Inversion of nuclear well-logging data using neural networks

This work looks at the application of neural networks in geophysical well‐logging problems and specifically their utilization for inversion of nuclear downhole data. Simulated neutron and γ‐ray fluxes at a given detector location within a neutron logging tool were inverted to obtain formation properties such as porosity, salinity and oil/water saturation. To achieve this, the forward particle‐radiation transport problem was first solved for different energy groups (47 neutron groups and 20 γ‐ray groups) using the multigroup code EVENT. A neural network for each of the neutron and γ‐ray energy groups was trained to re‐produce the detector fluxes using the forward modelling results from 504 scenarios. The networks were subsequently tested on unseen data sets and the unseen input parameters (formation properties) were then predicted using a global search procedure. The results obtained are very encouraging with formation properties being predicted to within 10% average relative error. The examples presented show that neural networks can be applied successfully to nuclear well‐logging problems. This enables the implementation of a fast inversion procedure, yielding quick and reliable values for unknown subsurface properties such as porosity, salinity and oil saturation.     

Inversion of time-dependent nuclear well-logging data using neural networks

The purpose of this work was to investigate a new and fast inversion methodology for the prediction of subsurface formation properties such as porosity, salinity and oil saturation, using time‐dependent nuclear well logging data. Although the ultimate aim is to apply the technique to real‐field data, an initial investigation as described in this paper, was first required; this has been carried out using simulation results from the time‐dependent radiation transport problem within a borehole. Simulated neutron and γ‐ray fluxes at two sodium iodide (NaI) detectors, one near and one far from a pulsed neutron source emitting at ～14 MeV, were used for the investigation. A total of 67 energy groups from the BUGLE96 cross section library together with 567 property combinations were employed for the original flux response generation, achieved by solving numerically the time‐dependent Boltzmann radiation transport equation in its even parity form. Material property combinations (scenarios) and their correspondent teaching outputs (flux response at detectors) are used to train the Artificial Neural Networks (ANNs) and test data is used to assess the accuracy of the ANNs. The trained networks are then used to produce a surrogate model of the expensive, in terms of computational time and resources, forward model with which a simple inversion method is applied to calculate material properties from the time evolution of flux responses at the two detectors. The inversion technique uses a fast surrogate model comprising 8026 artificial neural networks, which consist of an input layer with three input units (neurons) for porosity, salinity and oil saturation; and two hidden layers and one output neuron representing the scalar photon or neutron flux prediction at the detector. This is the first time this technique has been applied to invert pulsed neutron logging tool information and the results produced are very promising. The next step in the procedure is to apply the methodology to real data.     

Exploring seismic inversion methodologies for non‐stationary geological environments: a benchmark study between deterministic and geostatistical seismic inversion

This paper presents a comparison between subsurface impedance models derived from different deterministic and geostatistical seismic inversion methodologies applied to a challenging synthetic dataset. Geostatistical seismic inversion methodologies nowadays are common place in both industry and academia, contrasting with traditional deterministic seismic inversion methodologies that are becoming less used as part of the geo‐modelling workflow. While the first set of techniques allows the simultaneous inference of the best‐fit inverse model along with the spatial uncertainty of the subsurface elastic property of interest, the second family of inverse methodology has proven results in correctly predicting the subsurface elastic properties of interest with comparatively less computational cost. We present herein the results of a benchmark study performed over a realistic three‐dimensional non‐stationary synthetic dataset in order to assess the performance and convergence of different deterministic and geostatistical seismic inverse methodologies. We also compare and discuss the impact of the inversion parameterisation over the exploration of the model parameter space. The results show that the chosen seismic inversion methodology should always be dependent on the type and quantity of the available data, both seismic and well‐log, and the complexity of the geological environment versus the assumptions behind each inversion technique. The assessment of the model parameter space shows that the initial guess of traditional deterministic seismic inversion methodologies is of high importance since it will determine the location of the best‐fit inverse solution.     

Estimation of vertical water fluxes from temperature time series by the inverse numerical computer program FLUX‐BOT

The application of heat as a hydrological tracer has become a standard method for quantifying water fluxes between groundwater and surface water. The typical application is to estimate vertical water fluxes in the shallow subsurface beneath streams or lakes. For this purpose, time series of temperatures in the surface water and in the sediment are measured and evaluated by a vertical 1D representation of heat transport by advection and conduction. Several analytical solutions exist to calculate the vertical water flux from the measured temperatures. Although analytical solutions can be easily implemented, they are restricted to specific boundary conditions such as a sinusoidal upper temperature boundary. Numerical solutions offer higher flexibility in the selection of the boundary conditions. This, in turn, reduces the effort of data preprocessing, such as the extraction of the diurnal temperature variation from the raw data. Here, we present software to estimate water fluxes based on temperatures—FLUX‐BOT. FLUX‐BOT is a numerical code written in MATLAB that calculates vertical water fluxes in saturated sediments based on the inversion of measured temperature time series observed at multiple depths. FLUX‐BOT applies a centred Crank–Nicolson implicit finite difference scheme to solve the one‐dimensional heat advection–conduction equation. FLUX‐BOT includes functions for the inverse numerical routines, functions for visualizing the results, and a function for performing uncertainty analysis. We present applications of FLUX‐BOT to synthetic and to real temperature data to demonstrate its performance.     

Velocity model building from seismic reflection data by full‐waveform inversion

Full‐waveform inversion is re‐emerging as a powerful data‐fitting procedure for quantitative seismic imaging of the subsurface from wide‐azimuth seismic data. This method is suitable to build high‐resolution velocity models provided that the targeted area is sampled by both diving waves and reflected waves. However, the conventional formulation of full‐waveform inversion prevents the reconstruction of the small wavenumber components of the velocity model when the subsurface is sampled by reflected waves only. This typically occurs as the depth becomes significant with respect to the length of the receiver array. This study first aims to highlight the limits of the conventional form of full‐waveform inversion when applied to seismic reflection data, through a simple canonical example of seismic imaging and to propose a new inversion workflow that overcomes these limitations. The governing idea is to decompose the subsurface model as a background part, which we seek to update and a singular part that corresponds to some prior knowledge of the reflectivity. Forcing this scale uncoupling in the full‐waveform inversion formalism brings out the transmitted wavepaths that connect the sources and receivers to the reflectors in the sensitivity kernel of the full‐waveform inversion, which is otherwise dominated by the migration impulse responses formed by the correlation of the downgoing direct wavefields coming from the shot and receiver positions. This transmission regime makes full‐waveform inversion amenable to the update of the long‐to‐intermediate wavelengths of the background model from the wide scattering‐angle information. However, we show that this prior knowledge of the reflectivity does not prevent the use of a suitable misfit measurement based on cross‐correlation, to avoid cycle‐skipping issues as well as a suitable inversion domain as the pseudo‐depth domain that allows us to preserve the invariant property of the zero‐offset time. This latter feature is useful to avoid updating the reflectivity information at each non‐linear iteration of the full‐waveform inversion, hence considerably reducing the computational cost of the entire workflow. Prior information of the reflectivity in the full‐waveform inversion formalism, a robust misfit function that prevents cycle‐skipping issues and a suitable inversion domain that preserves the seismic invariant are the three key ingredients that should ensure well‐posedness and computational efficiency of full‐waveform inversion algorithms for seismic reflection data.     

Directional‐oriented wavefield imaging: a new wave‐based subsurface illumination imaging condition for reverse time migration

The key objective of an imaging algorithm is to produce accurate and high‐resolution images of the subsurface geology. However, significant wavefield distortions occur due to wave propagation through complex structures and irregular acquisition geometries causing uneven wavefield illumination at the target. Therefore, conventional imaging conditions are unable to correctly compensate for variable illumination effects. We propose a generalised wave‐based imaging condition, which incorporates a weighting function based on energy illumination at each subsurface reflection and azimuth angles. Our proposed imaging kernel, named as the directional‐oriented wavefield imaging, compensates for illumination effects produced by possible surface obstructions during acquisition, sparse geometries employed in the field, and complex velocity models. An integral part of the directional‐oriented wavefield imaging condition is a methodology for applying down‐going/up‐going wavefield decomposition to both source and receiver extrapolated wavefields. This type of wavefield decomposition eliminates low‐frequency artefacts and scattering noise caused by the two‐way wave equation and can facilitate the robust estimation for energy fluxes of wavefields required for the seismic illumination analysis. Then, based on the estimation of the respective wavefield propagation vectors and associated directions, we evaluate the illumination energy for each subsurface location as a function of image depth point and subsurface azimuth and reflection angles. Thus, the final directional‐oriented wavefield imaging kernel is a cross‐correlation of the decomposed source and receiver wavefields weighted by the illuminated energy estimated at each depth location. The application of the directional‐oriented wavefield imaging condition can be employed during the generation of both depth‐stacked images and azimuth–reflection angle‐domain common image gathers. Numerical examples using synthetic and real data demonstrate that the new imaging condition can properly image complex wave paths and produce high‐fidelity depth sections.     

脉冲中子双伽马谱饱和度测井方法及数值模拟研究

脉冲中子双伽马谱饱和度测井方法是利用特定的脉冲和测量时序设计,采用远、近伽马探测器记录非弹性散射和俘获伽马能谱以及伽马射线时间谱,通过获取C/O和地层宏观俘获截面等信息来确定地层含油饱和度.采用大直径仪器和BGO晶体探测器时,其采集的非弹性散射和俘获伽马能谱计数统计性优于国外仪器,重复脉冲发射中子后伽马射线时间谱仍满足指数衰减规律,且能使伽马射线时间谱的道计数累积,计数统计性好于常规中子寿命测井,得到的地层宏观俘获截面与单脉冲发射近似相同.在地层孔隙度未知的情况下,利用C/O和地层宏观俘获截面交会技术可以定量确定含油饱和度.     

Passive seismic data primary estimation and noise removal via focal‐denoising closed‐loop surface‐related multiple elimination based on 3D L1‐norm sparse inversion

Passive seismic has recently attracted a great deal of attention because non‐artificial source is used in subsurface imaging. The utilization of passive source is low cost compared with artificial‐source exploration. In general, constructing virtual shot gathers by using cross‐correlation is a preliminary step in passive seismic data processing, which provides the basis for applying conventional seismic processing methods. However, the subsurface structure is not uniformly illuminated by passive sources, which leads to that the ray path of passive seismic does not fit the hyperbolic hypothesis. Thereby, travel time is incorrect in the virtual shot gathers. Besides, the cross‐correlation results are contaminated by incoherent noise since the passive sources are always natural. Such noise is kinematically similar to seismic events and challenging to be attenuated, which will inevitably reduce the accuracy in the subsequent process. Although primary estimation for transient‐source seismic data has already been proposed, it is not feasible to noise‐source seismic data due to the incoherent noise. To overcome the above problems, we proposed to combine focal transform and local similarity into a highly integrated operator and then added it into the closed‐loop surface‐related multiple elimination based on the 3D L1‐norm sparse inversion framework. Results proved that the method was capable of reliably estimating noise‐free primaries and correcting travel time at far offsets for a foresaid virtual shot gathers in a simultaneous closed‐loop inversion manner.     

Combining 3D Hydraulic Tomography with Tracer Tests for Improved Transport Characterization

Hydraulic tomography (HT) is a method for resolving the spatial distribution of hydraulic parameters to some extent, but many details important for solute transport usually remain unresolved. We present a methodology to improve solute transport predictions by combining data from HT with the breakthrough curve (BTC) of a single forced‐gradient tracer test. We estimated the three dimensional (3D) hydraulic‐conductivity field in an alluvial aquifer by inverting tomographic pumping tests performed at the Hydrogeological Research Site Lauswiesen close to Tübingen, Germany, using a regularized pilot‐point method. We compared the estimated parameter field to available profiles of hydraulic‐conductivity variations from direct‐push injection logging (DPIL), and validated the hydraulic‐conductivity field with hydraulic‐head measurements of tests not used in the inversion. After validation, spatially uniform parameters for dual‐domain transport were estimated by fitting tracer data collected during a forced‐gradient tracer test. The dual‐domain assumption was used to parameterize effects of the unresolved heterogeneity of the aquifer and deemed necessary to fit the shape of the BTC using reasonable parameter values. The estimated hydraulic‐conductivity field and transport parameters were subsequently used to successfully predict a second independent tracer test. Our work provides an efficient and practical approach to predict solute transport in heterogeneous aquifers without performing elaborate field tracer tests with a tomographic layout.     

Advances in interpretation of subsurface processes with time‐lapse electrical imaging

Electrical geophysical methods, including electrical resistivity, time‐domain induced polarization, and complex resistivity, have become commonly used to image the near subsurface. Here, we outline their utility for time‐lapse imaging of hydrological, geochemical, and biogeochemical processes, focusing on new instrumentation, processing, and analysis techniques specific to monitoring. We review data collection procedures, parameters measured, and petrophysical relationships and then outline the state of the science with respect to inversion methodologies, including coupled inversion. We conclude by highlighting recent research focused on innovative applications of time‐lapse imaging in hydrology, biology, ecology, and geochemistry, among other areas of interest. Copyright © 2014 John Wiley & Sons, Ltd.     

Neutron capture logging calibration and data analysis for environmental contaminant assessment

This paper describes a method to calibrate a neutron capture sonde equipped with a high resolution γ-ray detector, and analyze log data. The method utilizes the 1460.8-keV passive γ-ray of ⁴⁰K, the 770.3-keV capture γ-ray of ³⁹K, and a capture γ-ray from a target element. An equation containing the spectral line intensities for the two capture γ-rays, nuclear capture data, and the detector efficiency function expresses the concentration of the target element as a multiple of the ³⁹K concentration. The concentration of ³⁹K is easily deduced from the ⁴⁰K concentration, which is calculated directly from the line intensity for the 1460.8-keV γ-ray in a passive γ-ray spectrum.The calibration automatically adjusts to changes in the neutron transport properties of the logged medium that may result, for example, from variations in the H density and the concentrations of neutron poisons. Fluctuations in the neutron source output are similarly accommodated. The calibration utilizes U.S. Department of Energy (DOE) passive γ-ray calibration standards that contain well established concentrations of K, U, and Th. The passive γ-rays from K, U, and Th (and the U and Th decay progenies) provide data for the detector efficiency function determination.Data for proof-of-principle demonstrations of the method were acquired by logging boreholes penetrating the shallow subsurface at a DOE waste site with a simple, reliable neutron capture logging system. The system had a ²⁵²Cf source and a high purity germanium (HPGe) detector. Time gating could not be used to sort signals originating from capture and activation, but the excellent energy resolution permitted capture γ-ray identifications based solely on the γ-ray energies. Cl, H, and other elements were detected and assessed.A conventional calibration and data analysis method was also employed. The method was specific to Cl and was based on measurements in two Cl-impregnated concrete blocks. Cl concentrations inferred with this method were often consistent with the concentrations determined with the new method. When the two methods produced different Cl concentrations, the discrepancies could be explained by variations in formation parameters.     

球坐标系下多震相走时三参数同时反演成像

球坐标系下多震相走时三参数(速度、震源位置和反射界面)同时反演需要解决两个关键问题:(1)球坐标系下3D速度模型中多次透射、反射(折射)及转换波精确、快速的射线追踪;(2)同时反演时三种不同参数间的强耦合问题.为此,我们将直角坐标系下分区多步不规则最短路径算法推广至球坐标系中,进行区域或者全球尺度的多震相射线追踪.然后将其与适合多参数同时反演的子空间算法相结合,形成一种球坐标系下联合多震相走时三参数同时反演的方法技术.与双参数(速度和反射界面或速度和震源位置)同时反演的数值模拟对比分析显示:三参数与双参数的同时反演结果大体接近,并且它们对到时数据中可容许的随机噪声不太敏感.结果说明本文中的同时反演成像为一种提高成像分辨率,同时反演速度、震源位置和反射界面的有效方法.     

A quasi three-dimensional model for flow and transport in unsaturated and saturated zones: 1. Implementation of the quasi two-dimensional case

A quasi three-dimensional (QUASI 3-D) model is presented for simulating the subsurface water flow and solute transport in the unsaturated and in the saturated zones of soil. The model is based on the assumptions of vertical flow in the unsaturated zone and essentially horizontal groundwater flow. The 1-D Richards equation for the unsaturated zone is coupled at the phreatic surface with the 2-D flow equation for the saturated zone. The latter was obtained by averaging 3-D flow equation in the saturated zone over the aquifer thickness. Unlike the Boussinesq equation for a leaky-phreatic aquifer, the developed model does not contain a storage term with specific yield and a source term for natural replenishment. Instead it includes a water flux term at the phreatic surface through which the Richards equation is linked with the groundwater flow equation. The vertical water flux in the saturated zone is evaluated on the basis of the fluid mass balance equation while the horizontal fluxes, in that equation, are prescribed by Darcy law. A 3-D transport equation is used to simulate the solute migration. A numerical algorithm to solve the problem for the general quasi 3-D case was developed. The developed methodology was exemplified for the quasi 2-D cross-sectional case (QUASI2D). Simulations for three synthetic problems demonstrate good agreement between the results obtained by QUASI2D and two fully 2-D flow and transport codes (SUTRA and 2DSOIL). Yet, simulations with the QUASI2D code were several times faster than those by the SUTRA and the 2DSOIL codes.     

Biofilm Detection in a Model Well‐Bore Environment Using Low‐Field NMR

This research addresses the challenges of the lack of non‐invasive methods and poor spatiotemporal resolution associated with monitoring biogeochemical activity central to bioremediation of subsurface contaminants. Remediation efforts often include growth of biofilm to contain or degrade chemical contaminants, such as nitrates, hydrocarbons, heavy metals, and some chlorinated solvents. Previous research indicates that nuclear magnetic resonance (NMR) is sensitive to the biogeochemical processes of biofilm accumulation. The current research focuses on developing methods to use low‐cost NMR technology to support in situ monitoring of biofilm growth and geochemical remediation processes in the subsurface. Biofilm was grown in a lab‐scale radial flow bioreactor designed to model the near wellbore subsurface environment. The Vista Clara Javelin NMR logging device, a slim down‐the‐borehole probe, collected NMR measurements over the course of eight days while biofilm was cultivated in the sand‐packed reactor. Measured NMR mean log T₂ relaxation times decreased from approximately 710 to 389 ms, indicating that the pore environment and bulk fluid properties were changing due to biofilm growth. Destructive sampling employing drop plate microbial population analysis and scanning electron and stereoscopic microscopy confirmed biofilm formation. Our findings demonstrate that the NMR logging tool can detect small to moderate changes in T₂ distribution associated with environmentally relevant quantities of biofilm in quartz sand.     

Geostatistical seismic inversion for non‐stationary patterns using direct sequential simulation and co‐simulation

Geostatistical seismic inversion methods are routinely used in reservoir characterisation studies because of their potential to infer the spatial distribution of the petro‐elastic properties of interest (e.g., density, elastic, and acoustic impedance) along with the associated spatial uncertainty. Within the geostatistical seismic inversion framework, the retrieved inverse elastic models are conditioned by a global probability distribution function and a global spatial continuity model as estimated from the available well‐log data for the entire inversion grid. However, the spatial distribution of the real subsurface elastic properties is complex, heterogeneous, and, in many cases, non‐stationary since they directly depend on the subsurface geology, i.e., the spatial distribution of the facies of interest. In these complex geological settings, the application of a single distribution function and a spatial continuity model is not enough to properly model the natural variability of the elastic properties of interest. In this study, we propose a three‐dimensional geostatistical inversion technique that is able to incorporate the reservoir's heterogeneities. This method uses a traditional geostatistical seismic inversion conditioned by local multi‐distribution functions and spatial continuity models under non‐stationary conditions. The procedure of the proposed methodology is based on a zonation criterion along the vertical direction of the reservoir grid. Each zone can be defined by conventional seismic interpretation, with the identification of the main seismic units and significant variations of seismic amplitudes. The proposed method was applied to a highly non‐stationary synthetic seismic dataset with different levels of noise. The results of this work clearly show the advantages of the proposed method against conventional geostatistical seismic inversion procedures. It is important to highlight the impact of this technique in terms of higher convergence between real and inverted reflection seismic data and the more realistic approximation towards the real subsurface geology comparing with traditional techniques.     

A robust approach to time‐to‐depth conversion and interval velocity estimation from time migration in the presence of lateral velocity variations

The problem of conversion from time‐migration velocity to an interval velocity in depth in the presence of lateral velocity variations can be reduced to solving a system of partial differential equations. In this paper, we formulate the problem as a non‐linear least‐squares optimization for seismic interval velocity and seek its solution iteratively. The input for the inversion is the Dix velocity, which also serves as an initial guess. The inversion gradually updates the interval velocity in order to account for lateral velocity variations that are neglected in the Dix inversion. The algorithm has a moderate cost thanks to regularization that speeds up convergence while ensuring a smooth output. The proposed method should be numerically robust compared to the previous approaches, which amount to extrapolation in depth monotonically. For a successful time‐to‐depth conversion, image‐ray caustics should be either nonexistent or excluded from the computational domain. The resulting velocity can be used in subsequent depth‐imaging model building. Both synthetic and field data examples demonstrate the applicability of the proposed approach.     

3-D simultaneous inversion for velocity and reflector geometry using multiple classes of arrivals in a spherical coordinate frame

The two key requirements in conducting 3-D simultaneous traveltime tomography on real data at the regional and global scale with multiple classes of arrival time information are (1) it needs an efficient and accurate arrival tracking algorithm for multiply transmitted, reflected (or refracted) and converted waves in a 3-D variable velocity model with embedded velocity discontinuities (or subsurface interfaces), and (2) a subdimensional inversion solver is required which can easily search for different types of model parameters to balance the trade-off between the different types of model parameter updated in the simultaneous inversion process. For these purposes, we first extend a popular grid/cell-based wavefront expanding ray tracing algorithm (the multistage irregular shortest-path ray tracing method), which previously worked only in Cartesian coordinate at the local scale, to spherical coordinates appropriate to the regional or global scale. We then incorporated a fashionable inversion solver (the subspace method) to formulate a simultaneous inversion algorithm, in which the multiple classes of arrivals (including direct and reflected arrivals from different velocity discontinuities) can be used to simultaneously update both the velocity fields and the reflector geometries. Numerical tests indicate that the new inversion method is both applicable and flexible in terms of computational efficiency and solution accuracy, and is not sensitive to a modest level of noise in the traveltime data. It offers several potential benefits over existing schemes for real data seismic imaging.     

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.