Offset Inversion Research Articles

Seismic Work Flow Characterizes Deep, Thin Formation Layers Offshore South China Sea

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper OTC 30164, “Deep and Thin Overpressure Reservoir Characterization of Paleogene Wenchang Formation in the Enping 17 Sag of the South China Sea,” by Jun Liu and Yingwei Li, CNOOC, and Donghai Liang, Schlumberger, et al. The paper has not been peer reviewed. Copyright 2021 Offshore Technology Conference. Reproduced by permission. The complete paper describes an integrated work flow for 3D seismic reservoir characterization of offshore deep and thin layers in the Eocene Wenchang formation (WCF) without sufficient well data. The work flow includes seismic data reprocessing, well-log-based rock physics analysis, seismic structure interpretation, 3D simultaneous amplitude variation with offset (AVO) inversion, 3D lithology prediction, and geological integrated analysis. Formation Development and Objectives The Pearl River Mouth basin (PRMB) on the northern continental margin of the South China Sea has undergone multistage extensional rifts. The Enping Sag lies in the Zhu1 depression, north of the PRMB, and consists of three subsags. Enping 17 is the largest and deepest sag, with an area of 550 km2, and the thickness of Eocene sediments is greater than 3000 m. The deep middle Eocene WCF, with gray lacustrine mudstones, is hydrocarbon-rich and is the major source rock in the area. A wildcat well had penetrated the WCF at an area with a vertical thickness of 380 m. During drilling, the mud weight was increased to 1.46 g/cm3 from 4570 m total vertical depth (TVD) downward because of increasing pore pressure and higher background gas abnormalities in the WCF. A high pore-pressure gradient of 14.5 KPa/m was measured by drillstem test (DST) at a depth of 4641.5 m TVD. Under the protection of the high pore pressure, the high-quality reservoir layer from 4642 to 4651 m TVD was encountered with 12% average porosity, 3.6-md permeability, and 47.1% saturation. Although a hydrocarbon sample was not obtained during the downhole test because of technical restrictions of DST in 1985, gas surge and a small amount of gas and condensate oil were observed after the test instruments were pulled to surface. With the subsequent development of field techniques, it was likely that current drilling and DST techniques could achieve productive oil flow in this layer.

Uncertainty estimation in AVO inversion using Bayesian dropout based deep learning

Amplitude versus offset (AVO) inversion is the process of transforming seismic reflection into elastic properties such as P- and S- impedance to estimate the interval properties and thickness of underlying geology using well log and post- or prestack seismic data. Recent applications of AVO inversion based on deep learning have shown excellent results and practical applicability. However, traditional deep learning methods yield only prediction results without any associated predictive uncertainty. Two types of predictive uncertainty should be considered: aleatoric uncertainty, which occurs when noisy data are included; and epistemic uncertainty, which is caused by a lack of data. To estimate the impedances and their uncertainties, Bayesian approximation using Monte Carlo dropout is applied, which simply approximates a Bayesian neural network. From the proposed method, we can not only predict impedances but also estimate their predictive uncertainties in the seismic survey area and determine whether prediction results are reliable.

Hierarchical Bayesian Probabilistic Seismic AVO Inversion Using Gibbs Sampling With IA2RMS Algorithm

From the observed seismic data, the estimation of elastic parameters and lithofacies of subsurface layers with seismic amplitude variation with offset (AVO) inversion plays an important role in reservoir characterization. The sequential estimation of elastic parameters and lithofacies in AVO inversion usually affect the prediction accuracies of model parameters without considering the prior information related to lithofacies. We propose a novel probabilistic AVO inversion approach in hierarchical Bayesian framework that combines a hierarchical iterative strategy with Gibbs-IA2RMS sampling, to estimate elastic parameters and lithofacies simultaneously. From the exact PP-wave reflection coefficient, we first derive the posterior distribution of model parameters involving a Bayesian hyper-parameter of lithofacies through the hierarchical prior probability distributions and the likelihood distribution of observed data. Based on Monte Carlo Markov chain approximation, we then introduce an iterative Gibbs-IA2RMS sampling to achieve the high sampling stability of the high-dimensional posterior PDF in AVO inversion. The algorithm realizes the adaptive construction of proposal distribution, and has a higher acceptance rate than the generic Metropolis-Hastings algorithm. The numerical results show that the approach effectively simulates the posterior distributions and inversion uncertainties of model parameters, and improves the computational efficiency of probabilistic AVO inversion. The applicability and validity of the proposed approach are also demonstrated with a field data application.

Bayesian Seismic AVO Inversion Using a Laterally Coupled Multimodal Prior Model

A Bayesian seismic amplitude versus offset (AVO) inversion scheme with a laterally coupled prior model for porosity, water saturation, and volume of clay is proposed. A 2-D section and a 3-D volume of an oil reservoir are studied. The oil reservoir is considered at the initial state, which entails gravitationally induced bimodality in the water saturations along vertical traces. A selection Gaussian random field (S-GRF) prior model, capable of representing this bimodality, is specified for porosity, water saturation, and volume of clay. The S-GRF is specified to have lateral correlation, which may reduce the impact of trace-unique signal errors in the seismic AVO data on the inversion results. The likelihood model is linear and Gaussian, for which the S-GRF prior model is conjugate; hence, the posterior model is also an S-GRF. The form of the posterior distribution is therefore known and its parameter values can be analytically computed. Real seismic AVO data from the 2-D section and the 3-D volume are inverted and the results appear to be reliable along validation wells and represent a geologically plausible reservoir design. Furthermore, a notable variance reduction in the laterally coupled posterior model relative to an alternative posterior model without lateral coupling is achieved.

Hybrid Inversion of Reservoir Parameters Based on Cosimulation and the Gradual Deformation Method

A new hybrid inversion methodology for petrophysical properties (porosity, water saturation, and volume of clay) based on partially stacked seismic angle gathers was presented. The innovation of this method is that it combines the advantages of high efficiency of analytical and semianalytical multistep petrophysical estimation with the advantages of spatial continuity and high resolution of geostatistical direct inversion of reservoir parameters. A trace-by-trace linearized amplitude versus offset (AVO) inversion and semianalytical petrophysical estimation approach could efficiently achieve a preliminary estimation of reservoir parameters under some assumptions and approximations. These laterally unconstrained preliminary estimation results are able to provide effective information for finer-resolution geostatistical simulation and improve the computational efficiency of stochastic optimization. The 3-D fast Fourier transform moving average (FFT-MA) geostatistical cosimulation and the stochastic optimization by gradual deformation method (GDM) improve the resolution and spatial continuity of the preliminary estimation results. At the same time, stochastic inversion overcomes the assumptions in the analytical inversion algorithm that the parameters need to conform to the logarithmic Gaussian distribution and the linear approximation of the Zoeppritz equation. The method was tested on a synthetic case and a real case. The results show that compared with the analytical and semianalytical methods, this hybrid inversion can obtain results with finer resolution and better spatial continuity, and the computational efficiency is significantly improved compared with the geostatistical direct inversion of reservoir parameters. Uncertainty evaluation can be obtained by performing statistical analysis on the multiple realizations of stochastic inversions.

Lithology, porosity and saturation joint prediction using stochastic rock physics modelling and litho-petro-elastic inversion

In this paper we present the application of a single-loop litho-petro-elastic (LPE) inversion, which is a data assimilation algorithm that uses nonlinear Zoeppritz reflectivity operators with sequential filtering. It integrates rock physics models with seismic amplitude variation with offset (AVO) inversion and Bayesian inversion to define lithology, elastic, and petrophysical properties in a single loop, thus, combining several steps of the conventional reservoir characterization workflow. In the conventional multistep approach, the lithology and petrophysical properties are generated sequentially from elastic properties after AVO inversion is performed, which can add prediction uncertainty at each step and produce results that are not correlated with each other. The LPE inversion ensures that the predicted properties maintain the relationships defined by the rock physics model. The LPE inversion was tested on data from offshore Australia with three wells, for a faulted reservoir zone containing oil with a gas cap. It provided robust predictions for lithology, porosity, and water saturation, which matched acceptably at the three wells. The algorithm also accounted for subsurface uncertainties as it produced prediction probabilities of facies, porosity, and water saturation using multidimensional probability density functions. This approach can be effectively used to classify reservoir properties in a single-loop workflow.

Basin-wide rock-physics analysis in Campeche Basin, Gulf of Mexico — Phase II: Reservoir rock and fluid properties

We present a basin-wide rock-physics analysis of reservoir rocks and fluid properties in Campeche Basin. Reservoir data from discovery wells are analyzed in terms of their relationship between P-wave velocity, density, porosity, clay content, Poisson's ratio (PR), and P-impedance (IP). The fluid properties are computed by using in-situ pressure, temperature, American Petroleum Institute gravity, gas-oil ratio, and volume of gas, oil, and water. Oil- and gas-saturated reservoir sands show strong PR anomalies compared to modeled water sand at equivalent depth. This suggests that PR anomalies can be used as a direct hydrocarbon indicator in the Tertiary sands in Campeche Basin. However, false PR anomalies due to residual gas or oil exist and compose about 30% of the total anomalies. The impact of fluid properties on IP and PR is calibrated using more than 30 discovery wells. These calibrated relationships between fluid properties and PR can be used to guide or constrain amplitude variation with offset inversion for better pore fluid discrimination.

Introduction to this special section: Rock physics

In simple terms, rock physics provides the much-needed link between measurable elastic properties of rocks and their intrinsic properties. This enables us to connect seismic data, well logs, and laboratory measurements to minerology, porosity, permeability, fluid saturations, and stress. Rock-physics relationships/models are used to understand seismic signatures in terms of reservoir properties that help in exploration risk mitigation. Traditionally, rock physics has played an irreplaceable role in amplitude variation with offset (AVO) modeling and inversion, 3D/4D close-the-loop studies, and seismic time-lapse analysis and interpretation. Today, rock-physics research and application have influenced a much wider space that spans digital rock physics, microseismic, and distributed acoustic sensing (DAS) data analysis. In this special section, we have included papers that cover much of these advanced methods, providing us with a better understanding of subsurface elastic and transport properties, thereby reducing bias and uncertainties in quantitative interpretation.

Fluid discrimination incorporating viscoelasticity and frequency-dependent amplitude variation with offsets inversion

Frequency-dependent amplitude versus offset (FAVO) inversion is a popular method to estimate the frequency-dependent elastic parameters by using amplitude and frequency information of pre-stack seismic data to guide fluid identification. Current frequency-dependent AVO inversion methods are mainly based on elastic theory without the consideration of the viscoelasticity of oil/gas. A fluid discrimination approach is proposed in this study by incorporating the viscoelasticity and relevant FAVO inversion. Based on viscoelastic and rock physics theories, a frequency-dependent viscoelastic solid-liquid decoupling fluid factor is initially constructed, and its sensitivity in fluid discrimination is compared with other conventional fluid factors. Furthermore, a novel reflectivity equation is derived in terms of the viscoelastic solid-liquid decoupling fluid factor. Due to the introduction of viscoelastic theory, the proposed reflectivity is related to frequency, which is more widely applicable than the traditional elastic reflectivity equation directly derived from the elastic reflectivity equation on frequency. Finally, a pragmatic frequency-dependent inversion method is introduced to verify the feasibility of the equation for frequency-dependent viscoelastic solid-liquid decoupling fluid factor prediction. Synthetic and field data examples demonstrate the feasibility and stability of the proposed approach in fluid discrimination.

Robust AVO inversion for the fluid factor and shear modulus

Seismic estimation of the fluid factor and shear modulus plays an important role in reservoir fluid identification and characterization. Various amplitude variation with offset inversion methods have been used to estimate these two parameters, which are generally based on approximate formulations of the Zoeppritz equations. However, the accuracy of these methods is limited because the forward modeling ability of approximate equations is incorrect under the conditions of strong impedance contrast and large incidence angles. Therefore, to improve the estimation accuracy, we have used the Zoeppritz equations to directly invert for the fluid factor and shear modulus. Based on the poroelasticity theory, we derive the Zoeppritz equations in a new form containing the fluid factor, shear modulus, density, and dry-rock velocity ratio squared. The objective function is then constructed using these equations in a Bayesian framework with the addition of a differentiable Laplace distribution blockiness constraint term to the prior model to enhance the fluid boundaries. Finally, the nonlinear objective function is solved by combining the Taylor expansion and the iterative reweighted least-squares algorithm. Numerical experiments indicate that the inversion accuracy of our method may heavily depend on the parameter of the dry-rock velocity ratio square that is assumed to be static. However, tests on synthetic and field data show that our method can estimate the fluid factor and shear modulus with satisfactory accuracy in the case of choosing a reasonable static value of this parameter. In addition, we determine that the accuracy of this method is higher than that of the linearized formulation.

Hydrocarbon Mapping on Reservoir Carbonate Using AVO Inversion Method

Amplitude Versus Offset (AVO) inversion has been applied for reservoir analysis focused on the horizon carbonate Peutu and Belumai. Simultaneous inversion analysis is used to determine gas anomaly inside carbonate-rocks and it’s spread laterally around target zones. It is based on the fact that small Vpand Vs value changes are going to show the better anomaly to identify reservoir fluid content. The AVO inversion method applies angle gather data as the input and then it is inverted to produce P impedance (Zp) and S impedance (Zs). Zp and Zs are derived to produce Lambda-Rho and Mu-Rho that are sensitive to fluid and lithology. Value of Mu-Rho between 44–65 Gpa gr/cc while value of Lambda-Rho smaller than 10 Gpa gr/cc (for carbonate-rock filled by fluid). This research found that Lambda-Rho is the best parameter to show the existence of hydrocarbon in the case of gas. While Mu-Rho is the best parameter to show the differences in lithology.

Estimation of Brittleness and Anisotropy Parameters in Transversely Isotropic Media With Vertical Axis of Symmetry

In the absence of fracture, the strata with horizontal interbedding structure can be approximately equivalent to transversely isotropic media with vertical axis of symmetry (VTI) in the sedimentary basin. Accurate estimation of Young’s modulus, Poisson’s ratio, and weak anisotropy (WA) parameters can provide basic information for further prediction of shale reservoir rock brittleness and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> stress. Based on the scattering theory and Born approximation, we derive the P-wave reflection coefficients involving Young’s modulus and Poisson’s ratio and WA parameters for an interface separating two elastic VTI media. Assuming in the case of shale, we modify this reflection coefficient to involve only three model parameters through a series of integration and simplification for stabler inversion. A Bayesian amplitude versus offset (AVO) inversion method is implemented to estimate the three attributes, which are then converted to calculate the brittleness-related and WA parameters. The numerical simulation results show that for AVO of III in the case of gas-bearing shale, the derived approximation has more accuracy than the Young’s modulus, Poisson’s ratio and density (YPD) equation, especially at large angle. Tests on synthetic and real seismic data verify that the established inversion strategy for VTI shale reservoirs is stable and accurate in the estimation of brittleness-related and WA parameters.

Adaptive individual weight-gain AVO inversion with smooth nonconvex regularization

Amplitude variation with offset (AVO) inversion is a widely used approach to obtain reliable estimates of elastic parameter in the fields of seismic exploration. However, the AVO inversion is an ill-posed problem because of the band-limited characteristic of seismic data. The regularization constraint plays an important role in improving inversion resolution. Total variation (TV) class regularization based on L $$_1$$ norm has been introduced in seismic inversion. But, these methods may underestimate the high-amplitude components and obtain low-resolution results. To tackle these issues, we propose to combine a smooth nonconvex regularization approach with adaptive individual weight-gain. Compared with the L $$_1$$ norm regularizers, the proposed smoothed nonconvex sparsity-inducing regularizers can lead to more accurate estimation for high-amplitude components. Different from previous regularization methods, the proposed approach also assigns different weight regularization parameters for different strata, which we call adaptive individual weight-gain strategy. To ensure sufficient minimization of the constructed objective function, a spectral Polak–Ribiere–Polyak conjugate gradient method with line search step size is used. Further, we prove that the proposed algorithm converges to a stationary point. The synthetic data tests illustrate that our approach has improved performance compared with the conventional TV class regularization methods. Field data example further verifies the higher resolution of the proposed approach.

Bayesian seismic amplitude variation with offset inversion for reservoir variables with bimodal spatial histograms

We consider seismic amplitude variation with offset (AVO) inversion for prediction of the reservoir properties porosity and water saturation. An oil reservoir at the initial state is studied; hence, gravitational effects dominate and keep hydrocarbons from mixing with water. Histograms of observations of water saturation along wells are consequently clearly bimodal, which is challenging to model. The seismic AVO inversion is cast into a Bayesian framework. The prior spatial model for porosity and water saturation is specified to be a selection Gaussian random field (S-GRF), which is capable of representing spatial variables with multimodal histograms. By using linear models for the seismic and rock-physics likelihoods, the posterior model is also an S-GRF. Hence, the Bayesian seismic inversion can be solved analytically, and the bimodal characteristics of water saturation can be reproduced. The methodology is defined and demonstrated on two synthetic cases inspired by real data from an oil reservoir, and thereafter applied to the real case. The well observations are fairly accurately reproduced and the inversion results are considered to be substantial improvements compared to standard spatial Gaussian models.

Bayesian Inversion of Time-Lapse Seismic AVO Data for Multimodal Reservoir Properties

We consider time-lapse seismic amplitude versus offset (AVO) inversion for the reservoir properties porosity and water saturation, with a focus on monitoring the evolution of water saturation in a dynamic setting of ongoing production. We operate in a Bayesian framework based on the integration of seismic AVO modeling and rock physics relations. One major challenge in the inversion of seismic data for reservoir properties is the multimodality of these properties. Fluid saturation is generally bimodal due to the gravity effect, and often distinctly so, with abrupt spatial mode transitions. The novelty of the proposed approach is the assumption of a selection Gaussian random field (S-GRF) for the prior spatial model of porosity and water saturation, which can represent the multimodal characteristics of these reservoir properties. The likelihood model is Gauss-linear and based on linearized seismic and rock physics models, which entails that the associated posterior model is also an S-GRF, with analytically assessable parameters. Hence, the posterior model is capable of representing multimodality and abrupt spatial mode transitions. Two realistic case studies are considered; the production of an oil reservoir in the North Sea, and the injection of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> into a subsurface potential CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> storage unit. Focus is on the movement of the oil–water-contacts along a vertical profile in the first case, and on the expansion of the CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> region in a cross section in the other, both of which can be inferred from the changes in the water saturations. The results are considered to be very encouraging and the proposed statistical formulation appears to be particularly well suited for fluid monitoring problems of the described type.

Application of brittleness index to interpret microseismic event distribution in a hydraulically fractured shale formation

Many factors can impact the location data of microseismic events, including natural fractures, rock lithology, in situ stress, and hydraulic-fracturing parameters. The distribution of microseismic events generally tends toward highly brittle areas or areas with brittle minerals. Moreover, location data of microseismic events lack effective evaluation methods. Therefore, we have developed a method to use lithologic information and prestack seismic data to explain the distribution of well Tian Xing microseismic events. We have analyzed the brittleness of the target formation through the well logs and core. We inverted the Young’s modulus and Poisson’s ratio based on simultaneous amplitude variation with offset inversion by the prestack seismic data. We then computed the 3D brittleness index (BI) property volume by Grieser and Rickman’s method. In addition, the microseismic event distribution and BI map were then combined to show the internal relationship between the two results. We found that the well logs and core analysis demonstrated that the target formation has high brittleness. Generally, areas with more natural fractures have a higher probability of inducing hydraulic fractures. However, the analysis results show that the BI has an impact on the distribution of hydraulic fractures. Therefore, BI explains the reason for the distribution of almost all events in the northeast of the perforation. These observations also supported the concept that microseismic events preferentially grow toward more brittle areas.

Integration of new interpretation, attribute analysis and inversion results for the Dampier Sub-basin, North West Shelf of Australia

The Davros-Typhon Multi-Client 3D surveys are located approximately 70km from the north-west coast of Australia, largely covering the NE trending Dampier Sub-basin and straddling the Rankin Trend within the Northern Carnarvon Basin. The basins within the North West Shelf formed as a result of seafloor spreading, associated with the breakup of the North West margin of East Gondwana. The combined, contiguous Davros-Typhon survey areas cover a number of significant discoveries and producing fields, which include both oil and gas accumulations. The key objective of the survey was to enhance the imaging of Triassic to Lower Cretaceous reservoir units and to develop a new interpretation framework, made possible by the modern broadband acquisition parameters and advanced processing techniques. Challenges associated with imaging and interpretation include the effects of high velocity carbonate overburden, steeply dipping structures, fault shadow and structural complexity at depth, which is critical for evaluation of reservoir targets. A major reprocessing effort was undertaken to further mitigate these issues, which included Davros and a number of adjacent existing 3D surveys, resulting in the Typhon Multi-Client 3D. CGG Multi-client and New Ventures geoscientists, in collaboration with CGG Seismic Imaging, have undertaken new interpretation and amplitude versus offset (AVO) inversion analysis using subsets of the Typhon 3D. The resulting volume-based attribute analysis and integration of new AVO inversion results demonstrates enhanced attribute quality for the reprocessed data and provides a platform for quantitative analysis over a large area of the Northern Carnarvon Basin.

AVO inversion using pseudoisotropic elastic properties

Amplitude variation with offset (AVO) inversion of an anisotropic data set is a challenging task. Nonnegligible differences in the anisotropy parameters between the various lithologies make the seismic data AVO response completely different from the isotropic synthetic seismogram. In this case, it is difficult to invert for VP/VSand density consistent with well-log data. AVO inversion using pseudoisotropic elastic properties is a practical solution to this problem. Verification of this method was performed using data from an offshore Western Australia field. It was found that wavelet extraction and density inversion are improved significantly by replacing the isotropic elastic properties with the pseudoisotropic properties. Inverted density shows reasonable quality and therefore can be included in the reservoir characterization study. Postinversion analyses can be performed effectively on the pseudoisotropic elastic properties because crossplot analysis shows the increased separation of different lithofacies due to contrasts in anisotropy parameters. This result could have significant implications for other fields, as shale constitutes most of the overburden in conventional oil and gas fields and often shows strong elastic anisotropy.

Direct inversion for reservoir parameters from prestack seismic data

Abstract Reliably estimating reservoir parameters is the final target in reservoir characterisation. Conventionally, estimating reservoir characters from seismic inversion is implemented by indirect approaches. The indirect estimation of reservoir parameters from inverted elastic parameters, however, will produce large bias due to the propagation of errors in the procedure of inversion. Therefore, directly obtaining reservoir parameters from prestack seismic data through a rock-physical model and prestack amplitude variation with offset (AVO) inversion is proposed. A generalised AVO equation in terms of oil-porosity (OP), sand indicator (SI) and density is derived by combining a physical rock model and the Aki–Richards equation in a whole system. This makes it possible to perform direct inversion for reservoir parameters. Next, under Bayesian theorem, we develop a robust prestack inversion approach based on the new AVO equation. Tests on synthetic seismic gathers show that it can dramatically reduce the prediction error of reservoir parameters. Furthermore, field data application illustrates that reliable reservoir parameters can be directly obtained from prestack inversion.

Elastic least-squares migration for quantitative reflection imaging of fracture compliances

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.