Inversion of controlled‐source electromagnetic data using a model‐based approach

A two‐and‐half dimensional model‐based inversion algorithm for the reconstruction of geometry and conductivity of unknown regions using marine controlled‐source electromagnetic (CSEM) data is presented. In the model‐based inversion, the inversion domain is described by the so‐called regional conductivity model and both geometry and material parameters associated with this model are reconstructed in the inversion process. This method has the advantage of using a priori information such as the background conductivity distribution, structural information extracted from seismic and/or gravity measurements, and/or inversion results a priori derived from a pixel‐based inversion method. By incorporating this a priori information, the number of unknown parameters to be retrieved becomes significantly reduced. The inversion method is the regularized Gauss‐Newton minimization scheme. The robustness of the inversion is enhanced by adopting nonlinear constraints and applying a quadratic line search algorithm to the optimization process. We also introduce the adjoint formulation to calculate the Jacobian matrix with respect to the geometrical parameters. The model‐based inversion method is validated by using several numerical examples including the inversion of the Troll field data. These results show that the model‐based inversion method can quantitatively reconstruct the shapes and conductivities of reservoirs.     

1D joint multi‐offset inversion of time‐domain marine controlled source electromagnetic data

The accurate estimation of sub‐seafloor resistivity features from marine controlled source electromagnetic data using inverse modelling is hindered due to the limitations of the inversion routines. The most commonly used one‐dimensional inversion techniques for resolving subsurface resistivity structures are gradient‐based methods, namely Occam and Marquardt. The first approach relies on the smoothness of the model and is recommended when there are no sharp resistivity boundaries. The Marquardt routine is relevant for many electromagnetic applications with sharp resistivity contrasts but subject to the appropriate choice of a starting model. In this paper, we explore the ability of different 1D inversion schemes to derive sub‐seafloor resistivity structures from time domain marine controlled source electromagnetic data measured along an 8‐km‐long profile in the German North Sea. Seismic reflection data reveal a dipping shallow amplitude anomaly that was the target of the controleld source electromagnetic survey. We tested four inversion schemes to find suitable starting models for the final Marquardt inversion. In this respect, as a first scenario, Occam inversion results are considered a starting model for the subsequent Marquardt inversion (Occam–Marquardt). As a second scenario, we employ a global method called Differential Evolution Adaptive Metropolis and sequentially incorporate it with Marquardt inversion. The third approach corresponds to Marquardt inversion introducing lateral constraints. Finally, we include the lateral constraints in Differential Evolution Adaptive Metropolis optimization, and the results are sequentially utilized by Marquardt inversion. Occam–Marquardt may provide accurate estimation of the subsurface features, but it is dependent on the appropriate conversion of different multi‐layered Occam model to an acceptable starting model for Marquardt inversion, which is not straightforward. Employing parameter spaces, the Differential Evolution Adaptive Metropolis approach can be pertinent to determine Marquardt a priori information; nevertheless, the uncertainties in Differential Evolution Adaptive Metropolis optimization will introduce some inaccuracies in Marquardt inversion results. Laterally constrained Marquardt may be promising to resolve sub‐seafloor features, but it is not stable if there are significant lateral changes of the sub‐seafloor structure due to the dependence of the method to the starting model. Including the lateral constraints in Differential Evolution Adaptive Metropolis approach allows for faster convergence of the routine with consistent results, furnishing more accurate estimation of a priori models for the subsequent Marquardt inversion.     

Joint parameter estimation from magnetic resonance and vertical electric soundings using a multi‐objective genetic algorithm

Magnetic resonance sounding (MRS) has increasingly become an important method in hydrogeophysics because it allows for estimations of essential hydraulic properties such as porosity and hydraulic conductivity. A resistivity model is required for magnetic resonance sounding modelling and inversion. Therefore, joint interpretation or inversion is favourable to reduce the ambiguities that arise in separate magnetic resonance sounding and vertical electrical sounding (VES) inversions. A new method is suggested for the joint inversion of magnetic resonance sounding and vertical electrical sounding data. A one‐dimensional blocky model with varying layer thicknesses is used for the subsurface discretization. Instead of conventional derivative‐based inversion schemes that are strongly dependent on initial models, a global multi‐objective optimization scheme (a genetic algorithm [GA] in this case) is preferred to examine a set of possible solutions in a predefined search space. Multi‐objective joint optimization avoids the domination of one objective over the other without applying a weighting scheme. The outcome is a group of non‐dominated optimal solutions referred to as the Pareto‐optimal set. Tests conducted using synthetic data show that the multi‐objective joint optimization approximates the joint model parameters within the experimental error level and illustrates the range of trade‐off solutions, which is useful for understanding the consistency and conflicts between two models and objectives. Overall, the Levenberg‐Marquardt inversion of field data measured during a survey on a North Sea island presents similar solutions. However, the multi‐objective genetic algorithm method presents an efficient method for exploring the search space by producing a set of non‐dominated solutions. Borehole data were used to provide a verification of the inversion outcomes and indicate that the suggested genetic algorithm method is complementary for derivative‐based inversions.     

Appraisal of a new 1D weighted joint inversion of ground based and helicopter‐borne electromagnetic data

In order to couple spatial data from frequency‐domain helicopter‐borne electromagnetics with electromagnetic measurements from ground geophysics (transient electromagnetics and radiomagnetotellurics), a common 1D weighted joint inversion algorithm for helicopter‐borne electromagnetics, transient electromagnetics and radiomagnetotellurics data has been developed. The depth of investigation of helicopter‐borne electromagnetics data is rather limited compared to time‐domain electromagnetics sounding methods on the ground. In order to improve the accuracy of model parameters of shallow depth as well as of greater depth, the helicopter‐borne electromagnetics, transient electromagnetics, and radiomagnetotellurics measurements can be combined by using a joint inversion methodology. The 1D joint inversion algorithm is tested for synthetic data of helicopter‐borne electromagnetics, transient electromagnetics and radiomagnetotellurics. The proposed concept of the joint inversion takes advantage of each method, thus providing the capability to resolve near surface (radiomagnetotellurics) and deeper electrical conductivity structures (transient electromagnetics) in combination with valuable spatial information (helicopter‐borne electromagnetics). Furthermore, the joint inversion has been applied on the field data (helicopter‐borne electromagnetics and transient electromagnetics) measured in the Cuxhaven area, Germany. In order to avoid the lessening of the resolution capacities of one data type, and thus balancing the use of inherent and ideally complementary information content, a parameter reweighting scheme that is based on the exploration depth ranges of the specific methods is proposed. A comparison of the conventional joint inversion algorithm, proposed by Jupp and Vozoff ( 1975 ), and of the newly developed algorithm is presented. The new algorithm employs the weighting on different model parameters differently. It is inferred from the synthetic and field data examples that the weighted joint inversion is more successful in explaining the subsurface than the classical joint inversion approach. In addition to this, the data fittings in weighted joint inversion are also improved.     

Identification of lateral discontinuities via multi‐offset phase analysis of surface wave data

Surface wave methods are based on the inversion of observed Rayleigh wave phase‐velocity dispersion curves. The goal is to estimate mainly the shear‐wave velocity profile of the investigated site. The model used for the interpretation is 1D, hence results obtained wherever lateral variations are present cannot be considered reliable. In this paper, we study four synthetic models, all with a lateral heterogeneity. When we process the entire corresponding seismograms with traditional f‐k approach, the resulting 1D profiles are representative of the subsurface properties averaged over the whole length of the receivers lines. These results show that classical analysis disregards evidences of sharp lateral velocity changes even when they show up in the raw seismograms. In our research, we implement and test over the same synthetic models, a novel robust automated method to check the appropriateness of 1D model assumption and locate the discontinuities. This new approach is a development of the recent multi‐offset phase analysis with the following further advantages: it does not need previous noise evaluation and more than one shot. Only once the discontinuities are clearly identified, we confidently perform classical f‐k dispersion curve extraction and inversion separately on both sides of the discontinuity. Thus the final results, obtained by putting side by side the 1D profiles, are correct 2D reconstructions of the discontinuous S‐wave distributions obtained without any additional ad‐hoc hypotheses.     

Simple relative space–time scaling of electrical and electromagnetic depth sounding arrays: implications for electrical static shift removal and joint DC-TEM data inversion with the most-squares criterion

A simple scaling relationship is shown to facilitate comparison, correlation and integration of data recorded using the common experimental configurations in electrical and electromagnetic depth sounding. Applications of the scheme to field data from typical geological and landfill environments show that it is robust and, where transient electromagnetic (TEM) data are available, enables easy identification and quantification of electrical static shift (galvanic distortion) in magnetotelluric and direct current (DC) sounding curves. TEM‐based procedures are suggested for both the direct removal of static shift in DC sounding curves and effective joint data inversion with the most‐squares criterion in the presence of static shift. A case study of aquifer characterization using sounding data from borehole sites in the Vale of York in England shows that static shift is a common problem in this glacial‐covered terrain and demonstrates the effectiveness of the proposed joint DC‐TEM inversion strategy in handling distorted soundings.     

Estimating gas saturation in a thin layer by using frequency‐dependent amplitude versus offset modelling

Various models have been proposed to link partial gas saturation to seismic attenuation and dispersion, suggesting that the reflection coefficient should be frequency‐dependent in many cases of practical importance. Previous approaches to studying this phenomenon typically have been limited to single‐interface models. Here, we propose a modelling technique that allows us to incorporate frequency‐dependent reflectivity into convolutional modelling. With this modelling framework, seismic data can be synthesised from well logs of velocity, density, porosity, and water saturation. This forward modelling could act as a basis for inversion schemes aimed at recovering gas saturation variations with depth. We present a Bayesian inversion scheme for a simple thin‐layer case and a particular rock physics model and show that, although the method is very sensitive to prior information and constraints, both gas saturation and layer thickness theoretically can be estimated in the case of interfering reflections.     

Estimating the elastic parameters of anisotropic media using a joint inversion of P-wave and SV-wave traveltime error

A method is presented to estimate the elastic parameters and thickness of media that are locally laterally homogeneous using P‐wave and vertically polarized shear‐wave (SV‐wave) data. This method is a ‘layer‐stripping’ technique, and it uses many aspects of common focal point (CFP) technology. For each layer, a focusing operator is computed using a model of the elastic parameters with which a CFP gather can be constructed using the seismic data. Assuming local homogeneity, the resulting differential time shifts (DTSs) represent error in the model due to anisotropy and error in thickness. In the (τ?p) domain, DTSs are traveltimes Δτ that connect error in layer thickness z, vertical slowness q, and ray parameter p. Series expansion is used to linearize Δτ with respect to error in the elastic parameters and thickness, and least‐squares inversion is used to update the model. For stability, joint inversion of P and SV data is employed and, as pure SV data are relatively rare, the use of mode‐converted (PSV) data to represent SV in the joint inversion is proposed. Analytic and synthetic examples are used to demonstrate the utility and practicality of this inversion.     

A joint inversion algorithm to process geoelectric and surface wave seismic data. Part II: applications

Seismic and geoelectric methods are often used in the exploration of near-surface structures. Generally, these two methods give, independently of one other, a sufficiently exact model of the geological structure. However, sometimes the inversion of the seismic or geoelectric data fails. These failures can be avoided by combining various methods in one joint inversion which leads to much better parameter estimations of the near-surface underground than the independent inversions. In the companion paper (Part I: basic ideas), it was demonstrated theoretically that a joint inversion, using dispersive Rayleigh and Love waves in combination with the well-known methods of DC resistivity sounding, such as Schlumberger, radial dipole-dipole and pole-pole arrays, provides a better parameter estimation. Two applications are shown: a five layer structure in Borsod County, Hungary, and a three-layer structure in Thüringen, Germany. Layer thicknesses, wave velocities and resistivities are determined. Of course, the field data sets obtained from the ‘real world’ are not as complete and as good as the synthetic data sets in the theoretical Part I. In both applications, relative model distances, in percentages, serve as quality control factors for the different inversions; the lower the relative distance, the better the inversion result. In the Borsod field case, Love wave group slowness data and Schlumberger, radial dipole-dipole and pole-pole (i.e two-electrode) data sets are processed. The independent inversion performed using the Love wave data leads to a relative model distance of 155%. An independent Schlumberger inversion results in 41%, a joint geoelectric inversion of all data sets in 15%, a joint inversion of Love wave data and all geoelectric data sets in 15% and the robust joint inversion of Love wave data and the three geoelectric data sets in 10%. In the Thüringen field case, only Rayleigh wave group slowness data and Schlumberger data were available. The independent inversion using Rayleigh wave data results in a relative model distance of 19%. The independent inversion performed using Schlumberger data leads to 34%, the joint and robust joint inversion of Rayleigh wave and Schlumberger data gave results of 18% and 20%, respectively.     

A joint inversion algorithm to process geoelectric and sutface wave seismic data. Part I: basic ideas1

For the exploration of near-surface structures, seismic and geoelectric methods are often applied. Usually, these two types of method give, independently of each other, a sufficiently exact model of the geological structure. However, sometimes the inversion of the seismic or geoelectric data fails. These failures can be avoided by combining various methods in one joint inversion which feads to much better parameter estimations of the model than the independent inversions. A suitable seismic method for exploring near-surface structures is the use of dispersive surface waves: the dispersive characteristics of Rayleigh and Love surface waves depend strongly on the structural and petrophysical (seismic velocities) features of the near-surface Underground. Geoelectric exploration of the structure Underground may be carried out with the well-known methods of DC resistivity sounding, such as the Schlumberger, the radial-dipole and the two-electrode arrays. The joint inversion algorithm is tested by means of synthetic data. It is demonstrated that the geoelectric joint inversion of Schlumberger, radial-dipole and two-electrode sounding data yields more reliable results than the single inversion of a single set of these data. The same holds for the seismic joint inversion of Love and Rayleigh group slowness data. The best inversion result is achieved by performing a joint inversion of both geoelectric and surface-wave data. The effect of noise on the accuracy of the solution for both Gaussian and non-Gaussian (sparsely distributed large) errors is analysed. After a comparison between least-square (LSQ) and least absolute deviation (LAD) inversion results, the LAD joint inversion is found to be an accurate and robust method.     

Geostatistical seismic Amplitude‐versus‐angle inversion

Seismic inversion plays an important role in reservoir modelling and characterisation due to its potential for assessing the spatial distribution of the sub‐surface petro‐elastic properties. Seismic amplitude‐versus‐angle inversion methodologies allow to retrieve P‐wave and S‐wave velocities and density individually allowing a better characterisation of existing litho‐fluid facies. We present an iterative geostatistical seismic amplitude‐versus‐angle inversion algorithm that inverts pre‐stack seismic data, sorted by angle gather, directly for: density; P‐wave; and S‐wave velocity models. The proposed iterative geostatistical inverse procedure is based on the use of stochastic sequential simulation and co‐simulation algorithms as the perturbation technique of the model parametre space; and the use of a genetic algorithm as a global optimiser to make the simulated elastic models converge from iteration to iteration. All the elastic models simulated during the iterative procedure honour the marginal prior distributions of P‐wave velocity, S‐wave velocity and density estimated from the available well‐log data, and the corresponding joint distributions between density versus P‐wave velocity and P‐wave versus S‐wave velocity. We successfully tested and implemented the proposed inversion procedure on a pre‐stack synthetic dataset, built from a real reservoir, and on a real pre‐stack seismic dataset acquired over a deep‐water gas reservoir. In both cases the results show a good convergence between real and synthetic seismic and reliable high‐resolution elastic sub‐surface Earth models.     

瑞雷波多阶模式频散曲线稀疏正则化反演方法研究

目前瑞雷波多阶模式频散曲线反演中仅考虑数据的拟合,缺乏对模型的约束,不能很好地刻画地层间断面的问题,针对此问题,研究了瑞雷波多阶模式频散曲线稀疏正则化反演方法.正演模拟基于广义反射-透射系数法,数值计算上采用一种快速求根方法,与二等分方法相比,能够在很短的时间内达到最优的收敛效果;反演建模时采用L1范数正则化方法对模型进行稀疏性刻画,使反演结果更加符合地质实际;在反问题的数值实现上,针对稀疏正则化模型提出一种隐式迭代正则化算法,其迭代算子具有非膨胀特性,可以收敛到极小化问题的解.数值实验结果表明,新的反演方案具有计算效率高,模型"逐块"光滑的特性刻画好,对非高斯噪声鲁棒性强的特点.     

Analysing two‐dimensional effects in central loop transient electromagnetic sounding data using a semi‐synthetic tipper approach

We present a simple and feasible approach to analyse and identify two‐dimensional effects in central loop transient electromagnetic sounding data and the correspondingly derived quasi two‐dimensional conductivity models. The proposed strategy is particularly useful in minimising interpretation errors. It is based on the calculation of a semi‐synthetic transient electromagnetic tipper at each sounding and for each observational transient time point. The semi‐synthetic transient electromagnetic tipper is derived from the measured vertical component of the induced voltage and the synthetically calculated horizontal component. The approach is computationally inexpensive and involves one two‐dimensional forward calculation of an obtained quasi two‐dimensional conductivity section. Based on a synthetic example, we demonstrate that the transient electromagnetic tipper approach is applicable in identifying which transient data points and which corresponding zones in a derived quasi two‐dimensional subsurface model are affected by two‐dimensional inhomogeneities. The one‐dimensional inversion of such data leads to false models. An application of the semi‐synthetic transient electromagnetic tipper to field data from the Azraq basin in Jordan reveals that, in total, eight of 80 investigated soundings are affected by two‐dimensional structures although the field data can be fitted optimally using one‐dimensional inversion techniques. The largest semi‐synthetic tipper response occurs in a 300 m‐wide region around a strong lateral resistivity contrast. The approach is useful for analysing structural features in derived quasi two‐dimensional sections and for qualitatively investigating how these features affect the transient response. To avoid misinterpretation, these identified zones corresponding to large tipper values are excluded from the interpretation of a quasi two‐dimensional conductivity model. Based on the semi‐synthetic study, we also demonstrate that a quantitative interpretation of the horizontal voltage response (e.g. by inversion) is usually not feasible as it requires the exact sensor position to be known. Although a tipper derived purely from field data is useful as a qualitative tool for identifying two‐dimensional distortion effects, it is only feasible if the sensor setup is sufficiently accurate. Our proposed semi‐synthetic transient electromagnetic tipper approach is particularly feasible as an a posteriori approach if no horizontal components are recorded or if the sensor setup in the field is not sufficiently accurate.     

Joint inversion of surface wave dispersion curves and reflection travel times via multi-objective evolutionary algorithms

Due to the character of seismic energy generation and propagation, shallow high-resolution seismic-reflection surveys often fail in the identification of the shallowest horizons and, due to the limited offsets, accuracy of velocity analyses is often not very high.In recent years, Rayleigh wave dispersion analysis have proved to have good potential also for near-surface applications but dispersion curve inversion and related uncertainty evaluation pose serious problems to a completely stand-alone application.In order to overcome these problems a joint inversion scheme is proposed, which is based on the identification of the Pareto front, performed in the framework of a Multi-Objective Evolutionary Algorithm (MOEA). Seismic data considered to design the two objectives are the Rayleigh wave dispersion curve and reflection travel times.We initially analyse a set of synthetic cases and evaluate the obtained results. A significant improvement of the retrieved models is observed as long as reflection travel times are added to the dispersion curve alone.Furthermore, the proposed methodology also provides relevant indications about the consistency of the overall inversion process. In fact, the distribution of the models in the objective space, the trend of the objectives over the passing generations and the evolution of the Pareto front can provide useful information to evaluate the provisional tentative interpretation (number of strata and reflector identification) inherently adopted for the data inversion.On the basis of the results obtained from the tests on the synthetic datasets, the analyses of a field dataset are interpreted as possible evidence of lateral heterogeneities.     

基于改进海洋捕食者优化算法和瑞雷波频散曲线的近地表地层参数反演

面波勘探是获取近地表地质结构的重要手段,利用瑞雷波频散曲线可以反演得到地层横波速度和厚度或泊松比等参数.本文提出了一种新的优化策略来处理瑞雷波频散曲线的反演问题.改进海洋捕食者算法（ACMPA）是一种改进混沌初始化,引入自适应步长和精英竞赛机制优化的反演算法.采用混沌映射进行种群位置初始化,提高初始化种群位置的质量;加入自适应函数,增强全局搜索能力;引入精英等级制度,避免算法陷入局部极值点,从而从局部和全局寻优进行优化,提高反演的收敛速度.通过正演模拟和实测数据进行测试分析,证明了改进的海洋捕食者优化算法的有效性与稳定性.该方法可以利用瑞雷波频散曲线信息反演得到近地表地层的介质参数,其收敛精度和收敛范围明显优于其他优化算法,具有较强的应用前景.

     

Application of the continuous wavelet transform of gravity and magnetic data to estimate sub‐basalt sediment thickness

The Continuous Wavelet Transform was recently proposed for the interpretation of gravity and magnetic potential data. We utilize the Continuous Wavelet Transform of gravity and magnetic data to address one of the most common issues in exploration geophysics: mapping of sub‐basaltic sedimentary strata. We observe that the magnetic response of the basaltic layer is dominant in a three‐layer case of a basalt‐sediment‐basement, whereas the gravity signal is dominated by the base of the sediment. Thus the Continuous Wavelet Transform of the magnetic data is related to the thickness of the basalt and the Continuous Wavelet Transform of the gravity data is related mostly to the bottom of the sediment. These observations are demonstrated with a synthetic model and a few field examples. Derived depths using Continuous Wavelet Transform are in good agreement with known vertical cross‐sections. Therefore, Continuous Wavelet Transform analysis of both gravity and magnetic data offers a possibility for primary information of sub‐basaltic sediment thickness, which can provide a basis for further detailed modelling.     

Combined straightforward inversion of resistivity and induced polarization (time-domain) sounding data

It is proposed that the Straightforward Inversion Scheme (SIS) developed by the authors for 1D inversion of resistivity sounding and magneto-telluric sounding data can also be used in similar fashion for time-domain induced polarization sounding data. The necessary formulations based on dynamic dipole theory are presented. It is shown that by using induced polarization potential, measured at the instant when steady state current is switched off, an equation can be developed for apparent ‘chargeability–resistivity’ which is similar to the one for apparent resistivity. The two data sets of apparent resistivity and apparent chargeability–resistivity can be inverted in a combined manner, using SIS for a common uniform thickness layer earth model to estimate the respective subsurface distributions of resistivity and chargeability–resistivity. The quotient of the two profiles will give the sought after chargeability profile. A brief outline of SIS is provided for completeness. Three theoretical models are included to confirm the efficacy of SIS software by inverting only the synthetic resistivity sounding data. Then one synthetic data set based on a geological model and three field data sets (combination of resistivity and IP soundings) from diverse geological and geographical regions are included as validation of the proposal. It is hoped that the proposed scheme would complement the resistivity interpretation with special reference to shaly sand formations.     

Three‐term inversion of prestack seismic data using a weighted l2, 1 mixed norm

We present a new inversion method to estimate, from prestack seismic data, blocky P‐ and S‐wave velocity and density images and the associated sparse reflectivity levels. The method uses the three‐term Aki and Richards approximation to linearise the seismic inversion problem. To this end, we adopt a weighted mixed l_{2, 1}‐norm that promotes structured forms of sparsity, thus leading to blocky solutions in time. In addition, our algorithm incorporates a covariance or scale matrix to simultaneously constrain P‐ and S‐wave velocities and density. This a priori information is obtained by nearby well‐log data. We also include a term containing a low‐frequency background model. The l_{2, 1} mixed norm leads to a convex objective function that can be minimised using proximal algorithms. In particular, we use the fast iterative shrinkage‐thresholding algorithm. A key advantage of this algorithm is that it only requires matrix–vector multiplications and no direct matrix inversion. The latter makes our algorithm numerically stable, easy to apply, and economical in terms of computational cost. Tests on synthetic and field data show that the proposed method, contrarily to conventional l₂‐ or l₁‐norm regularised solutions, is able to provide consistent blocky and/or sparse estimators of P‐ and S‐wave velocities and density from a noisy and limited number of observations.     

Three‐dimensional VS profiling using microtremors in Kushiro,Japan

A practical method is presented for determining three‐dimensional S‐wave velocity (V_S) profile from microtremor measurements. Frequency–wave number (f–k) spectral analyses of microtremor array records are combined, for this purpose, with microtremor horizontal‐to‐vertical (H/V) spectral ratio techniques. To demonstrate the effectiveness of the proposed method, microtremor measurements using arrays of sensors were conducted at six sites in the city of Kushiro, Japan. The spectral analyses of the array records yield dispersion characteristics of Rayleigh waves and H/V spectra of surface waves, and joint inversion of these data results in V_S profiles down to bedrock at the sites. Conventional microtremor measurements were performed at 230 stations within Kushiro city, resulting in the H/V spectra within the city. Three‐dimensional V_S structure is then estimated from inversion of the H/V spectra with the V_S values determined from the microtremor array data. This reveals three‐dimensional V_S profile of Kushiro city, together with an unknown hidden valley that crosses the central part of the city. The estimated V_S profile is consistent with available velocity logs and results of subsequent borings, indicating the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Elastic full waveform inversion of multi‐component OBC seismic data

Elastic full waveform inversion of seismic reflection data represents a data‐driven form of analysis leading to quantification of sub‐surface parameters in depth. In previous studies attention has been given to P‐wave data recorded in the marine environment, using either acoustic or elastic inversion schemes. In this paper we exploit both P‐waves and mode‐converted S‐waves in the marine environment in the inversion for both P‐ and S‐wave velocities by using wide‐angle, multi‐component, ocean‐bottom cable seismic data. An elastic waveform inversion scheme operating in the time domain was used, allowing accurate modelling of the full wavefield, including the elastic amplitude variation with offset response of reflected arrivals and mode‐converted events. A series of one‐ and two‐dimensional synthetic examples are presented, demonstrating the ability to invert for and thereby to quantify both P‐ and S‐wave velocities for different velocity models. In particular, for more realistic low velocity models, including a typically soft seabed, an effective strategy for inversion is proposed to exploit both P‐ and mode‐converted PS‐waves. Whilst P‐wave events are exploited for inversion for P‐wave velocity, examples show the contribution of both P‐ and PS‐waves to the successful recovery of S‐wave velocity.