Luminescence thermochronometry of feldspar minerals: Optimisation of measurement conditions for the derivation of thermal kinetic parameters using isothermal holding experiments

Luminescence thermochronometry is sensitive to very low temperatures (below ∼120 °C), and enables the resolution of thermal histories over sub-Quaternary timescales. Here we apply a multi-elevated-temperature post-infrared infrared-stimulated luminescence (MET-pIR-IRSL) measurement protocol to feldspar minerals to extract thermal histories. These thermal histories depend on the thermal stability of the MET signal, and are based on the thermal kinetic parameters extracted from isothermal decay experiments. However, the derived thermal kinetic parameters vary with experimental conditions, specifically with the isothermal holding temperatures (ITL) used. We analyse samples with independently known thermal histories, together with synthetic thermal history samples and samples with unknown thermal histories to test the validity of thermal kinetic parameters obtained from different combinations of isothermal holding data. This approach is tested on feldspars of different mineralogies and lithologies. We find that the temperatures inferred from inverting the data change, depending both on the number and on the highest ITL temperature used for thermal kinetic parameter derivation. Analysed samples validate the MET-pIR-IRSL protocol for extracting thermal histories, and we suggest that four isothermal holding temperatures between 190 and 250 °C are used for appropriate thermal kinetic parameter derivation.     

Photographing layer thicknesses and discontinuities in a marble quarry with 3D GPR visualisation

An important problem of marble-quarry management is assessing the quality and the homogeneity of quarry blocks before excavation. In this study, we decided to image the limestone, which we studied in a marble quarry, in terms of layer thickness, discontinuities and cavities using the ground-penetrating-radar (GPR) method. The method was successfully applied to detect and map the fractures with the cavities in a marble layer according to depth in the Ankara City Polatli Town (Turkey) region, which represents upper Miocene–Pliocene lacustrine carbonate rocks.This paper is based on interactive transparent 3D visualisation of the 2D GPR profiles to determine changes in layer thickness and discontinuities. In addition, this paper indicates the importance of the appropriate opacity-function construction to obtain transparent 3D visualisation. Firstly we acquired and processed parallel 2D GPR profile data, then we assigned two different amplitude–colour ranges using a limited number of colours to determine the layer thickness and its discontinuities separately. We obtained a 3D volume using parallel 2D GPR data and displayed a limited amplitude range by arranging an opacity function. Therefore, we obtained transparent 3D blocks for thickness and discontinuities, and we formulated an interactive 3D display to image the horizontal, vertical and inclined discontinuities and their directions in the x–y plane versus depth. The GPR results were compared with the petrographical investigation on the basis of textural and mineralogical compositions. The vesicular textures within carbonate platform were supported by the GPR results.     

Magnetic basement: gravity‐guided magnetic source depth analysis and interpretation

We present a new integrated approach to the interpretation of magnetic basement that is based on recognition of characteristic patterns in distributions and alignments of magnetic source depth solutions above and below the surface of magnetic basement. This approach integrates a quantitative analysis of depth solutions, obtained by 2D Werner deconvolution of the magnetic data, with a qualitative evaluation of the Bouguer gravity anomalies. The crystalline/metamorphic basement and sedimentary cover have different origins, tectonic histories, lithologies and magnetic properties. These differences result in different geometries of magnetic sources associated with faults, fracture zones, igneous intrusions, erosional truncations, subcrop edges and other structural discontinuities. Properly tuned, 2D Werner deconvolution is able to resolve the intra‐sedimentary and intra‐basement magnetic source geometries into distinctly different distributions and alignments of calculated depth solutions. An empirical set of criteria, basement indicators, was developed for identification and correlation of the basement surface. The ambiguity of basement correlation with limited or non‐existent well control, which is common for onshore frontier and offshore explorations, can be reduced by incorporating the Bouguer gravity data into the process of correlation.     

An algorithm for fast 3D inversion of surface electrical resistivity tomography data: application on imaging buried antiquities

In this work a new algorithm for the fast and efficient 3D inversion of conventional 2D surface electrical resistivity tomography lines is presented. The proposed approach lies on the assumption that for every surface measurement there is a large number of 3D parameters with very small absolute Jacobian matrix values, which can be excluded in advance from the Jacobian matrix calculation, as they do not contribute significant information in the inversion procedure. A sensitivity analysis for both homogeneous and inhomogeneous earth models showed that each measurement has a specific region of influence, which can be limited to parameters in a critical rectangular prism volume. Application of the proposed algorithm accelerated almost three times the Jacobian (sensitivity) matrix calculation for the data sets tested in this work. Moreover, application of the least squares regression iterative inversion technique, resulted in a new 3D resistivity inversion algorithm more than 2.7 times faster and with computer memory requirements less than half compared to the original algorithm. The efficiency and accuracy of the algorithm was verified using synthetic models representing typical archaeological structures, as well as field data collected from two archaeological sites in Greece, employing different electrode configurations. The applicability of the presented approach is demonstrated for archaeological investigations and the basic idea of the proposed algorithm can be easily extended for the inversion of other geophysical data.     

Compressive sensing approach for two‐dimensional magnetotelluric inversion using wavelet dictionaries

We present a 2D inversion scheme for magnetotelluric data, where the conductivity structure is parameterised with different wavelet functions that are collected in a wavelet‐based dictionary. The inversion model estimate is regularised in terms of wavelet coefficient sparsity following the compressive sensing approach. However, when the model is expressed on the basis of a single wavelet family only, the geometrical appearance of model features reflects the shape of the wavelet functions. Combining two or more wavelet families in a dictionary provides greater flexibility to represent the model structure, permitting, for example, the simultaneous occurrence of smooth and sharp anomalies within the same model. We show that the application of the sparsity regularisation scheme with wavelet dictionaries provides the user with a number of different model classes that may explain the data to the same extent. For a real data example from the Dead Sea Transform, we show that the use of such a scheme can be beneficial to evaluate the geometries of conductivity anomalies and to understand the effect of regularisation on the model estimate.     

二维叠后地震数据的平稳随机介质参数估计

随机介质参数估计是随机介质理论应用于地震勘探的关键.本文提出了一种从二维叠后地震数据中估计平稳随机介质参数的方法.文中阐述了二维叠后地震数据与随机介质波阻抗模型的关系,以及随机介质自相关函数参数的估计原理和方法,并结合实例详细介绍了应用功率谱法进行随机介质参数估计的具体步骤;通过多个二维理论模型的估计试验,验证了方法的可行性和正确性;还对实际地震数据进行了随机介质参数的估计试验,结果表明,随机介质参数可以为三角洲沉积相的进一步划分提供参考,反映了该方法有较好的应用前景.相比前人的研究,本文所提出的随机介质参数估计方法是一种真正的二维算法,特别是能给出自相关角度θ的估计,这种基于功率谱的估计方法具有直观且高效率的优点,但也存在着误差较大的问题,需要进一步的改进和完善.     

Data Analysis and Modeling to Optimize Thermal Treatment Cost and Performance

The objective of in situ thermal treatment is typically to reduce the contaminant mass or average soil concentration below a specified value. Evaluation of whether the objective has been met is usually made by averaging soil concentrations from a limited number of soil samples. Results from several field sites indicate large performance uncertainty using this approach, even when the number of samples is large. We propose a method to estimate average soil concentration by fitting a log normal probability model to thermal mass recovery data. A statistical approach is presented for making termination decisions from mass recovery data, soil sample data, or both for an entire treatment volume or for subregions that explicitly considers estimation uncertainty which is coupled to a stochastic optimization algorithm to identify monitoring strategies to meet objectives with minimum expected cost. Early termination of heating in regions that reach cleanup targets sooner enables operating costs to be reduced while ensuring a high likelihood of meeting remediation objectives. Results for an example problem demonstrate that significant performance improvement and cost reductions can be achieved using this approach.     

From surface wave inversion to seismic site response prediction: Beyond the 1D approach

Surface wave methods consist of the extraction and inversion of the Rayleigh wave phase-velocity dispersion curve to recover the (usually 1D) shear-wave velocity profile. In the literature, uncertainty due to data error has not received much attention, but the discussion about uncertainty due to model error is even poorer. Even with an unrealistic noise-free dataset and an exact forward model, an inappropriate parameterization can generate solutions very far from the actual soil structure. In general, the model used for the dispersion curve interpretation is 1D. Hence, when the velocity distribution is laterally heterogeneous, model errors can have significant consequences on the reliability of the resulting shear-wave velocity distribution. From a poor velocity reconstruction, an unsatisfactory, and often dangerous site response analysis follows. In fact, shear wave measurements play a relevant role in seismic ground motion amplification estimation. In this paper, we discuss the possibility of processing the seismograms using a multi-offset phase analysis (MOPA), in order to derive soil elastic parameters for weak motion predictions. This technique allows the detection and location of the lateral discontinuities, and a better model parameterization. In fact, once the discontinuities are identified, we can split the profile into several, truly 1D, parts. The use of the standard 1D dispersion curve extraction and inversion for each side of the heterogeneity generates velocity profiles that we can put side by side to get correct 2D reconstructions of the shear-wave distributions. From 2D velocity reconstruction, we can calculate the site response that may be significantly different from the site response generated from a traditional 1D analysis of the same seismograms. In this work, we discuss the site responses of two synthetic examples with lateral heterogeneities. We show how misleading a 1D analysis may be if applied to a truly 2D velocity distribution, particularly in terms of site response prediction.     

2D PP/PS-stereotomography: Application to a real 2D-OBC dataset

It has been shown on an ‘ideal’ synthetic dataset that PP/PS‐stereotomography can estimate an accurate velocity model without any pairing of PP‐ and PS‐events. The P‐wave velocity model is first estimated using PP data and then, fixing this velocity field, the S‐wave velocity is estimated using the PS data. This method needed to be evaluated further and we present here the first application of PP/PS‐stereotomography to a real dataset: the 2D East‐West Mahogany OBC line (Gulf of Mexico). We are here confronted with data which do not fit our working assumptions: coherent noise (due to an approximate separation of PP‐ and PS‐events and some remaining multiples), probably some anisotropy and 3D effects. With a careful selection of the stereotomographic picks, which allows one to decrease the effect of the picked coherent noise by the automatic picker, our application can demonstrate the relevance of our approach in the upper part of the profile, where anisotropy and 3D effects might be low. We can thus estimate, without any pairing of PP‐ and PS‐events, a velocity field which provides not only flat common image gathers, but also PP‐ and PS‐depth migrated images located at the same positions. For the deeper part of the profile, a significant shift in depth appears. In addition to possible anisotropy, 3D effects and a more complex velocity field (‘salt body’), this is due to the quality of the PZ‐ and X‐components profiles: The PZ‐component profile where the PP‐stereotomographic picking is performed, is polluted by conflicting converted or multiple events and the X‐component profile, where the PS‐stereotomographic picking is performed, is highly noisy. This study emphasizes the need to develop accurate selection criteria for the stereotomographic picks.     

Optimizing a layered and laterally constrained 2D inversion of resistivity data using Broyden's update and 1D derivatives

Dense profile-oriented resistivity data allows for 2D and 3D inversions. However, huge amounts of data make it practically impossible to do full 2D or 3D inversions on a routine basis. Therefore, a number of approximations have been suggested over the years to speed up computations. We suggest using a combination of Broyden's update on the Jacobian matrix with derivatives calculated using a 1D formulation on a parameterized 2D model of locally 1D layered models. The approximations bring down the effective number of 2D forward responses to a minimum, which again gives us the ability to invert very large sections. Broyden's update is not as useful with a parameterized problem as is the case with a smooth minimum structure problem that has been the usual application. 1D derivatives, however, seem to be very effective when initiating a full 2D solution with Broyden's update. We compare the different methods using two different kinds of data on two synthetic models and on two field examples. The most effective and reliable optimization combines 1D derivatives with a full 2D solution and Broyden's update. When using Broyden's update the Jacobian matrix needs to be reset every once in a while. We do this whenever the difference in data residual from the previous iteration is less than 5%. This combined inversion method reduces the computation time approximately a factor of 3 without losing model resolution.     

The Uncertainty of 2D Models Along Wide Angle Seismic Profiles

The estimation of uncertainty for any geophysical model is important for determining how reliable the model is. It is especially important for subjective trial and error modelling techniques like forward ray-tracing modelling of wide-angle seismic data when the final result is very dependent on the interpreter’s knowledge of the area and experience. In this kind of modelling, it is common to encounter over interpretation of the seismic data without checking the uncertainty of the result, especially in the deep parts that are not constrained with other a priori knowledge. In this paper, we propose a method of estimating the uncertainty of the final models based on a one dimensional method of small error propagation generalized for 2D profiles. With a simple approximation, we estimate the uncertainty for published interpretative models of selected profiles from seismic experiments in the Central Europe. We conclude that for typical wide angle seismic profiles we can reliably interpret four layered models of the Earth’s crust based on traveltimes fitting. We also show how the number of layers influence obtained uncertainties. Estimated uncertainties for both the velocity fields and the boundaries between layers are important for future tectonic and geodynamic interpretation of those profiles.     

Sharp boundary inversion of 2D magnetotelluric data

We consider 2D earth models consisting of laterally variable layers. Boundaries between layers are described by their depths at a set of nodes and interpolated laterally between nodes. Conductivity within each layer is described by values at a set of nodes fixed within each layer, and is interpolated laterally within each layer. Within the set of possible models of this sort, we iteratively invert magnetotelluric data for models minimizing the lateral roughness of the layer boundaries, and the lateral roughness of conductivities within layers, for a given level of data misfit. This stabilizes the inverse problem and avoids superfluous detail. This approach allows the determination of boundary positions between geological units with sharp discontinuities in properties across boundaries, while sharing the stability features of recent smooth conductivity distribution inversions.
We compare sharp boundary inversion results with smooth conductivity distribution inversion results on a numerical example, and on inversion of field data from the Columbia River flood basalts of Washington State. In the synthetic example, where true positions and resistivities are known, sharp boundary inversion results determine both layer boundary locations and layer resistivities accurately. In inversion of Columbia flood basalt data, sharp boundary inversion recovers a model with substantially less internal variation within units, and less ambiguity in both the depth to base of the basalts and depth to resistive basement.     

Large‐scale 3D inversion of potential field data

Inversion of gravity and/or magnetic data attempts to recover the density and/or magnetic susceptibility distribution in a 3D earth model for subsequent geological interpretation. This is a challenging problem for a number of reasons. First, airborne gravity and magnetic surveys are characterized by very large data volumes. Second, the 3D modelling of data from large‐scale surveys is a computationally challenging problem. Third, gravity and magnetic data are finite and noisy and their inversion is ill posed so regularization must be introduced for the recovery of the most geologically plausible solutions from an infinite number of mathematically equivalent solutions. These difficulties and how they can be addressed in terms of large‐scale 3D potential field inversion are discussed in this paper. Since potential fields are linear, they lend themselves to full parallelization with near‐linear scaling on modern parallel computers. Moreover, we exploit the fact that an instrument’s sensitivity (or footprint) is considerably smaller than the survey area. As multiple footprints superimpose themselves over the same 3D earth model, the sensitivity matrix for the entire earth model is constructed. We use the re‐weighted regularized conjugate gradient method for minimizing the objective functional and incorporate a wide variety of regularization options. We demonstrate our approach with the 3D inversion of 1743 line km of FALCON gravity gradiometry and magnetic data acquired over the Timmins district in Ontario, Canada. Our results are shown to be in good agreement with independent interpretations of the same data.     

3‐D uncertainty‐based topographic change detection with structure‐from‐motion photogrammetry: precision maps for ground control and directly georeferenced surveys

Structure‐from‐motion (SfM) photogrammetry is revolutionising the collection of detailed topographic data, but insight into geomorphological processes is currently restricted by our limited understanding of SfM survey uncertainties. Here, we present an approach that, for the first time, specifically accounts for the spatially variable precision inherent to photo‐based surveys, and enables confidence‐bounded quantification of 3D topographic change. The method uses novel 3D precision maps that describe the 3D photogrammetric and georeferencing uncertainty, and determines change through an adapted state‐of‐the‐art fully 3D point‐cloud comparison (M3C2), which is particularly valuable for complex topography. We introduce this method by: (1) using simulated UAV surveys, processed in photogrammetric software, to illustrate the spatial variability of precision and the relative influences of photogrammetric (e.g. image network geometry, tie point quality) and georeferencing (e.g. control measurement) considerations; (2) we then present a new Monte Carlo procedure for deriving this information using standard SfM software and integrate it into confidence‐bounded change detection; before (3) demonstrating geomorphological application in which we use benchmark TLS data for validation and then estimate sediment budgets through differencing annual SfM surveys of an eroding badland. We show how 3D precision maps enable more probable erosion patterns to be identified than existing analyses, and how a similar overall survey precision could have been achieved with direct survey georeferencing for camera position data with precision half as good as the GCPs'. Where precision is limited by weak georeferencing (e.g. camera positions with multi‐metre precision, such as from a consumer UAV), then overall survey precision can scale as n^‐½ of the control precision (n = number of images). Our method also provides variance–covariance information for all parameters. Thus, we now open the door for SfM practitioners to use the comprehensive analyses that have underpinned rigorous photogrammetric approaches over the last half‐century. Copyright © 2017 John Wiley & Sons, Ltd.     

Time series analysis of infrared satellite data for detecting thermal anomalies: a hybrid approach

We developed and tested an automated algorithm that analyzes thermal infrared satellite time series data to detect and quantify the excess energy radiated from thermal anomalies such as active volcanoes. Our algorithm enhances the previously developed MODVOLC approach, a simple point operation, by adding a more complex time series component based on the methods of the Robust Satellite Techniques (RST) algorithm. Using test sites at Anatahan and Kīlauea volcanoes, the hybrid time series approach detected ~15% more thermal anomalies than MODVOLC with very few, if any, known false detections. We also tested gas flares in the Cantarell oil field in the Gulf of Mexico as an end-member scenario representing very persistent thermal anomalies. At Cantarell, the hybrid algorithm showed only a slight improvement, but it did identify flares that were undetected by MODVOLC. We estimate that at least 80 MODIS images for each calendar month are required to create good reference images necessary for the time series analysis of the hybrid algorithm. The improved performance of the new algorithm over MODVOLC will result in the detection of low temperature thermal anomalies that will be useful in improving our ability to document Earth’s volcanic eruptions, as well as detecting low temperature thermal precursors to larger eruptions.     

3D sparse-data Kirchhoff redatuming

Wave‐equation redatuming can be a very efficient method of overcoming the overburden imprint on the target area. Owing to the growing amount of 3D data, it is increasingly important to develop a feasible method for the redatuming of 3D prestack data. Common 3D acquisition designs produce relatively sparse data sets, which cannot be redatumed successfully by applying conventional wave‐equation redatuming. We propose a redatuming approach that can be used to perform wave‐equation redatuming of sparse 3D data. In this new approach, additional information about the medium velocity below the new datum is included, i.e. redatumed root‐mean‐square (RMS) velocities, which can be extracted from the input data set by conventional velocity analysis, are used. Inclusion of this additional information has the following implications: (i) it becomes possible to simplify the 4D redatuming integral into a 2D integral such that the number of traces needed to calculate one output time sample and the computational effort are both reduced; (ii) the information about the subsurface enables an infill of traces which are needed for the integral calculation but which are missing in the sparse input data set. Two tests applying this new approach to fully sampled 2D data show satisfactory results, implying that this method can certainly be used for the redatuming of sparse 3D data sets.     

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.     

An inverse method of modeling thermal histories from apatite fission-track data

Apatite fission-track (FT) ages and track length distributions are important sources of information about the thermal histories of rocks. Recent advances in the understanding of track annealing in apatite provide a solution to the forward problem of predicting FT ages and track length distributions that result from a given thermal history. In this paper, a method is presented to address the inverse problem—estimation of the thermal history from FT data. The inverse method uses an iterative approach (the downhill simplex) to systematically modify a starting thermal history to achieve satisfactory statistical agreement between the predicted and observed FT age and track length distribution. However, because of analytical uncertainties, a unique thermal history does not exist. Monte Carlo simulations are used to take into account the uncertainties in the data and yield a spectrum of possible thermal histories. The results are based on the isothermal annealing model of Laslett et al. ([1], Chem. Geol. Isot. Geosci. Sect., Vol. 65) but because the method uses forward predictions and not an analytical formula specific to a single annealing model, alternative annealing models could be used within the same framework. This method is an improvement in interpreting fission-track data because the range of thermal histories permitted by the data can be evaluated.To demonstrate the method, it is applied to several sets of test data created by forward modeling of idealized thermal histories. The results show that the age at which the sample cooled through its closure temperature and the most general features of the thermal history are revealed. However, data from partially annealed samples have wide spectra that reflect large uncertainties in the form of the thermal history. For such samples, FT data alone are not likely to provide strong tests of geologic hypotheses. Conversely, geologic information may play a crucial role in constraining the thermal history spectrum. In application to uplift-related cooling, this inverse method can provide much more realistic assessments of the cooling rate and its uncertainty than are otherwise possible.     

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.