering (reflection and transmission) due to wave propagation across hydraulic fractures, and (2) tube-wave generation due to incident plane P waves. The fracture is represented by the nonwelded interface boundary conditions. We use an appropriate form of the representation theorem in order to correctly handle the multiple scattering due to nonwelded interfaces. Our approach can implement any model that has so far been developed. We consider a recent model which includes simultaneous effects of fluid viscosity, dynamic fluid flow, and fracture compliance. The derived equation offers a number of important insights. We recognize that the effective generation amplitude contains the simultaneous effect of both tube-wave generation and scattering. This leads to a new physical understanding indicating that the tube waves are scattered immediately after generation. We show that this scattering is nonlinear with respect to interface compliance. This physical mechanism can be implicitly accounted for by considering more realistic boundary conditions. We also illustrate the application of the new equation in order to predict the complex signature of the total tube wavefield, including generation and scattering at multiple hydraulic fractures. A new formulation for focusing analyses is also derived in order to image and characterize the hydraulic fractures. The obtained results and discussions are important for interpretation, modeling, and imaging using low-frequency guided waves, in the presence of multiple fractures along a cylindrical inclusion.

@en

Characterizing fracture is important in order to understand how groundwater is transported and stored in fractured environments, to assess contaminant transport through fractures, as well to evaluate the mechanical behaviour of a fractured rock mass. In this research, we have investigated through careful laboratory experiments the amplitude versus offset (AVO) response of seismic reflections from a fracture. We use the linear slip boundary condition at the fracture and estimate the angle-dependent reflection response due to a single fracture. The observed angle-dependent reflectivity is inverted to obtain the fracture compliance and aperture. Two detailed laboratory experiments are performed - one using laterally homogeneous fracture and another using laterally heterogeneous fracture (partly air-filled and partly water-filled). Our results demonstrate that normal compliance (inverse stiffness) of a fracture can be quite accurately estimated from the AVO inversion of P-P reflected waves. It is also possible to obtain the non-zero tangential compliance. The existence of fluid in the fracture can be predicted. Distinction of the fracture infills and quantification of the fracture aperture are possible. This finding will be crucial for numerous new applications in civil and geotechnical engineering, hydrogeophysics, as well as in other areas of earth sciences and non-destructive material testing. @en

Fluid-filled fractures and fissures often determine the pathways and volume of fluid movement. They are critically important in crustal seismology and in the exploration of geothermal and hydrocarbon reservoirs. We introduce a model for tube-wave scattering and generation at dipping, parallel-wall fractures intersecting a fluid-filled borehole. A new equation reveals the interaction of tube wavefield with multiple, closely-spaced fractures, showing that the fracture dip significantly affects the tube waves. Numerical modeling demonstrates the possibility of imaging these fractures using a focusing analysis. The focused traces correspond well with the known fracture density, aperture and dip angles. Testing the method on a VSP dataset obtained at a fault-damaged zone in the Median Tectonic Line, Japan presents evidences of tube waves being generated and scattered at open fractures and thin cataclasite layers. This finding leads to a new possibility for imaging, characterizing and monitoring in-situ hydraulic properties of dipping fractures using the tube wavefield. @en

The reflection seismic method is the most frequently used exploration method for imaging and monitoring subsurface structures with high resolution. It has proven its qualities from the scale of regional seismology to the scale of near-surface applications that look just a few meters below the surface. The reflection method uses controlled active sources at known positions to give rise to reflections recorded at known receiver positions. The reflections’ two-wave travel time is used to extract desired information about and image the subsurface structures. When active sources are unavailable or undesired, one can retrieve body-wave reflections from application of seismic interferometry (SI) to sources of opportunity—quakes, tremors, ambient noise, or even man-made sources not connected to the exploration campaign. We show examples of imaging of subsurface structures using reflections retrieved from quakes and ambient noise. We apply SI by autocorrelation to global earthquake to image seismic and aseismic parts of the Nazca plate and the Moho at these places, SI by multidimensional deconvolution to P-wave coda from local earthquakes to image the Moho and the crust at the same places, and SI by autocorrelation to deep moonquakes to image the lunar Moho and to ambient noise to monitor CO2 sequestration. @en