Modelling of magnetic data for scaling geology

Interpretation of magnetic data can be carried out either in the space or frequency domain. The interpretation in the frequency domain is computationally convenient because convolution becomes multiplication. The frequency domain approach assumes that the magnetic sources distribution has a random and uncorrelated distribution. This approach is modified to include random and fractal distribution of sources on the basis of borehole data. The physical properties of the rocks exhibit scaling behaviour which can be defined as P(k) = Ak^?β, where P(k) is the power spectrum as a function of wave number (k), and A and β are the constant and scaling exponent, respectively. A white noise distribution corresponds to β = 0. The high resolution methods of power spectral estimation e.g. maximum entropy method and multi‐taper method produce smooth spectra. Therefore, estimation of scaling exponents is more reliable. The values of β are found to be related to the lithology and heterogeneities in the crust. The modelling of magnetic data for scaling distribution of sources leads to an improved method of interpreting the magnetic data known as the scaling spectral method. The method has found applicability in estimating the basement depth, Curie depth and filtering of magnetic data.     

Mapping of magnetic basement in Central India from aeromagnetic data for scaling geology

The Central Indian region has a complex geology covering the Godavari Graben, the Bastar Craton (including the Chhattisgarh Basin), the Eastern Ghat Mobile Belt, the Mahanadi Graben and some part of the Deccan Trap, the northern Singhbhum Orogen and the eastern Dharwar Craton. The region is well covered by reconnaissance‐scale aeromagnetic data, analysed for the estimation of basement and shallow anomalous magnetic sources depth using scaling spectral method. The shallow magnetic anomalies are found to vary from 1 to 3 km, whereas magnetic basement depth values are found to vary from 2 to 7 km. The shallowest basement depth of 2 km corresponds to the Kanker granites, a part of the Bastar Craton, whereas the deepest basement depth of 7 km is for the Godavari Basin and the southeastern part of the Eastern Ghat Mobile Belt near the Parvatipuram Bobbili fault. The estimated basement depth values correlate well with the values found from earlier geophysical studies. The earlier geophysical studies are limited to few tectonic units, whereas our estimation provides detailed magnetic basement mapping in the region. The magnetic basement and shallow depth values in the region indicate complex tectonic, heterogeneity, and intrusive bodies at different depths, which can be attributed to different thermo‐tectonic processes since Precambrian.     

磁变仪标度值自动测定电路的改进

介绍了改进后的磁变仪标度值自动测定电路的主要特性、电路工作原理和使用注意事项,提供了电路原理图。     

Estimation of a non-stationary prior covariance from seismic data

Non-stationarity in statistical properties of the subsurface is often ignored. In a classical linear Bayesian inversion setting of seismic data, the prior distribution of physical parameters is often assumed to be stationary. Here we propose a new method of handling non-stationarity in the variance of physical parameters in seismic data. We propose to infer the model variance prior to inversion using maximum likelihood estimators in a sliding window approach. A traditional, and a localized shrinkage estimator is defined for inferring the prior model variance. The estimators are assessed in a synthetic base case with heterogeneous variance of the acoustic impedance in a zero-offset seismic cross section. Subsequently, this data is inverted for acoustic impedance using a non-stationary model set up with the inferred variances. Results indicate that prediction as well as posterior resolution is greatly improved using the non-stationary model compared with a common prior model with stationary variance. The localized shrinkage predictor is shown to be slightly more robust than the traditional estimator in terms of amplitude differences in the variance of acoustic impedance and size of local neighbourhood. Finally, we apply the methodology to a real data set from the North Sea basin. Inversion results show a more realistic posterior model than using a conventional approach with stationary variance.     

Depth and structural index from normalized local wavenumber of 2D magnetic anomalies

Recent improvements in the local wavenumber approach have made it possible to estimate both the depth and model type of buried bodies from magnetic data. However, these improvements require calculation of third‐order derivatives of the magnetic field, which greatly enhances noise. As a result, the improvements are restricted to data of high quality. We present an alternative method to estimate both the depth and model type using the first‐order local wavenumber approach without the need for third‐order derivatives of the field. Our method is based on normalization of the first‐order local wavenumber anomalies and provides a generalized equation to estimate the depth of some 2D magnetic sources regardless of the source structure. Information about the nature of the sources is obtained after the source location has been estimated. The method was tested using synthetic magnetic anomaly data with random noise and using three field examples.     

A note on a non-stationary model for seismic P-waves

Further evidence supporting a non-stationary model for seismic P-waves from underground nuclear explosions are given. Results of fitting this model are compared with findings of Töksoz, Ben-Menaheim and Harkrider (1964) and Helmberger and Harkrider (1972). A method of studying dependence of the principle parameters of this model on yield of event is briefly discussed.     

On a continuous spectral algorithm for simulating non-stationary Gaussian random fields

This paper presents an algorithm for simulating Gaussian random fields with zero mean and non-stationary covariance functions. The simulated field is obtained as a weighted sum of cosine waves with random frequencies and random phases, with weights that depend on the location-specific spectral density associated with the target non-stationary covariance. The applicability and accuracy of the algorithm are illustrated through synthetic examples, in which scalar and vector random fields with non-stationary Gaussian, exponential, Matérn or compactly-supported covariance models are simulated.     

Depth determination of small shallow earthquakes in eastern Canada from maximum power Rg/Sg spectral ratio

For small earthquakes, focal depths can be estimated jointly when epicenters are located using the arrival times of Pg and Sg waves recorded at seismic stations close to the event. However, if regional network coverage is sparse, this approach does not give accurate results. An alternative solution is the use of the regional depth-phase modeling (RDPM) method when such depth phases are available. Small, shallow earthquakes can generate Rg waves, the amplitudes of which approximately attenuate exponentially with focal depth; whereas, the amplitudes of Sg waves are, on average, less dependent on focal depth. Based on these features, a method using the maximum power spectral ratio (MPSR) between the Rg and Sg segments was developed to determine focal depth. Tests show the focal depth solutions obtained by the MPSR and RDPM methods for five events in an earthquake swarm and one event acquired by inspection are in good agreement. The error in the MPSR-determined focal depth caused by the error in the epicentral distance is in the order of 0.1 km. The error in the focal depth when using a default focal mechanism is in the order of 0.5 km. The quality factor, Q does not generate a significant error. Using the average of focal depths can provide a more reliable solution. Using an azimuth of approximately 45° from the strike direction to generate the synthetic ratio curve can reduce the error. As with any other earthquake locating technique, a reasonable regional crustal model is required when the MPSR method is used. Case studies show that the MPSR method can be used to successfully determine focal depths for events as small as m _N 1.6.     

Depth from extreme points method for gravity gradient tensor data

The ‘depth from extreme points’ method is an important tool to estimate the depth of sources of gravity and magnetic data. In order to interpret gravity gradient tensor data conveniently, formulas for the tensor data form regarding depth from the extreme points method were calculated in this paper. Then, all of the gradient tensor components were directly used to interpret the causative source. Beyond the g_zz component, also the g_xx and g_yy components can be used to obtain depth information. In addition, the total horizontal derivative of the depth from extreme points of the gradient tensor can be used to describe the edge information of geologic sources. In this paper, we investigated the consistency of the homogeneity degree calculated by using the different components, which leads to the calculated depth being confirmed. Therefore, a more integrated interpretation can be obtained by using the gradient tensor components. Different synthetic models were used with and without noise to test the new approach, showing stability, accuracy and speed. The proposed method proved to be a useful tool for gradient tensor data interpretation. Finally, the proposed method was applied to full tensor gradient data acquired over the Vinton Salt Dome, Louisiana, USA, and the results are in agreement with those obtained in previous research studies.     

Depth and shape estimates from simultaneous inversion of magnetic fields and their gradient components using differential similarity transforms

The differential similarity transform of a magnetic anomaly is a linear combination of its intensity and gradient components. This transform is sensitive to the distance between a chosen central point of similarity and the source and depends on the degree of homogeneity of the field. Taking advantage of this property, a new field inversion method resulting in the evaluation of source position and shape type is proposed and implemented. The field gradient components are measured directly in magnetic gradiometry, or they can be calculated from the measured field data. Regional and local linear backgrounds are accounted for by the method. The method can be applied on either regularly or irregularly-spaced data sets, on even or uneven surfaces of observation. The solving of the systems of equations is not necessary. A semi-automated inversion for both location and shape of the sources is implemented. Model and field tests illustrate the effectiveness of the proposed inversion technique for depth and shape estimates.     

Basement geology beneath the northeast Thelon Basin,Nunavut: insights from integrating new gravity,magnetic and geological data

Current models for unconformity‐associated uranium deposits predict fluid flow and ore deposition along reactivated faults in >1.76 Ga basement beneath Mesoproterozoic siliciclastic basins. In frontier regions such as the Thelon Basin in the Kivalliq region of Nunavut, little is known about the sub‐basin distribution of units and structures, making exploration targeting very tenuous. We constructed a geological map of the basement beneath the unconformity by extrapolating exposed features into the subsurface. The new map is constrained by detailed geological, geophysical, and rock property observations of outcrops adjacent to the basin and by aeromagnetic and gravity data over the geophysically transparent sedimentary basin. From rock property measurements, it is clear that the diverse magnetic and density characteristics of major rock packages provide quantitative three‐dimensional constraints. Gravity profiles forward modelled in four cross sections define broad synforms of the Amer Belt and Archean volcanic rocks that are consistent with the structural style outside the basin. Major lithotectonic entities beneath the unconformity include: supracrustal rocks of the Archean Woodburn Lake group and Marjorie Hills meta sedimentary gneiss and associated mixed granitoid and amphibolitic gneiss; the Amer Mylonite Zone and inferred mafic intrusions oriented parallel and sub‐parallel; other igneous intrusions of 2.6 Ga, 1.83 Ga, and 1.75 Ga vintage; and the <2.3 Ga to >1.84 Ga Amer Group. Four main brittle regional fault arrays (040°–060°, 075°–90°, 120°, and 150°) controlled development and preservation of the basin. The reactivated intersections of such faults along fertile basement units such as the Rumble assemblage, Marjorie Hills assemblage, Nueltin igneous rocks, and Pitz formation are the best targets for uranium exploration.     

A new least-squares minimization approach to depth and shape determination from magnetic data

We have developed a least‐squares minimization approach to depth determination using numerical second horizontal derivative anomalies obtained from magnetic data with filters of successive window lengths (graticule spacings). The problem of depth determination from second‐derivative magnetic anomalies has been transformed into finding a solution to a non‐linear equation of the form, f(z) = 0. Formulae have been derived for a sphere, a horizontal cylinder, a dike and a geological contact. Procedures are also formulated to estimate the magnetic angle and the amplitude coefficient. We have also developed a simple method to define simultaneously the shape (shape factor) and the depth of a buried structure from magnetic data. The method is based on computing the variance of depths determined from all second‐derivative anomaly profiles using the above method. The variance is considered a criterion for determining the correct shape and depth of the buried structure. When the correct shape factor is used, the variance of depths is less than the variances computed using incorrect shape factors. The method is applied to synthetic data with and without random errors, complicated regionals, and interference from neighbouring magnetic rocks. Finally, the method is tested on a field example from India. In all the cases examined, the depth and the shape parameters are found to be in good agreement with the actual parameters.     

On the determination of the atmospheric ozone profile for ground based microwave measurements

It is shown how to retrieve the atmospheric ozone profile by means of ground based microwave measurements of the radiative intensity. Chahine's iteration method is used. The method is tested by a numerical experiment. The retrieval rms about the mean error is approximately 0.4 ppm. The required measurement accuracy for the brightness temperatures is ±0.01 K.     

Research Note: Compact Depth from Extreme Points: a tool for fast potential field imaging

We propose a fast method for imaging potential field sources. The new method is a variant of the “Depth from Extreme Points,” which yields an image of a quantity proportional to the source distribution (magnetization or density). Such transformed field is here transformed into source‐density units by determining a constant with adequate physical dimension by a linear regression of the observed field versus the field computed from the “Depth from Extreme Points” image. Such source images are often smooth and too extended, reflecting the loss of spatial resolution for increasing altitudes. Consequently, they also present too low values of the source density. We here show that this initial image can be improved and made more compact to achieve a more realistic model, which reproduces a field consistent with the observed one. The new algorithm, which is called “Compact Depth from Extreme Points” iteratively produces different source distributions models, with an increasing degree of compactness and, correspondingly, increasing source‐density values. This is done through weighting the model with a compacting function. The compacting function may be conveniently expressed as a matrix that is modified at any iteration, based on the model obtained in the previous step. At any iteration step the process may be stopped when the density reaches values higher than prefixed bounds based on known or assumed geological information. As no matrix inversion is needed, the method is fast and allows analysing massive datasets. Due to the high stability of the “Depth from Extreme Points” transformation, the algorithm may be also applied to any derivatives of the measured field, thus yielding an improved resolution. The method is investigated by application to 2D and 3D synthetic gravity source distributions, and the imaged sources are a good reconstruction of the geometry and density distributions of the causative bodies. Finally, the method is applied to microgravity data to model underground crypts in St. Venceslas Church, Tovacov, Czech Republic.     

Testing a scaling law for the earthquake recurrence time distributions

The earthquake recurrence time distribution in a given space-time window is being studied, using earthquake catalogues from different seismic regions (Southern California, Canada, and Central Asia). The quality of the available catalogues, taking into account the completeness of the magnitude, is examined. Based on the analysis of the catalogues, it was determined that the probability densities of the earthquake recurrence times can be described by a universal gamma distribution, in which the time is normalized with the mean rate of occurrence. The results show a deviation from the gamma distribution at the short interevent times, suggesting the existence of clustering. This holds from worldwide to local scales and for quite different tectonic environments.     

Ecohydrological modelling in a deciduous boreal forest: Model evaluation for application in non-stationary climates

Soil moisture is an important driver of growth in boreal Alaska, but estimating soil hydraulic parameters can be challenging in this data-sparse region. Parameter estimation is further complicated in regions with rapidly warming climate, where there is a need to minimize model error dependence on interannual climate variations. To better identify soil hydraulic parameters and quantify energy and water balance and soil moisture dynamics, we applied the physically based, one-dimensional ecohydrological Simultaneous Heat and Water (SHAW) model, loosely coupled with the Geophysical Institute of Permafrost Laboratory (GIPL) model, to an upland deciduous forest stand in interior Alaska over a 13-year period. Using a Generalized Likelihood Uncertainty Estimation parameterisation, SHAW reproduced interannual and vertical spatial variability of soil moisture during a five-year validation period quite well, with root mean squared error (RMSE) of volumetric water content at 0.5 m as low as 0.020 cm³/cm³. Many parameter sets reproduced reasonable soil moisture dynamics, suggesting considerable equifinality. Model performance generally declined in the eight-year validation period, indicating some overfitting and demonstrating the importance of interannual variability in model evaluation. We compared the performance of parameter sets selected based on traditional performance measures such as the RMSE that minimize error in soil moisture simulation, with one that is designed to minimize the dependence of model error on interannual climate variability using a new diagnostic approach we call CSMP, which stands for Climate Sensitivity of Model Performance. Use of the CSMP approach moderately decreases traditional model performance but may be more suitable for climate change applications, for which it is important that model error is independent from climate variability. These findings illustrate (1) that the SHAW model, coupled with GIPL, can adequately simulate soil moisture dynamics in this boreal deciduous region, (2) the importance of interannual variability in model parameterisation, and (3) a novel objective function for parameter selection to improve applicability in non-stationary climates.     

磁化强度矢量反演新方法及其在卡拉塔格铜多金属矿床找矿中的应用

磁异常的反演是地球物理勘探的重要手段,三维磁化率反演是磁异常定量解释中的一种重要方法.由于剩磁的存在使得磁化方向与地磁场方向产生偏差,从而影响了磁异常反演与解释的精度.本文基于磁异常模量反演和磁化强度矢量反演方法得到了一种新的磁化强度矢量反演方法.与以往的磁化强度矢量反演方法相比,该方法以磁异常模量反演得到的磁化率模型为约束,采用L_p范数正则化方法求解,提高了磁化强度矢量反演的精度和效率.本文通过模拟试验的反演计算,验证了这种磁化强度矢量反演方法的有效性.最后,将本文方法应用于新疆东天山卡拉塔格地区航磁数据的解释,获得了地下空间不同磁性差异的磁性体的空间分布特征,为进一步分析研究区隐伏矿床提供了重要信息.     

洛川黄土-古土壤剖面环境剂量率测量的对比

如何准确测量环境剂量率是释光和电子自旋共振测年技术的关键之一.本文选择了几种环境剂量率的主要室内测量方法,对洛川黄土-古土壤这个典型的均匀剖面进行测量对比研究,同时检验Daybreak公司生产的厚源ZnS Alpha计数仪的测量精度.