Hydraulic Tomography Offers Improved Imaging of Heterogeneity in Fractured Rocks

Fractured rocks have presented formidable challenges for accurately predicting groundwater flow and contaminant transport. This is mainly due to our difficulty in mapping the fracture‐rock matrix system, their hydraulic properties and connectivity at resolutions that are meaningful for groundwater modeling. Over the last several decades, considerable effort has gone into creating maps of subsurface heterogeneity in hydraulic conductivity (K) and specific storage (S_s) of fractured rocks. Developed methods include kriging, stochastic simulation, stochastic inverse modeling, and hydraulic tomography. In this article, I review the evolution of various heterogeneity mapping approaches and contend that hydraulic tomography, a recently developed aquifer characterization technique for unconsolidated deposits, is also a promising approach in yielding robust maps (or tomograms) of K and S_s heterogeneity for fractured rocks. While hydraulic tomography has recently been shown to be a robust technique, the resolution of the K and S_s tomograms mainly depends on the density of pumping and monitoring locations and the quality of data. The resolution will be improved through the development of new devices for higher density monitoring of pressure responses at discrete intervals in boreholes and potentially through the integration of other data from single‐hole tests, borehole flowmeter profiling, and tracer tests. Other data from temperature and geophysical surveys as well as geological investigations may improve the accuracy of the maps, but more research is needed. Technological advances will undoubtedly lead to more accurate maps. However, more effort should go into evaluating these maps so that one can gain more confidence in their reliability.     

A probability-weighted moment test to assess simple scaling

We present a statistically robust approach based on probability weighted moments to assess the presence of simple scaling in geophysical processes. The proposed approach is different from current approaches which rely on estimation of high order moments. High order moments of simple scaling processes (distributions) may not have theoretically defined values and consequently, their empirical estimates are highly variable and do not converge with increasing sample size. They are, therefore, not an appropriate tool for inference. On the other hand we show that the probability weighted moments of such processes (distributions) do exist and, hence, their empirical estimates are more robust. These moments, therefore, provide an appropriate tool for inferring the presence of scaling. We illustrate this using simulated Levystable processes and then draw inference on the nature of scaling in fluctuations of a spatial rainfall process.     

A probability-weighted moment test to assess simple scaling

We present a statistically robust approach based on probability weighted moments to assess the presence of simple scaling in geophysical processes. The proposed approach is different from current approaches which rely on estimation of high order moments. High order moments of simple scaling processes (distributions) may not have theoretically defined values and consequently, their empirical estimates are highly variable and do not converge with increasing sample size. They are, therefore, not an appropriate tool for inference. On the other hand we show that the probability weighted moments of such processes (distributions) do exist and, hence, their empirical estimates are more robust. These moments, therefore, provide an appropriate tool for inferring the presence of scaling. We illustrate this using simulated Levystable processes and then draw inference on the nature of scaling in fluctuations of a spatial rainfall process.     

Simultaneous time-lapse electrical resistivity inversion

Time-lapse monitoring is a powerful tool for observing dynamic changes in the subsurface. In particular it offers the potential for achieving inversion results with increased fidelity through the inclusion of complementary information from multiple time-steps. This inclusion of complementary information can reduce the need for spatial smoothing, without adding inversion artifacts to the resulting images. Commonly used time-lapse inversion methods include the ratio method, cascaded time-lapse inversion, difference inversion and differencing independent inversions. We introduce two additional methods in which both time-lapse data sets are inverted simultaneously. In the first, called temporally constrained time-lapse inversion, inversion of both datasets is done under a single optimization procedure and constraints are added to the regularization to ensure that the changes from one time to another are smooth. In the second method, called simultaneous time-lapse inversion, the inversions at time 1 and time 2 are performed simultaneously and constraints of smoothness and closeness to a reference model are applied to the difference image produced at each iteration, and subsequently, the constraints are updated at each iteration. Through both a numerical and a field example we compare the results of common time-lapse inversion methods as well as the introduced approaches. We found that of the commonly used time-lapse inversion methods the difference inversion method produced the best resolution of time-lapse changes and was the most robust in the presence of noise. However, we found that the alternative approach of simultaneous time-lapse inversion produced the best reconstruction of modeled EC changes in the numerical example and easily interpretable high resolution difference images in the field example. Moreover, there was less tailoring of regularization parameters with our simultaneous time-lapse approach, suggesting that it will lend itself well to an automated inversion code.     

First‐arrival traveltime tomography with modified total‐variation regularization

First‐arrival traveltime tomography is a robust tool for near‐surface velocity estimation. A common approach to stabilizing the ill‐posed inverse problem is to apply Tikhonov regularization to the inversion. However, the Tikhonov regularization method recovers smooth local structures while blurring the sharp features in the model solution. We present a first‐arrival traveltime tomography method with modified total‐variation regularization to preserve sharp velocity contrasts and improve the accuracy of velocity inversion. To solve the minimization problem of the new traveltime tomography method, we decouple the original optimization problem into the two following subproblems: a standard traveltime tomography problem with the traditional Tikhonov regularization and a L₂ total‐variation problem. We apply the conjugate gradient method and split‐Bregman iterative method to solve these two subproblems, respectively. Our synthetic examples show that the new method produces higher resolution models than the conventional traveltime tomography with Tikhonov regularization, and creates less artefacts than the total variation regularization method for the models with sharp interfaces. For the field data, pre‐stack time migration sections show that the modified total‐variation traveltime tomography produces a near‐surface velocity model, which makes statics corrections more accurate.     

Tomographic Imaging of Thermally Induced Fractures in Granite Using Bayesian Inversion

— The internal structure of rock samples studied in laboratory experiments can be described by a variety of physical parameters. Some of them, like the velocity of acoustic waves, enhanced velocity or quality factor can be reconstructed by means of ultrasonic tomography. This article presents the results of classical velocity tomography imaging, accompanied by the results of attenuation tomography and recently introduced enhanced velocity tomography obtained for a Lac Du Bonnet granite sample subjected to thermal stresses. To invert acoustic data recorded during six heating cycles, a Bayesian inversion scheme accompanied by a genetic algorithm optimization approach and the robust Cauchy norm have been used. To obtain the highest possible spatial resolution of images the inversion was performed in two steps. In the first step a crude parameterization of the sample was used. The result of this stage was next taken as an a priori model for a final inversion with refined parameterization. The choice of parameterization (cell sizes) and damping parameters at both stages was based on an analysis of the resolution operator. Both velocity and enhanced velocity tomography accurately imaged changes in the rock microstructure caused by thermal stresses. However, enhanced velocity tomography gave a much better spatial resolution than velocity tomography. On the other hand, attenuation tomography based on inversion of pulse rise times was able to image only a rough structure of the sample and it has difficulty with reasonable imaging of the crack formed in the sixth heating cycle.     

Multi-trace basis-pursuit seismic inversion for resolution enhancement

Seismic inversion is an important tool that transfers interface information of seismic data to formation information, which renders the seismic data easily understood by geologists or petroleum engineers. In this study, a novel multi-trace basis-pursuit inversion method based on the Bayesian theory is proposed to enhance the vertical resolution and overcome the lateral instability of inversion results between different traces occasionally seen in the traditional trace-by-trace basis-pursuit inversion method. The Markov process is initially introduced to describe the relationship between adjacent seismic traces and their correlation, which we then close couple in the equation of our new inversion method. A recursive function is further derived to simplify the inversion process by considering the particularity of the coefficient matrix in the multi-trace inversion equation. A series of numerical-analysis and field data examples demonstrates that both the traditional and the new methods for P-wave impedance inversion are helpful in enhancing the resolution of thin beds that are usually difficult to discern from original seismic profiles, thus highlighting the importance of acoustic-impedance inversion for thin bed interpretation. Furthermore, in addition to yielding thin bed inversion results with enhanced lateral continuity and high vertical resolution, our proposed method is robust to noise and cannot be easily contaminated by it, which we verify using both synthetic and field data.     

Seismic Tomography by Monte Carlo Sampling

The paper discusses the performance and robustness of the Bayesian (probabilistic) approach to seismic tomography enhanced by the numerical Monte Carlo sampling technique. The approach is compared with two other popular techniques, namely the damped least-squares (LSQR) method and the general optimization approach. The theoretical considerations are illustrated by an analysis of seismic data from the Rudna (Poland) copper mine. Contrary to the LSQR and optimization techniques the Bayesian approach allows for construction of not only the “best-fitting” model of the sought velocity distribution but also other estimators, for example the average model which is often expected to be a more robust estimator than the maximum likelihood solution. We demonstrate that using the Markov Chain Monte Carlo sampling technique within the Bayesian approach opens up the possibility of analyzing tomography imaging uncertainties with minimal additional computational effort compared to the robust optimization approach. On the basis of the considered example it is concluded that the Monte Carlo based Bayesian approach offers new possibilities of robust and reliable tomography imaging.     

一种基于遗传算法的测井曲线高分辨率处理方法

测井曲线高分辨率处理是提高薄层测井解释精度的一条重要途径.在纵向分辨率匹配技术基础上,利用遗传算法进行测井曲线分辨率处理：先由遗传算法在频率域确定滤波器,然后使用分辨率匹配技术提高测井曲线分辨率.利用该方法对中原油田和新疆塔河油田多口井的八侧向、深感应、自然伽马等多种方法的测井数据进行处理,测井曲线的分辨率得到明显提高,使得其更加适合薄层高分辨率处理解释的需要.     

基于交叉梯度约束的地震初至纵波与瑞雷面波联合反演

本文提出了一种初至纵波(P波)与瑞雷面波的交叉梯度联合反演策略.通过对初至P波进行全波形反演可以获得近地表P波速度结构;通过对仅含瑞雷面波信息的地震数据转换到频率-波数域进行加窗振幅波形反演(Windowed-Amplitude Waveform Inversion,w-AWI)可获得近地表横波(S波)速度结构.在二者反演的目标函数中均加入P波速度和S波速度的交叉梯度作为正则化约束项,使得在反演过程中P波速度和S波速度相互制约,相互约束,从而实现对地震初至P波与瑞雷面波的联合反演.数值模拟结果表明交叉梯度联合反演可以提高S波速度反演分辨率,而P波速度反演结果并没有得到提高.实际资料的反演结果表明,交叉梯度联合反演能够获得更加可信的近地表速度结构.     

Local and controlled prestack depth migration in complex areas

Prestack depth migrations based on wavefield extrapolation may be computationally expensive, especially in 3D. They are also very dependent on the acquisition geometry and are not flexible regarding the geometry of the imaging zone. Moreover, they do not deal with all types of wave, considering only primary reflection events through the model. Integral approaches using precalculated Green's functions, such as Kirchhoff migration and Born-based imaging, may overcome these problems. In the present paper, both finite-difference traveltimes and wavefront construction are used to obtain asymptotic Green's functions, and a generalized diffraction tomography is applied as an example of Born-based acoustic imaging. Target-orientated imaging is easy to perform, from any type of survey and subselection of shot/receiver pairs. Multifield imaging is possible using Green's functions that take into account, for instance, reflections at model boundaries. This may help to recover parts of complex structures which would be missing using a paraxial wave equation approach. Finally, a numerical evaluation of the resolution, or point-spread, function at any point of the depth-migrated section provides valuable information, either at the survey planning stage or for the interpretation.     

地震井间曲射线反射加透射层析（CCRTT）

本文提出了一种新的地震井间层析方法，即曲射线反射＋透射（ＣＣＲＴＴ）层析方法。该方法可以提高对油气储层层析成像的分辨率。适合用于储油层薄且与周围地层速度对比差大的油区。文中还从理论上ＣＣＲＴＴ可以提高分辨，使成像射线分布均匀，改善图像重建质量，对油田资料用ＣＣＲＴＴ图象重建的结果可以分辨１ｍ厚的油层。     

Source side seismic tomography(3STomo):A novelmethod to image the subsurface structure beneath seismically active region

We propose a novel seismic tomography method,Source Side Seismic Tomography(3STomo),which is designed particularly to image the subsurface structure beneath seismically active regions.Unlike the teleseismic tomography,in which the data are relative traveltime residuals between closely spaced stations for each teleseismic event,3STomo uses relative traveltime shifts between earthquakes within the study region for each distant station.Given the relatively evener distribution of global seismic stations,this method has unique advantages for imaging the structure beneath regions that have numerous earthquakes but lack of dense seismic stations,for example,some subduction zones and spreading ridges in the ocean.In addition,3STomo has potentially better vertical resolution at shallow depths than the traditional teleseismic tomography.The effect of the inaccurate source parameters on its resolution can be minimized by using depth phases and the technique of joint source and structure inversion.Numerical experiments and application to Luzon Island,Philippines show that 3STomo can be a valuable tool to investigate the subsurface structure beneath some areas where the traditional method cannot be applied to,or at least it can be used as a complementary component of conventional teleseismic tomography to obtain better back-azimuth coverage and achieve higher resolution at shallow depths in the inversion.     

A review of the influencing factors on teleseismic traveltime tomography

Teleseismic traveltime tomography is an important tool for investigating the crust and mantle structure of the Earth. The imaging quality of teleseismic traveltime tomography is affected by many factors, such as mantle heterogeneities, source uncertainties and random noise. Many previous studies have investigated these factors separately. An integral study of these factors is absent. To provide some guidelines for teleseismic traveltime tomography, we discussed four main influencing factors:the ...     

频率域2.5-D井间波形层析成像及其实际应用

从频率域3-D声波波动方程出发,结合井间观测方式的特点,基于Tarantola广义反演理论,提出了一种频率域2.5-D井间波形层析成像方法.数值模型试验结果表明：该方法对薄层厚度的分辨能力能达到约主频波长的1/4,且分辨率显著高于走时层析成像,尤其垂直分辨率有实质改善.模拟资料的抗噪试验表明：在信噪比为0.8的情况下,随机噪声对波形层析成像的影响较小;而相干噪声对全波形层析成像的影响显著,特别是初至波附近的强振幅干扰影响更为严重.井间实际资料的试处理结果表明：波形层析成像能很好地刻画井间介质的分布情况与储层连通性,对于油藏开发阶段的方案实施具有指导意义.     

Empirical nonergodic shaking scenarios based on spatial correlation models: An application to central Italy

This paper provides a new methodological framework to generate empirical ground shaking scenarios, designed for engineering applications and civil protection planning. The methodology is useful both to reconstruct the ground motion pattern of past events and to generate future shaking scenarios, in regions where strong‐motion datasets from multiple events and multiple stations are available. The proposed methodology combines (1) an ad‐hoc nonergodic ground motion model (GMM) with (2) a spatial correlation model for the source region‐, site‐, and path‐systematic residual terms, and (3) a model of the remaining aleatory error to take into account for directivity effects. The associated variability is a function of the type of scenario generated (bedrock or site, past or future event) and it is minimal for source areas where several events have occurred and for sites where recordings are available. In order to develop the region‐specific fully nonergodic GMM and to compute robust estimation of the residual terms, the approach is calibrated on a highly dense dataset compiled for the area of central Italy. Example tests demonstrate the validity of the approach, which allows to simulate acceleration response spectra at unsampled sites, as well as to capture peculiar physical features of ground motion patterns in the region. The proposed approach could be usefully adopted for data‐driven simulations of ground shaking maps, as alternative or complementary tool to physic‐based and stochastic‐based approaches.     

Comparison of approaches for predicting solute transport: sandbox experiments

The main purpose of this paper was to compare three approaches for predicting solute transport. The approaches include: (1) an effective parameter/macrodispersion approach (Gelhar and Axness 1983); (2) a heterogeneous approach using ordinary kriging based on core samples; and (3) a heterogeneous approach based on hydraulic tomography. We conducted our comparison in a heterogeneous sandbox aquifer. The aquifer was first characterized by taking 48 core samples to obtain local-scale hydraulic conductivity (K). The spatial statistics of these K values were then used to calculate the effective parameters. These K values and their statistics were also used for kriging to obtain a heterogeneous K field. In parallel, we performed a hydraulic tomography survey using hydraulic tests conducted in a dipole fashion with the drawdown data analyzed using the sequential successive linear estimator code (Yeh and Liu 2000) to obtain a K distribution (or K tomogram). The effective parameters and the heterogeneous K fields from kriging and hydraulic tomography were used in forward simulations of a dipole conservative tracer test. The simulated and observed breakthrough curves and their temporal moments were compared. Results show an improvement in predictions of drawdown behavior and tracer transport when the K tomogram from hydraulic tomography was used. This suggests that the high-resolution prediction of solute transport is possible without collecting a large number of small-scale samples to estimate flow and transport properties that are costly to obtain at the field scale.     

Discrete cosine transform for parameter space reduction in Bayesian electrical resistivity tomography

Electrical resistivity tomography is a non-linear and ill-posed geophysical inverse problem that is usually solved through gradient-descent methods. This strategy is computationally fast and easy to implement but impedes accurate uncertainty appraisals. We present a probabilistic approach to two-dimensional electrical resistivity tomography in which a Markov chain Monte Carlo algorithm is used to numerically evaluate the posterior probability density function that fully quantifies the uncertainty affecting the recovered solution. The main drawback of Markov chain Monte Carlo approaches is related to the considerable number of sampled models needed to achieve accurate posterior assessments in high-dimensional parameter spaces. Therefore, to reduce the computational burden of the inversion process, we employ the differential evolution Markov chain, a hybrid method between non-linear optimization and Markov chain Monte Carlo sampling, which exploits multiple and interactive chains to speed up the probabilistic sampling. Moreover, the discrete cosine transform reparameterization is employed to reduce the dimensionality of the parameter space removing the high-frequency components of the resistivity model which are not sensitive to data. In this framework, the unknown parameters become the series of coefficients associated with the retained discrete cosine transform basis functions. First, synthetic data inversions are used to validate the proposed method and to demonstrate the benefits provided by the discrete cosine transform compression. To this end, we compare the outcomes of the implemented approach with those provided by a differential evolution Markov chain algorithm running in the full, un-reduced model space. Then, we apply the method to invert field data acquired along a river embankment. The results yielded by the implemented approach are also benchmarked against a standard local inversion algorithm. The proposed Bayesian inversion provides posterior mean models in agreement with the predictions achieved by the gradient-based inversion, but it also provides model uncertainties, which can be used for penetration depth and resolution limit identification.     

Quantitative imaging of complex structures from dense wide-aperture seismic data by multiscale traveltime and waveform inversions: a case study

An integrated multiscale seismic imaging flow is applied to dense onshore wide‐aperture seismic data recorded in a complex geological setting (thrust belt). An initial P‐wave velocity macromodel is first developed by first‐arrival traveltime tomography. This model is used as an initial guess for subsequent full‐waveform tomography, which leads to greatly improved spatial resolution of the P‐wave velocity model. However, the application of full‐waveform tomography to the high‐frequency part of the source bandwidth is difficult, due to the non‐linearity of this kind of method. Moreover, it is computationally expensive at high frequencies since a finite‐difference method is used to model the wave propagation. Hence, full‐waveform tomography was complemented by asymptotic prestack depth migration to process the full‐source bandwidth and develop a sharp image of the short wavelengths. The final traveltime tomography model and two smoothed versions of the final full‐waveform tomography model were used as a macromodel for the prestack depth migration. In this study, wide‐aperture multifold seismic data are used. After specific preprocessing of the data, 16 frequency components ranging from 5.4 Hz to 20 Hz were inverted in cascade by the full‐waveform tomography algorithm. The full‐waveform tomography successfully imaged SW‐dipping structures previously identified as high‐resistivity bodies. The relevance of the full‐waveform tomography models is demonstrated locally by comparison with a coincident vertical seismic profiling (VSP) log available on the profile. The prestack depth‐migrated images, inferred from the traveltime, and the smoothed full‐waveform tomography macromodels are shown to be, on the whole, consistent with the final full‐waveform tomography model. A more detailed analysis, based on common‐image gather computations, and local comparison with the VSP log revealed that the most accurate migrated sections are those obtained from the full‐waveform tomography macromodels. A resolution analysis suggests that the asymptotic prestack depth migration successfully migrated the wide‐aperture components of the data, allowing medium wavelengths in addition to the short wavelengths of the structure to be imaged. The processing flow that we applied to dense wide‐aperture seismic data is shown to provide a promising approach, complementary to more classical seismic reflection data processing, to quantitative imaging of complex geological structures.