Laterally constrained inversion of helicopter-borne frequency-domain electromagnetic data

Helicopter-borne frequency-domain electromagnetic (HEM) surveys are used for fast high-resolution, three-dimensional resistivity mapping. Standard interpretation tools are often based on layered earth inversion procedures which, in general, explain the HEM data sufficiently. As a HEM system is moved while measuring, noise on the data is a common problem. Generally, noisy data will be smoothed prior to inversion using appropriate low-pass filters and consequently information may be lost.For the first time the laterally constrained inversion (LCI) technique has been applied to HEM data combined with the automatic generation of dynamic starting models. The latter is important because it takes the penetration depth of the electromagnetic fields, which can heavily vary in survey areas with different geological settings, into account. The LCI technique, which has been applied to diverse airborne and ground geophysical data sets, has proven to be able to improve the HEM inversion results of layered earth structures. Although single-site 1-D inversion is generally faster and — in case of strong lateral resistivity variations — more flexible, LCI produces resistivity — depth sections which are nearly identical to those derived from noise-free data.The LCI results are compared with standard single-site Marquardt–Levenberg inversion procedures on the basis of synthetic data as well as field data. The model chosen for the generation of synthetic data represents a layered earth structure having an inhomogeneous top layer in order to study the influence of shallow resistivity variations on the resolution of deep horizontal conductors in one-dimensional inversion results. The field data example comprises a wide resistivity range in a sedimentary as well as hard-rock environment.If a sufficient resistivity contrast between air and subsurface exists, the LCI technique is also very useful in correcting for incorrect system altitude measurements by using the altitude as a constrained inversion parameter.     

含激电效应的航空瞬变电磁数据横向约束反演

受激电效应影响,航空瞬变电磁响应曲线经常出现异常快速衰减和符号反转现象,使用Cole-Cole模型的等效电阻率代替原模型实电阻率能很好的解释该现象,但由于激电多个参数的引入,使得反演多解性问题更加严重.本文基于Cole-Cole模型实现了航空瞬变电磁一维正演,采用横向约束反演同时计算激电参数及层厚,增加约束条件改善多解...     

The inversion of surface wave data

Observations of surface waves depend both on the structure traversed and the nature of the source, and therefore inversion of surface wave data can yield information about both structure and sources. The available methods for structural inversion are compared and discussed and a suggestion made for improved source inversion.     

Improved Monte Carlo inversion of surface wave data

Inversion of surface wave data suffers from solution non‐uniqueness and is hence strongly biased by the initial model. The Monte Carlo approach can handle this non‐uniqueness by evidencing the local minima but it is inefficient for high dimensionality problems and makes use of subjective criteria, such as misfit thresholds, to interpret the results. If a smart sampling of the model parameter space, which exploits scale properties of the modal curves, is introduced the method becomes more efficient and with respect to traditional global search methods it avoids the subjective use of control parameters that are barely related to the physical problem. The results are interpreted drawing inference by means of a statistical test that selects an ensemble of feasible shear wave velocity models according to data quality and model parameterization. Tests on synthetic data demonstrate that the application of scale properties concentrates the sampling of model parameter space in high probability density zones and makes it poorly sensitive to the initial boundary of the model parameters. Tests on synthetic and field data, where boreholes are available, prove that the statistical test selects final results that are consistent with the true model and which are sensitive to data quality. The implemented strategies make the Monte Carlo inversion efficient for practical applications and able to effectively retrieve subsoil models even in complex and challenging situations such as velocity inversions.     

地面磁共振与瞬变电磁横向约束联合反演方法研究

大地电阻率分布信息是影响磁共振地下水探测反演结果准确性的重要因素.在众多电磁法勘探技术中,瞬变电磁法具有高分辨率、高效率和大探测深度等优势,能准确探测地下几百米范围内的电阻率分布信息.因此磁共振与瞬变电磁联合解释方法具有重要意义.然而,利用单一测点拼接的磁共振与瞬变电磁联合解释方法进行模拟二维反演时存在解释结果不唯一,容易出现错误异常体等问题,尤其在复杂地质情况下,同一测线上相邻测点探测结果连续性差,解释结果偏离实际.基于此,本文提出磁共振与瞬变电磁横向约束联合反演方法（Laterally Constrained Inversion,简称LCI）,重点引入外推积分法（quadrature with extrapolation,简称QWE）,解决了传统正演过程中基于直接数值积分方法引起的求解效率低的问题,保证了联合反演方法的顺利实施,进而以相邻测点地下结构应具备连续性为依据,引入横向约束反演思想,通过在联合反演目标函数中加入相邻测点间各模型参数约束矩阵,提高磁共振解释结果准确性,加强探测剖面地质结构和含水模型连续性.经过理论模型证实,本文提出的LCI方法能有效提高传统一维反演结果的稳定性和唯一性.最后,对安徽黄山野外实际探测数据进行横向约束联合反演,验证了磁共振与瞬变电磁LCI联合反演方法的实用性.本文的研究成果将为磁共振与瞬变电磁空间约束联合反演奠定基础.

     

Multi-offset phase analysis of surface wave data (MOPA)

Inaccuracy in the shear wave velocity profile inverted from surface wave data manifests from both modelling error and data uncertainty. An alternative method for dispersion curve evaluation by weighted linear regression of phase-offset data can be applied to both equispaced and non-equispaced data for objective identification of these often overlooked error sources.From field data, near-field effects are noted to at most half a wavelength and lateral discontinuities identified by marked changes in wavenumber with offset. Transition frequencies to dominant higher modes appear lower than when identified from standard plane-wave transform methods. Effects can be discriminated by their frequency, position or offset dependence.When a non-corrupt dispersion curve is extracted, the errors are up to 5% at low frequency. Through theoretical Gaussian error propagation analysis, the resulting shear wave velocity profile shows up to 18% uncertainty at depth.     

Piecewise 1D laterally constrained inversion of resistivity data

In a sedimentary environment, layered models are often capable of representing the actual geology more accurately than smooth minimum structure models. Furthermore, interval thicknesses and resistivities are often the parameters to which non‐geophysicist experts can relate and base decisions on when using them in waste site remediation, groundwater modelling and physical planning. We present a laterally constrained inversion scheme for continuous resistivity data based on a layered earth model (1D). All 1D data sets and models are inverted as one system, producing layered sections with lateral smooth transitions. The models are regularized through laterally equal constraints that tie interface depths and resistivities of adjacent layers. Prior information, e.g. originating from electric logs, migrates through the lateral constraints to the adjacent models, making resolution of equivalences possible to some extent. Information from areas with well‐resolved parameters will migrate through the constraints in a similar way to help resolve the poorly constrained parameters. The estimated model is complemented by a full sensitivity analysis of the model parameters, supporting quantitative evaluation of the inversion result. Examples from synthetic 2D models show that the model recognition of a sublayered 2D wedge model is improved using the laterally constrained inversion approach when compared with a section of combined 1D models and when compared with a 2D minimum structure inversion. Case histories with data from two different continuous DC systems support the conclusions drawn from the synthetic example.     

大地电磁与接收函数结构约束联合反演

本文基于拟牛顿法对大地电磁与接收函数进行联合反演,提出了新的联合约束算子,实现了电阻率模型和速度模型之间的相似度约束.该方法给予两种模型足够的变化自由度,同时又约束两种模型向耦合方向演化.根据联合约束算子在反演迭代中的变化趋势,以及两种模型的空间梯度分布,可以判断电阻率模型和速度模型是否耦合.合成数据和野外实测结果表明,联合反演相对于单独反演可以提高电阻率和速度模型之间耦合程度,同时也能保持较好的数据拟合.联合反演提高了大地电磁的纵向分辨率,一定程度降低了大地电磁的非唯一性.

     

Seismic characterization of shallow bedrock sites with multimodal Monte Carlo inversion of surface wave data

Sites with a limited overburden over a stiff basement are of particular relevance for seismic site response. The characterization of such stratigraphies by means of surface wave methods poses some difficulties in interpretation. Indeed the presence of sharp seismic contrasts between the sediments and the shallow bedrock is likely to cause a relevance of higher modes in the surface wave apparent dispersion curve, which must be properly taken into account in order to provide reliable results. In this study a Monte Carlo algorithm based on a multimodal misfit function has been used for the inversion of experimental dispersion curves. Case histories related to the characterization of stations of the Italian accelerometric network are reported. Spectral ratios and amplification functions associated to each site are moreover evaluated to provide an independent benchmark test. The results show the robustness of the inversion method in such non-trivial conditions and the possibility of getting an estimate of uncertainty related to solution non-uniqueness.     

测井、井间地震与地面地震数据联合约束下的地质统计学随机建模方法研究

利用能够整合测井信息与井间地震信息的地质统计学随机模拟方法,结合传统的地质统计学反演思路,得到了一种能够同时整合测井、井间地震与地面地震三种先验信息的地质统计学反演与储层建模方法.由于井间射线信息、测井信息与地面地震数据在随机反演与建模过程当中都得到了尊重,因此与传统地质统计学反演仅利用了测井与地面地震数据相比,本文的地质统计学反演与建模方法更充分地利用了先验信息,有效提高了反演的精度,降低了随机建模中的多解性.基于理论数据的测试证实了上述观点.     

Site effects in Mexico City: Constraints from surface wave inversion of shallow refraction data

In order to understand and simulate site effects on strong ground motion records of recent earthquakes in Mexico City, it is fundamental to determine the in situ elastic and anelastic properties of the shallow stratigraphy of the basin. The main properties of interest are the shear wave velocities and Q-quality factors and their correlation with similar parameters in zones of the city. Despite population density and paved surfaces, it is feasible to gather shallow refraction data to obtain laterally homogeneous subsoil structures at some locations. We focused our analysis in the Texcoco Lake region of the northeastern Mexico City basin. This area consists of unconsolidated clay sediments, similar to those of the lake bed zone in Mexico City, where ground motion amplification and long duration disturbances are commonly observed. We recorded Rayleigh and Love waves using explosive and sledgehammer sources and 4.5 Hz vertical and horizontal geophones, respectively. Additionally, for the explosive source, we recorded three-component seismograms using 1 Hz seismometers. We obtained phase velocity dispersion curves from ray parameter-frequency domain analyses and inverted them for vertical distribution of S wave velocity. The initial model was obtained from a standard first-break refraction analysis. We also obtained an estimation of the Q_S shear wave quality factor for the uppermost stratigraphy. Results compare well with tilt and cone penetrometer resistance measurements at the same test site, emphasizing the importance of these studies for engineering purposes.     

测井、井间地震与地面地震数据联合约束下的地质统计学随机建模方法研究

利用能够整合测井信息与井间地震信息的地质统计学随机模拟方法,结合传统的地质统计学反演思路,得到了一种能够同时整合测井、井间地震与地面地震三种先验信息的地质统计学反演与储层建模方法.由于井间射线信息、测井信息与地面地震数据在随机反演与建模过程当中都得到了尊重,因此与传统地质统计学反演仅利用了测井与地面地震数据相比,本文的地质统计学反演与建模方法更充分地利用了先验信息,有效提高了反演的精度,降低了随机建模中的多解性.基于理论数据的测试证实了上述观点.     

Sharp spatially constrained inversion with applications to transient electromagnetic data

Time‐domain electromagnetic data are conveniently inverted by using smoothly varying 1D models with fixed vertical discretization. The vertical smoothness of the obtained models stems from the application of Occam‐type regularization constraints, which are meant to address the ill‐posedness of the problem. An important side effect of such regularization, however, is that horizontal layer boundaries can no longer be accurately reproduced as the model is required to be smooth. This issue can be overcome by inverting for fewer layers with variable thicknesses; nevertheless, to decide on a particular and constant number of layers for the parameterization of a large survey inversion can be equally problematic. Here, we present a focusing regularization technique to obtain the best of both methodologies. The new focusing approach allows for accurate reconstruction of resistivity distributions using a fixed vertical discretization while preserving the capability to reproduce horizontal boundaries. The formulation is flexible and can be coupled with traditional lateral/spatial smoothness constraints in order to resolve interfaces in stratified soils with no additional hypothesis about the number of layers. The method relies on minimizing the number of layers of non‐vanishing resistivity gradient, instead of minimizing the norm of the model variation itself. This approach ensures that the results are consistent with the measured data while favouring, at the same time, the retrieval of horizontal abrupt changes. In addition, the focusing regularization can also be applied in the horizontal direction in order to promote the reconstruction of lateral boundaries such as faults. We present the theoretical framework of our regularization methodology and illustrate its capabilities by means of both synthetic and field data sets. We further demonstrate how the concept has been integrated in our existing spatially constrained inversion formalism and show its application to large‐scale time‐domain electromagnetic data inversions.     

Constructing a discrete fracture network constrained by seismic inversion data

Rock fractures are of great practical importance to petroleum reservoir engineering because they provide pathways for fluid flow, especially in reservoirs with low matrix permeability, where they constitute the primary flow conduits. Understanding the spatial distribution of natural fracture networks is thus key to optimising production. The impact of fracture systems on fluid flow patterns can be predicted using discrete fracture network models, which allow not only the 6 independent components of the second‐rank permeability tensor to be estimated, but also the 21 independent components of the fully anisotropic fourth‐rank elastic stiffness tensor, from which the elastic and seismic properties of the fractured rock medium can be predicted. As they are stochastically generated, discrete fracture network realisations are inherently non‐unique. It is thus important to constrain their construction, so as to reduce their range of variability and, hence, the uncertainty of fractured rock properties derived from them. This paper presents the underlying theory and implementation of a method for constructing a geologically realistic discrete fracture network, constrained by seismic amplitude variation with offset and azimuth data. Several different formulations are described, depending on the type of seismic data and prior geologic information available, and the relative strengths and weaknesses of each approach are compared. Potential applications of the method are numerous, including the prediction of fluid flow, elastic and seismic properties of fractured reservoirs, model‐based inversion of seismic amplitude variation with offset and azimuth data, and the optimal placement and orientation of infill wells to maximise production.     

三维井地磁测联合约束反演

井中磁测在铁矿等磁性金属矿床勘查中具有举足轻重的作用.针对磁性金属矿床深部资源勘查中存在的有效信号弱、矿体形态复杂等技术难题,本文利用井中三分量磁测资料和地面磁测资料直接反演地下空间磁化率的分布情况,充分发挥纵、横向分辨率高的优势,通过磁化率的变化来确定矿（化）体的范围.分析了磁化率和磁场H_ax、H_ay、Z_a、ΔT各参量之间的关系,导出了磁化率反演方程;将钻孔编录、磁化率测井等结果作为约束条件构建了目标函数.以组合倾斜板状体模型为例,验证了方法的有效性,并在青海野马泉铁多金属矿区开展应用试验,试验结果与已有地质资料基本一致.该方法有效抑制了因反演数据源单一、缺乏约束条件而造成反演结果的多解性,实现了磁测资料的精细反演解释,为查明地下矿体空间位置、形态及规模,提高找矿效果,提供了一种新的解决方案.

     

Addressing non-uniqueness in linearized multichannel surface wave inversion

The multichannel analysis of the surface waves method is based on the inversion of observed Rayleigh-wave phase-velocity dispersion curves to estimate the shear-wave velocity profile of the site under investigation. This inverse problem is nonlinear and it is often solved using 'local' or linearized inversion strategies. Among linearized inversion algorithms, least-squares methods are widely used in research and prevailing in commercial software; the main drawback of this class of methods is their limited capability to explore the model parameter space. The possibility for the estimated solution to be trapped in local minima of the objective function strongly depends on the degree of nonuniqueness of the problem, which can be reduced by an adequate model parameterization and/or imposing constraints on the solution.
In this article, a linearized algorithm based on inequality constraints is introduced for the inversion of observed dispersion curves; this provides a flexible way to insert a priori information as well as physical constraints into the inversion process. As linearized inversion methods are strongly dependent on the choice of the initial model and on the accuracy of partial derivative calculations, these factors are carefully reviewed. Attention is also focused on the appraisal of the inverted solution, using resolution analysis and uncertainty estimation together with a posteriori effective-velocity modelling. Efficiency and stability of the proposed approach are demonstrated using both synthetic and real data; in the latter case, cross-hole S-wave velocity measurements are blind-compared with the results of the inversion process.     

基于协同克里金方法的重力梯度全张量三维约束反演

随着重力梯度全张量测量技术的日趋成熟,重力梯度全张量数据的三维反演技术日益受到重视与关注.全张量数据反演与重力数据反演一样仍然面临着严重的多解性问题.本文将基于地质统计学的协同克里金方法应用于重力梯度全张量数据三维反演,建立了密度约束下的多变量协同克里金联合反演方程,以降低反演的多解性.模型试验表明密度信息的加入能够有效降低反演的多解性,提高反演结果的分辨率,尤其是纵向分辨率能够得到显著提高.最后对美国德克萨斯州一个岩丘区所获得实际资料的应用表明了本文方法的实用性.     

基于稀疏约束反演的三维混采数据分离

混合震源采集技术相对于传统的地震数据采集,在极大提高采集效率的同时引入了混叠噪声,很大程度上影响了成像结果的精度.二维混采数据中,我们通常利用混叠噪声在非共炮域呈非相干分布这一特点来压制混叠噪声,从而实现混合震源数据分离.相对于二维混采数据,三维混采数据具有数据量巨大,构建混合震源算子困难,混合度的增加引入了高强度混叠噪声的特点.针对上述问题,本文采用稀疏约束反演方法在Radon域实现混采数据分离,混叠噪声强度比较大的情况下,稀疏约束反演方法能够得到更高精度的分离结果;利用震源激发的GPS时间通过长记录的方式在共接收点道集对上一次迭代分离结果做混合、伪分离,实现了单个共接收点道集自身混合、伪分离,避免了对整个数据做运算,同时不需要构建混合震源算子.通过模拟数据和实际数据计算来验证上述方法的适用性.

     

Global surface wave inversion with model constraints‡

Practical applications of surface wave inversion demand reliable inverted shear‐wave profiles and a rigorous assessment of the uncertainty associated to the inverted parameters. As a matter of fact, the surface wave inverse problem is severely affected by solution non‐uniqueness: the degree of non‐uniqueness is closely related to the complexity of the observed dispersion pattern and to the experimental inaccuracies in dispersion measurements. Moreover, inversion pitfalls may be connected to specific problems such as inadequate model parametrization and incorrect identification of the surface wave modes. Consequently, it is essential to tune the inversion problem to the specific dataset under examination to avoid unnecessary computations and possible misinterpretations. In the heuristic inversion algorithm presented in this paper, different types of model constraints can be easily introduced to bias constructively the solution towards realistic estimates of the 1D shear‐wave profile. This approach merges the advantages of global inversion, like the extended exploration of the parameter space and a theoretically rigorous assessment of the uncertainties on the inverted parameters, with the practical approach of Lagrange multipliers, which is often used in deterministic inversion, which helps inversion to converge towards models with desired properties (e.g., ‘smooth’ or ‘minimum norm' models). In addition, two different forward kernels can be alternatively selected for direct‐problem computations: either the conventional modal inversion or, instead, the direct minimization of the secular function, which allows the interpreter to avoid mode identification. A rigorous uncertainty assessment of the model parameters is performed by posterior covariance analysis on the accepted solutions and the modal superposition associated to the inverted models is investigated by full‐waveform modelling. This way, the interpreter has several tools to address the more probable sources of inversion pitfalls within the framework of a rigorous and well‐tested global inversion algorithm. The effectiveness and the versatility of this approach, as well as the impact of the interpreter's choices on the final solution and on its posterior uncertainty, are illustrated using both synthetic and real data. In the latter case, the inverted shear velocity profiles are blind compared with borehole data.     

航空电磁拟三维模型空间约束反演

为了克服时间域航空电磁数据单点反演结果中常见的电阻率或层厚度横向突变造成数据难以解释的问题,通过引入双向约束实现航空电磁拟三维空间约束反演.除考虑沿测线方向相邻测点之间的横向约束外,同时还考虑了垂直测线方向测点在空间上的相互约束.为此,首先设计拟三维模型中固定层厚和可变层厚两种空间约束反演方案,然后通过在目标函数中引入沿测线和垂直测线方向上的模型参数约束矩阵,并使用L-BFGS算法使目标函数最小化,获得最优拟三维模型空间反演解.基于理论模型和实测数据反演,对单点反演与两种空间约束反演方案的有效性进行比较,证明本文空间约束反演算法对于噪声的压制效果好,反演的界面连续光滑,同时内存需求和反演时间少,是一种快速有效的反演策略.