Determination of gravity anomaly at sea level from inversion of satellite gravity gradiometric data

Gravity gradients can be used to determine the local gravity field of the Earth. This paper investigates downward continuation of all elements of the disturbing gravitational tensor at satellite level using the second-order partial derivatives of the extended Stokes formula in the local-north oriented frame to determine the gravity anomaly at sea level. It considers the inversion of each gradient separately as well as their joint inversion. Numerical studies show that the gradients T_zz, T_xx, T_yy and T_xz have similar capability of being continued downward to sea level in the presence of white noise, while the gradient T_yz is considerably worse than the others. The bias-corrected joint inversion process shows the possibility of recovering the gravity anomaly with 1 mGal accuracy. Variance component estimation is also tested to update the observation weights in the joint inversion.     

An overview of surface wave methods and a reliability study of a simplified inversion technique

Following a brief overview of the history and the development of the Surface Wave Method—with a focus on techniques for processing and inverting field data—a Simplified Inversion Method (SIM) is described, which constitutes an improvement of the Satoh et al. (1991) [1] method. The SIM is a direct inversion method of surface wave dispersion data, making use of a penetration depth coefficient, a_R, whose value is a function of Poisson's ratio and the overall shape of the dispersion curve. In the present study the coefficient a_R has been evaluated using data from (a) an extensive database compiled from the technical literature and containing results of inverted surface wave measurements and nearby cross-hole/down-hole measurements, (b) results of side by side surface wave and cross-hole measurements, performed at five sites in the course of this study, (c) finite element analyses simulating the performance of surface wave measurements and thus providing “virtual” data, and (d) applying a current advanced inversion code, available on the Web. Based on all the above data, optimum values of a_R (and of the corresponding uncertainty of the derived V_so vs. depth profile) have been estimated. These values were found to be independent of depth from ground surface. The results of all analyses and comparisons indicate that for the majority of realistic soil profiles (including cases of normal and inverse dispersion conditions) the proposed SIM provides very reliable V_so vs. depth profiles when a value of a_R=0.63–0.67 is used in the inversion process. It is concluded that the SIM can be used with confidence as a direct inversion method of surface wave dispersion data.     

Is the lower mantle homogeneous?

Comparison of some array dt/dΔ studies with the global travel times of Dziewonski and Anderson (1983) leads to the conclusion that a discontinuity in the P travel times between 80° and 85° is consistent with both sets of data. This discontinuity in dt/dΔ corresponds to an increase in velocity of about 0.1 km/sec between depths of 2400 and 2600 km. Models of the P velocity distribution which match the Dziewonski and Anderson travel times reasonable well have the shadow zone for short-period “diffracted” P beginning at about 110° arc distance.     

Adaptive reconstruction method of impedance model with absolute and relative constraints

Inversion for seismic impedance is an ill-posed and band-limited problem so that inversion results are non-unique and unstable and low and high frequency components of inversion results are missed. Combining regularization with constraints of sonic log data and geological structure information can help to alleviate these problems. To achieve this, we developed an inversion method by constructing a new objective function which includes edge-preserving regularization and soft constraint based on Markov random field (MRF). The method directly introduces absolute constraints with prior impedance and sonic log data in the objective function and indirectly achieves relative constraints with geologic structures of layer interfaces and faults by adjusting the regularization parameter which is the scaling parameter δ. Moreover, we improved the inversion result using anisotropic diffusion smoothing method. Optimization approach utilized in inversion is a fast simulated annealing (FSA). We test the method on both synthetic and field data examples. Tests on 2-D synthetic data indicate that aspects of the discontinuity in the inversion results are significantly improved by adding δ values in faults and layer interfaces. We obtained better results by combining the first-order neighborhood and the third-order neighborhood of MRF. The inversion results of the field data provide more detailed information of the layers. The results of nearby faults were improved by introducing the geological structure constraints.     

An overview of surface wave methods and a reliability study of a simplified inversion technique

Following a brief overview of the history and the development of the Surface Wave Method—with a focus on techniques for processing and inverting field data—a Simplified Inversion Method (SIM) is described, which constitutes an improvement of the Satoh et al. (1991) [1] method. The SIM is a direct inversion method of surface wave dispersion data, making use of a penetration depth coefficient, a_R, whose value is a function of Poisson's ratio and the overall shape of the dispersion curve. In the present study the coefficient a_R has been evaluated using data from (a) an extensive database compiled from the technical literature and containing results of inverted surface wave measurements and nearby cross-hole/down-hole measurements, (b) results of side by side surface wave and cross-hole measurements, performed at five sites in the course of this study, (c) finite element analyses simulating the performance of surface wave measurements and thus providing “virtual” data, and (d) applying a current advanced inversion code, available on the Web. Based on all the above data, optimum values of a_R (and of the corresponding uncertainty of the derived V_so vs. depth profile) have been estimated. These values were found to be independent of depth from ground surface. The results of all analyses and comparisons indicate that for the majority of realistic soil profiles (including cases of normal and inverse dispersion conditions) the proposed SIM provides very reliable V_so vs. depth profiles when a value of a_R=0.63–0.67 is used in the inversion process. It is concluded that the SIM can be used with confidence as a direct inversion method of surface wave dispersion data.     

Numerical simulation of (T 2, T 1) 2D NMR and fluid responses

One-dimensional nuclear magnetic resonance (1D NMR) logging technology is limited for fluid typing, while two-dimensional nuclear magnetic resonance (2D NMR) logging can provide more parameters including longitudinal relaxation time (T ₁) and transverse relaxation time (T ₂) relative to fluid types in porous media. Based on the 2D NMR relaxation mechanism in a gradient magnetic field, echo train simulation and 2D NMR inversion are discussed in detail. For 2D NMR inversion, a hybrid inversion method is proposed based on the damping least squares method (LSQR) and an improved truncated singular value decomposition (TSVD) algorithm. A series of spin echoes are first simulated with multiple waiting times (T _W s) in a gradient magnetic field for given fluid models and these synthesized echo trains are inverted by the hybrid method. The inversion results are consistent with given models. Moreover, the numerical simulation of various fluid models such as the gas-water, light oil-water, and vicious oil-water models were carried out with different echo spacings (T _E s) and T _W s by this hybrid method. Finally, the influences of different signal-to-noise ratios (SNRs) on inversion results in various fluid models are studied. The numerical simulations show that the hybrid method and optimized observation parameters are applicable to fluid typing of gas-water and oil-water models.     

Array analysis of lateral inhomogeneities in the deep mantle

P-wave slowness and azimuth anomalies at LASA are critically dependent on the array configuration. This agrees with the interpretation that the anomalies arise by scattering at small-scale randomly distributed inhomogeneities in the crust and uppermost mantle beneath the array. Of particular importance is the result that numerous configurations can be chosen which yield ( dT/dΔ, ?) anomalies which are inconsistent with recent interpretations including a lateral inhomogeneity at the base of the mantle beneath Hawaii. Also configurations giving ( dT/dΔ, ?) anomalies inconsistent with the existence of mantle plumes under Iceland or the Galapagos Islands are found.     

Pore geometry of sandstone derived from pulsed field gradient NMR

Several parameters of pore geometry are needed for estimating permeability which is a key parameter for the characterization of reservoir sandstones. Powerful techniques for probing the pore space are the self-diffusion and the relaxation time NMR methods. However, the quality of results depends on the petrophysical model which underlies the interpretation of measurements. We applied the pulsed field gradient nuclear magnetic resonance (PFG-NMR) technique and measured time-dependent self-diffusion coefficients, D(Δ), of water in anhydrite cemented sandstones with low porosity and high tortuosity. The conventional method of fitting data with a function (Padé approximation) of the surface-to-volume ratio and the tortuosity yielded uncertain results. As part of a novel approach, we developed a numerical simulation code based on physical principles and a fractal pore space model. We compared our method with the Padé approximation and tested with data from the literature. For porous media with low tortuosity values and simple geometry such as randomly packed glass beads, both methods are in good agreement and give similar results. In sedimentary rocks, however, the new method of calculation is able to determine more accurate details of the pore geometry. However, its main advantage occurs in porous media with fractal geometry or with constricted pores, where the D(Δ)/D₀ curves deviate from the characteristic shape that is found for randomly packed glass beads.     

Shear-wave velocity estimation using a combination of ambient noise from small aperture array and small-scale active seismic measurements: a case study in the area of the natural gas fields of Northern Germany

In recent years, numerous induced seismic events have occurred in the proximity of the natural gas field in Northern Germany. To monitor the seismicity and to asses the seismic hazard potential, a local monitoring network was installed in the area. Focusing on the seismicity hazard assessment, a major challenge is the characterisation of potential site effects due to local soil characteristics. This is quantitatively performed by estimating the shear-wave velocity (V _s) variation with subsurface layer thickness. Such local effects can only be covered with a coarse spatial resolution due to the limited number of monitoring stations. Profiles were determined at three test sites (Langwedel, Walle and Bomlitz) by using a combined approach of small aperture 2D array ambient noise and small-scale active 1D measurements. The high-resolution frequency-wavenumber (HRFK), spatial autocorrelation (SPAC) and multichannel analysis of surface waves (MASW) methods were applied to the recorded ambient noise and active seismic data using various array sizes supplemented by the active measurements. This jointly allowed obtaining phase velocity dispersion curves covering a wide frequency range from 2 up to 32 Hz. The inversion of the obtained dispersion curves results in average S-wave velocity profiles down to depths of 70 m, identifying thin near-surface layers of a few meters as well as thicker layers of tens of meters in greater depth. A comparison with available borehole data shows a good correlation with the layering. Additionally, to asses the impact of a seismic event at the test sites, PGV estimations for various seismic events were performed. The final results of the test surveys demonstrate that the combined approach represents a suitable tool for near-surface characterisation, which can be used to improve the seismic hazard assessment in the area of the natural gas fields in Northern Germany.     

Global Optimisation of Time Domain Electromagnetic Data Using Very Fast Simulated Annealing

--Efficacy of the global optimisation technique is demonstrated in the inversion of time domain electromagnetic data. Transient EM responses observed using a coincident loops system along several profiles and different time channels over a plate like conducting body are inverted, using very fast simulated annealing (VFSA) as an optimisation tool. Three time channels for each profile are considered in the inversion. Study reveals that only one run of global inversion considering a single multi-channel profile is not enough to resolve all the nine model parameters of a plate-like conducting body. However, the global inversion of a single multi-channel profile with several runs yields a mean model that is quite close to the true model. Considering many profiles and time channels together in the global inversion can yield reliable estimates of all the parameters. Computationally, this is not an efficient procedure. Analysis of the results shows, however, that two distant profiles are enough to yield all the model parameters reliably, even after one run of the global inversion. Both noise-free and noisy synthetic data are used in the inversion. Finally, field data are also inverted to study the performance of the global inversion.     

Three‐dimensional potential field data inversion with L0 quasinorm sparse constraints

The quantitative explanation of the potential field data of three‐dimensional geological structures remains one of the most challenging issues in modern geophysical inversion. Obtaining a stable solution that can simultaneously resolve complicated geological structures is a critical inverse problem in the geophysics field. I have developed a new method for determining a three‐dimensional petrophysical property distribution, which produces a corresponding potential field anomaly. In contrast with the tradition inverse algorithm, my inversion method proposes a new model norm, which incorporates two important weighting functions. One is the L0 quasi norm (enforcing sparse constraints), and the other is depth‐weighting that counteracts the influence of source depth on the resulting potential field data of the solution. Sparseness constraints are imposed by using the L0 quasinorm on model parameters. To solve the representation problem, an L0 quasinorm minimisation model with different smooth approximations is proposed. Hence, the data space (N) method, which is much smaller than model space (M), combined with the gradient‐projected method, and the model space, combined with the modified Newton method for L0 quasinorm sparse constraints, leads to a computationally efficient method by using an N × N system versus an M × M one because N ? M. Tests on synthetic data and real datasets demonstrate the stability and validity of the L0 quasinorm spare norms inversion method. With the aim of obtaining the blocky results, the inversion method with the L0 quasinorm sparse constraints method performs better than the traditional L2 norm (standard Tikhonov regularisation). It can obtain the focus and sparse results easily. Then, the Bouguer anomaly survey data of the salt dome, offshore Louisiana, is considered as a real case study. The real inversion result shows that the inclusion the L0 quasinorm sparse constraints leads to a simpler and better resolved solution, and the density distribution is obtained in this area to reveal its geological structure. These results confirm the validity of the L0 quasinorm sparse constraints method and indicate its application for other potential field data inversions and the exploration of geological structures.     

Three-dimensional inversion of the single-profile magnetotelluric data

It is preferable to use the three-dimensional (3D) magnetotelluric inversion, which provides volumetric geoelectric models, to handle the array input data. However, the soundings are frequently conducted on the single profiles or on the profiles that are considerably spaced apart from each other. We explore the possibilities of the 3D inversion of such data by the example of a three-layer model containing three local inhomogeneities. We previously showed that the simple processing of the data and their 1D or 2D inversion enable reconstructing the background cross section and locating all the three inhomogeneities. In the present paper, we use this information for constructing several versions of the starting model and carrying out the smoothing 3D inversion of the data. The experiments show that if the background cross section is incorporated into the starting model, the final model provided by the inversion closely reproduces the real distribution of all geoelectric parameters. At the same time, if the starting model that hosts the inhomogeneities has the form of a homogeneous half-space, the inversion is not able to reconstruct an adequate final model.

     

基于阵列感应与自然电位联合反演地层水电阻率

原状地层水电阻率是重要的储层参数,也是进行精细储层评价的基础.基于泥浆侵入数值模拟与侵入过程中井周岩石物理特征分析,确定了薄膜电位的产生位置,针对储层高、低侵等不同侵入特征,提出了可适用于包括存在"低阻环"等不同侵入特征时储层电阻率分布的"五参数"地层模型,基于几何因子理论与有限元方法,建立了阵列感应与自然电位测井联合反演算法,实现了地层电阻率参数反演,重构了地层径向电阻率剖面,进而精确求取了地层水电阻率.通过对实际资料处理表明:反演算法稳定可靠,"五参数"模型能很好地表征储层电阻率分布形态,重构储层电阻率剖面,确定薄膜电位产生位置;基于阵列感应与自然电位的联合反演,能精确计算原状地层水电阻率,为储层评价与流体性质识别提供依据.     

Estimation of site amplification,attenuation and source spectra of S-waves in the East-Central Iran

Generalized inversion of the S-wave amplitude spectra from the strong-motion network data in the East-Central Iran has been used to estimate simultaneously source parameters, site response and the S-wave attenuation (Q_s). In this regard, 190 three-component records were used corresponded to 40 earthquakes with the magnitudes M3.5–M7.3. These earthquakes were recorded at 42 stations in the hypocentral distance range from 9 to 200 km. The inverse problem was solved in 20 logarithmically equally spaced points in the frequency band from 0.4 to 15 Hz. The frequency-dependent site amplification was imposed, as a constraint, on two reference site responses in order to remove the undetermined degree of freedom in the inversion and obtain a unique inverse solution. Also, a geometrical spreading factor was assumed for removing the trade-off between geometrical spreading and anelastic attenuation. Different source parameters, such as seismic moment (M₀), seismic energy (E_s), corner frequency (f_c) and Brune stress drop (Δσ), were estimated for each event by fitting an ω² model to the spectra obtained from the inversion. The stress drop values of earthquakes, obtained in this research, are in good agreement with those of other studies. Also average site response values were correlated to the average shear wave velocities in the uppermost 30 m, in high and low frequency bands. The peak frequencies of site amplifications, estimated by the generalized inversion method, where in good agreement with those of horizontal to vertical (H/V) spectral ratios for the S-wave portion of records. However, no perfect matching in amplitude was obtained due to the deficiencies of the H/V ratio technique. By supposing a free shape for Q factor, a frequency dependent function was found, the logarithm of which could be approximated by a linear function, Q(f)=151f^0.75. The uncertainties of model parameters have been evaluated by covariance matrix of least-square fit. The residuals were also analyzed in order to assess the validity of the model. The analysis of residuals with respect to magnitude and distance indicates that they are distributed normally with approximately zero mean. The robustness of the results has been studied concerning their sensitivities to the omission of different datasets, selected randomly from original database. The results obtained here can be used in predicting ground-motion parameters applying stochastic methods.     

Evidence for a sharp increase in P-wave velocity at about 770 km depth

Slowness data from earthquakes in the Mindanao and Philippine regions recorded at the Warramunga array indicate a small, but abrupt, decrease in dT/dΔ at a distance of 29.5°. There is evidence also of a triplication in the P travel-time curve at about this distance. These data strongly suggest the presence of a rapid or discontinuous velocity increase of about 2% in P-wave velocity at a depth of about 770 km. Such a velocity increase is consistent with the occurrence of more than one phase change between 600 and 900 km, as predicted by the pyrolite model of Ringwood.Previous observations of increasing dT/dΔ with distance may have resulted from the predominance of the 650-km branch as it approaches its cusp. If so, then it is not necessary to invoke a decrease in velocity with depth near 800 km to explain the increase in mdT/dΔ observed between 32–34°.     

重力及其垂直梯度交叉约束联合密度结构反演方法

重力垂直梯度能突出浅部地质目标, 具有较高的水平分辨率, 而重力异常则可以更好地保留较深场源的信息, 重力与重力梯度联合勘探常用来获取不同深度场源的异常特征.本文提出重力及其垂直梯度交叉约束联合密度结构反演方法, 其采用交叉梯度实现重力与重力梯度数据联合反演, 并将二者单独反演结果作为归一化权函数约束联合反演过程.该方法可有效改善不同参量反演结果集中于异常变化较大区域的缺点, 提升不同深度场源的分辨率, 更加准确地揭示深部场源的分布.模型试验结果表明该方法能清晰恢复不同深度场源的密度结构分布特征, 且具有良好抗噪能力.针对辽源采空区勘查开展重力与其垂直梯度联合测量, 利用本文数据联合反演圈定出了6个采空区, 与以往已知矿点位置完全一致, 且与高密度电阻率法解释结果吻合良好, 为区域规划建设提供了准确的依据.此外, 我们还对长白山火山地区卫星重力及其梯度数据进行反演, 估计了岩浆囊的位置和范围, 且与前人地球物理勘探结果较为吻合, 进一步证明了本文方法的实用性.

     

4He/3He thermochronometry

Using classical diffusion theory, we present a mathematical technique for the determination of ⁴He concentration profiles in minerals. This approach should prove useful for constraining the low-temperature cooling histories of individual samples and for correcting (U–Th)/He ages for partial diffusive loss. The calculation assumes that the mineral of interest contains an artificially produced and uniform distribution of ³He obtained by proton irradiation [Shuster et al., Earth Planet. Sci. Lett. 217 (2004) 19–32]. In minerals devoid of natural helium, this isotope allows measurement of He diffusion coefficients; in minerals with measurable radiogenic He, it permits determination of ⁴He profiles arising during ingrowth and diffusion in nature. The ⁴He profile can be extracted from stepwise degassing experiments in which the ⁴He/³He ratio is measured. The evolution of the ⁴He/³He ratio as a function of cumulative ³He released can be compared with forward models to constrain the shape of the profile. Alternatively, we present a linear inversion that can be used to directly solve for the unknown ⁴He distribution. The inversion incorporates a standard regularization technique to filter the influence of random measurement errors on the solution. Using either approach we show that stepwise degassing data can yield robust and high-resolution information on the ⁴He profile. Profiles of radiogenic He are a sensitive function of the time–Temperate (t–T) path that a cooling sample experienced. Thus, by step heating a proton-irradiated sample it is possible to restrict the sample’s acceptable t–T paths. The sensitivity of this approach was explored by forward-modeling ⁴He profiles resulting from a range of realistic t–T paths, using apatite as an example. Results indicate that ⁴He profiles provide rich information on t–T paths, especially when the profiles are coupled with (U–Th)/He cooling ages on the same sample. Samples that experienced only moderate diffusive loss have ⁴He concentration profiles that are rounded at the edge but uniform in the core of the diffusion domain. Such profiles can be identified by nearly invariant ⁴He/³He ratios after the first few to few tens of percent of ³He have been extracted by step heating. We show how such data can be used to correct (U–Th)/He ages for partial diffusive loss.     

U-series dating of bone in an open system: The diffusion-adsorption-decay model

A new theory is described for the uptake of U in an open system applied to the dating of archaeological bones. Analytical solutions are obtained for the rate of radioactive decay of ²³⁸U, ²³⁴U and ²³⁰Th as a function of position for the case where both ²³⁸U and ²³⁴U diffuse across a bone, and where external supply of ²³⁴U is not in equilibrium with ²³⁸U. The new theory constitutes a forward model for predicting ²³⁸U, ²³⁴U and ²³⁰Th activity profiles across a bone given an age and diffusion coefficient. The forward model can be used in an inversion process whereby observations of activity profiles of ²³⁸U, ²³⁴U and ²³⁰Th as a function of position are used to infer the bone age of a sample together with robust measures of uncertainty. Differences from previous studies are that no closed system assumptions are required and no apparent age calculations necessary, while diffusion of ²³⁴U across the bone is accounted for in the inversion process. The procedure also does not require U-concentration profiles for the calculation of model parameters. The measurement of U-concentration profiles are, however, useful for the assessment of the reliability of the calculated results. Because of the assumption of constant ²³⁴U/²³⁸U ratios at the boundaries of the bone, DAD age results are generally older than closed system U-series results derived from the same isotopic data. Allowance is made for both correlated and uncorrelated errors in activity measurements as well as theoretical error caused by inhomogeneities in the sample. The implementation of the new approach (which we term the DAD model for Diffusion–Adsorption–Decay) is straightforward and efficient enough to allow estimation of age and its uncertainty on a desktop computer. Software for performing age estimation with the new model is available from the corresponding author.     

核磁共振共轭梯度解谱方法研究

核磁共振（NMR）解谱技术是核磁共振资料应用的基础和关键.本文将核磁共振解谱的混定线性反演问题转化为求目标函数极小值的最优化问题,然后利用共轭梯度算法具有二次终止性、收敛速度快的特点解决上述最优化问题.将该方法应用于无噪声和不同信噪比的理论数据解谱以及岩心NMR实验解谱并与真谱及实验室国外软件解谱结果对比表明：在信噪比SNR≥5时解谱结果和真谱符合得很好,谱线光滑连续;随着信噪比的降低对初始点的要求随之提高;两块岩心解谱结果与实验室结果符合得很好,利用解谱结果计算的核磁孔隙度与实验室氦孔隙度绝对误差分别为0.78%和0.57%.因此,本文方法有效、实用,具有较强的抗噪能力,对初始点的要求不高,能够应用于生产和科研实践中.     

Velocity and Attenuation Structure of the Tibetan Lithosphere Under the Hi-CLIMB Array From the Modeling of Pn Attributes

Using seismic data from regional earthquakes in Tibet recorded by the Hi-CLIMB experiment, Pn attributes are used to constrain the velocity gradient and attenuation structure of the Tibetan lithosphere under the Hi-CLIMB array. Numerical modeling is performed using the spectral-element method (SEM) for laterally varying upper-mantle velocity and attenuation, and the seismic attributes considered include the Pn travel-time, envelope amplitude, and pulse frequency. The results from the SEM modeling provide two alternative models for the upper-mantle beneath the Hi-CLIMB array in Tibet. The first model is derived from the 3D velocity model of Griffin et al. (Bull Seism Soc Am 101:1938–1947, 2011) with a constant upper-mantle velocity gradient, and laterally varying upper mantle attenuation. The second model has a laterally varying upper-mantle velocity gradient, and constant upper-mantle attenuation. In both cases, the Qiangtang terrane is distinguished from the Lhasa terrane by a change in Moho depth and upper-mantle velocities. The lower upper-mantle velocities, as well as higher Pn attenuation, suggest hotter temperatures beneath the Qiangtang terrane as compared to the Lhasa terrane. Although the fits to the Pn amplitude and pulse frequency data are comparable between the two models, the first model with the constant upper-mantle velocity gradient fits the travel times somewhat better in relation to the data errors.