3-D synthetic near surface data set with frequency-domain electromagnetic induction data
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Realistic three-dimensional exhaustive data set that mimics a near surface mining landfill deposit of waste fine-shaly sands. The data set is composed by petrophysical properties and frequency domain electromagnetic induction (FDEM) data and was created with the purpose of testing algorithms for near-surface modeling and characterization using electromagnetic data. The set of petrophysical properties include porosity, water saturation, particle density and density. Each property corresponds to a single geostatistical realization. The three-dimensional model has a dimension of 150 by 200 by 4 meters (i.e., length, width, depth) with a cell size of 0.5 m by 0.5 m by 0.1 m, respectively (grid size of 300 x 400 x 40). The model grid has 4.8 million cells.<br> Porosity and particle density were modelled based on samples of fine-shaly sands collected at a mine tailing in Portugal for which we investigated porosity, specific weight and particle density. The results of these investigations were used to generate three-dimensional models of subsurface rock properties with unconditional stochastic sequential simulation (Deutsch & Journel, 1998).<br> Porosity was modelled with an omnidirectional spherical variogram model in the horizontal direction. The variogram model has a horizontal range of 10 m, a vertical range of 1 m and a nugget effect of 0.2 % of the total variance of the data. This variogram model describes the expected spatial distribution of this property in the mine tailing. To ensure plausibility between rock properties, particle density and water saturation models were generated with stochastic sequential co-simulation (Deutsch & Journel, 1998) conditioned to the porosity model. For particle density we imposed an omnidirectional spherical variogram model in the horizontal direction with a range of 10 m, a vertical range of 1 m and a nugget effect of 0.2 % of the total variance of the data, and the correlation between porosity and particle density from the lab measurements. For water saturation we imposed an omnidirectional spherical variogram model in the horizontal direction with a range of 16 m, a vertical range of 2 m and a nugget effect of 0.1 (%). For the co-simulation we imposed a correlation between porosity and water content, borrowed from Bhanbhro et al. (2013) and Dumont et al. (2016). The pore fluid was defined as consisting in 80% of water and 20% of leachate, having a density of 0.99114 g/cm3 at a temperature of 30ºC (Souza et al., 2014). The density was mathematically calculated from porosity and particle density models and the density of the pore fluid by using a simple volumetric average of the geological material densities and its relationship to porosity (Mavko et al., 2009), <em>d</em><sub><em>b</em> </sub>= (1 - Ø) <em>d<sub>0</sub></em> Ø <em>d<sub>fl</sub></em> , where <em>d<sub>0</sub></em> is the density of the mineral grains, <em>d<sub>fl</sub></em> is the density of the pore fluids, and Ø is porosity. The electrical conductivity (EC) was created based on the well-known empirical relationship of Archie’s law (Archie, 1942). We first calculate electrical conductivity using the following equation, <em>R<sub>t</sub></em> = <em>a</em> <em>S<sub>w</sub><sup>-n</sup></em> Ø<sup><em>-m</em></sup> <em>R<sub>w</sub></em> , where <em>a</em> is the tortuosity constant, assumed as 0.88, <em>S<sub>w</sub></em> is the water saturation, <em>n</em> is the saturation exponent, assumed as 2, Ø is the porosity, <em>m</em> is the cementation exponent, assumed as 1.37, and <em>R<sub>w</sub></em> is the electrical resistivity of the pore fluid, assumed as 0.25. From the lithology and range of porosity values of the mining landfill model, the values of <em>a</em>, <em>n</em> and <em>m</em> were defined from Keller (1987). The electrical resistivity of the pore fluid was defined based on its composition and density (Keller, 1987). The EC was calculated based on Archie´s second law (Archie, 1942), where conductivity of the partially saturated rock (<em>c<sub>t</sub></em>) is the inverse of its resistivity (<em>R<sub>t</sub></em>), <em>c<sub>t</sub></em> = 1 / <em>R<sub>t </sub></em> (Mavko et al., 2009). Since the relationship between magnetic minerals and the magnetic properties of the rocks depends primarily of the composition and grain size of them (Butler, 2005), the magnetic susceptibility (MS) was modelled using the common range of magnetic susceptibility for unconsolidated sediments (Hudson et al., 1999) with unconditional stochastic sequential simulation (Deutsch & Journel, 1998), imposing an omnidirectional spherical variogram model in the horizontal direction with a range of 20 m, a vertical range of 4 m and a nugget effect of 0.1 % of the total variance. From the resulting three-dimensional models of EC and MS, we retrieved nine equally spaced boreholes along the same yz profile. These borehole data might be used as experimental data for modelling workflows, including geophysical inversion. FDEM data, both the in-phase (IP) and quadrature-phase (QP), were calculated using a 1-D forward model (Hanssens et al., 2019). The acquisition configuration replicates one of the most common sensors for FDEM near-surface surveys, namely the DUALEM-421S (DUALEM Inc., Milton, Canada). It considers two loop-loop coil orientations, a horizontal coplanar (HCP) and a perpendicular one (PRP), with the normal 3 offsets per coil orientation for this equipment, 1, 2 and 4 meters for HCP, and 1.1, 2.1 and 4.1 meters for PRP, plus an extra offset per coil orientation, 10 meters for HCP and 10.1 meters for PRP, ensuring a theoretical larger depth of investigation. The FDEM data were calculated defining the operating frequency of the sensor as 9000 Hz, with an elevation to the surface of 0.15 m.
本数据集为逼真的三维全量数据集，用于模拟近地表采矿填埋场的细粒泥质砂废料堆积体。数据集由岩石物理属性数据与频域电磁感应（frequency domain electromagnetic induction, FDEM）数据组成，旨在测试基于电磁数据开展近地表建模与特征刻画的算法。所包含的岩石物理属性包括孔隙度、含水饱和度、颗粒密度与体积密度，每一项属性均对应独立的地质统计实现结果。本三维模型的尺寸为150×200×4米（分别对应长度、宽度、深度），网格单元尺寸依次为0.5m×0.5m×0.1m，总网格数为300×400×40，总计480万个网格单元。<br>孔隙度与颗粒密度的建模基于葡萄牙某矿山尾矿库采集的细粒泥质砂样品，本次研究针对该样品开展了孔隙度、比重与颗粒密度的测试。基于测试结果，采用无条件随机序贯模拟（Deutsch & Journel, 1998）生成了地下岩石属性的三维模型。<br>孔隙度采用水平方向全向球形变差函数模型进行建模，该变差函数模型的水平变程为10米，垂直变程为1米，块金效应为数据总方差的0.2%，用于表征该属性在尾矿库中的预期空间分布特征。为保证各岩石属性间的合理性，颗粒密度与含水饱和度模型采用以孔隙度模型为约束的随机序贯协同模拟（Deutsch & Journel, 1998）生成。针对颗粒密度，本次建模采用水平方向全向球形变差函数模型，其水平变程为10米、垂直变程为1米、块金效应为数据总方差的0.2%，同时约束为实验室测得的孔隙度与颗粒密度间的相关性。针对含水饱和度，本次建模采用水平方向全向球形变差函数模型，其水平变程为16米、垂直变程为2米、块金效应为总方差的0.1%。本次协同模拟采用了源自Bhanbhro等（2013）与Dumont等（2016）的孔隙度与含水含量相关性约束。<br>孔隙流体由80%的水与20%的渗滤液组成，在30℃下的密度为0.99114 g/cm³（Souza等，2014）。体积密度通过孔隙度、颗粒密度模型与孔隙流体密度，基于地质材料密度的简单体积平均法及其与孔隙度的关系进行数学计算（Mavko等，2009），计算公式为：<em>d</em><sub><em>b</em></sub> = (1 - Ø) <em>d</em><sub>0</sub> + Ø <em>d</em><sub>fl</sub>，其中<em>d</em><sub>0</sub>为矿物颗粒密度，<em>d</em><sub>fl</sub>为孔隙流体密度，Ø为孔隙度。<br>电导率（electrical conductivity, EC）基于经典的阿尔奇经验公式（Archie, 1942）生成。首先通过以下公式计算电阻率<em>R</em><sub>t</sub>：<em>R</em><sub>t</sub> = <em>a</em> <em>S</em><sub>w</sub><sup>-<em>n</em></sup> Ø<sup>-<em>m</em></sup> <em>R</em><sub>w</sub>，其中<em>a</em>为迂曲度常数（取值0.88），<em>S</em><sub>w</sub>为含水饱和度，<em>n</em>为饱和度指数（取值2），Ø为孔隙度，<em>m</em>为胶结指数（取值1.37），<em>R</em><sub>w</sub>为孔隙流体电阻率（取值0.25）。基于本采矿填埋场模型的岩性与孔隙度取值范围，<em>a</em>、<em>n</em>与<em>m</em>的取值参考Keller（1987）确定；孔隙流体电阻率则基于其组分与密度确定（Keller, 1987）。电导率则基于阿尔奇第二定律（Archie, 1942）计算：部分饱和岩石的电导率<em>c</em><sub>t</sub>为其电阻率<em>R</em><sub>t</sub>的倒数，即<em>c</em><sub>t</sub> = 1 / <em>R</em><sub>t</sub>（Mavko等，2009）。<br>由于岩石中磁性矿物与岩石磁学性质的关系主要取决于矿物组分与颗粒粒径（Butler, 2005），磁化率（magnetic susceptibility, MS）采用非固结沉积物的常见磁化率取值范围，通过无条件随机序贯模拟（Deutsch & Journel, 1998）建模，约束为水平方向全向球形变差函数模型，其水平变程为20米、垂直变程为4米、块金效应为总方差的0.1%。<br>基于最终生成的电导率与磁化率三维模型，我们沿同一yz剖面提取了9个等间距钻孔数据，此类钻孔数据可作为包括地球物理反演在内的建模工作流程的实验数据。频域电磁感应（FDEM）数据（包括同相分量IP与正交分量QP）通过一维正演模型计算得到（Hanssens等，2019）。采集参数复刻了FDEM近地表勘探中最常用的传感器之一——DUALEM-421S型传感器（加拿大米尔顿市DUALEM公司）。该传感器包含两种线圈配置：水平共面式（HCP）与垂直正交式（PRP），每种配置均采用该设备标准的3种偏移距：HCP配置的偏移距为1、2、4米，PRP配置的偏移距为1.1、2.1、4.1米；同时额外增加1种偏移距，HCP配置为10米，PRP配置为10.1米，以提升理论探测深度。本次FDEM数据计算时，传感器工作频率设为9000Hz，离地高度为0.15米。
