Topographical effect of high embankments on resistivity investigation of the underlying permafrost table
高路堤地形对下伏多年冻土表电阻率调查的影响

Yanhui You¹, Xicai Pan², Wei Fu³, Yun Wang³, Qihao Yu¹, Lei Guo¹, Xinbin Wang^1*

State Key Laboratory of Frozen Soils Engineering, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou,730000, China
中国科学院西北生态环境资源研究院冻土工程国家重点实验室，兰州，730000，中国

State Key Laboratory of Soil and Sustainable Agriculture, Institute of Soil Science, Chinese Academy of Sciences, Nanjing, 210008, China
中国科学院南京土壤研究所，土壤与农业可持续发展国家重点实验室，南京，210008，中国

Second Highway Consultants Co.,Ltd., China Communications Construction Corporation, Wuhan 430056, China
第二公路勘察设计院有限公司，中国交通建设股份有限公司，武汉 430056，中国

* Correspondence to: Xinbin Wang
* 通讯作者：Xinbin Wang

E-mail: wangxinbin@lzb.ac.cn

Abstract

Resistivity investigation has been effectively used in assessing the risks of embankment deformation and failure. A 2-dimensional (2D) approximation of the surveyed object is commonly assumed for a survey line on the road surface. However, it might not meet the approximation when the resistivity investigation is conducted over a raised high embankment, in this condition regular inversions might yield erroneous results. This study explored the topographical effect of a high embankment on the resistivity measurements by forward and inverse modeling of a 3D high embankment model. The results show that a 2D approximation of the survey lines on the road surface significantly increases the apparent resistivity within the depth of the raised embankment. The maximum relative errors reached 21% and 11% for the road shoulder and midline survey lines, respectively. The biased apparent resistivity resulted in an inverted resistivity higher than the true values, although resistivity contrasts can still identify the interfaces between layers. A geometric factor corrected the biased apparent resistivity to eliminate the high embankment topographical effect. Inversion results of the corrected apparent resistivity agreed well with the forwarding model. The method was then verified by field application. The apparent resistivity of the field data collected on a high embankment in permafrost regions on the Qinghai-Tibet Plateau was corrected before inversion. The permafrost table derived from the inverted resistivity was verified by borehole temperature. These findings indicate that the topographical influence of high embankments on the resistivity measurement should be considered. A correction of the apparent resistivity is indispensable for a quantitative interpretation of the inverted resistivity.
电阻率调查已有效用于评估堤坝变形和破坏的风险。对于路面上的测量线，通常假设被调查对象为二维（2D）近似。然而，当在高堤坝上进行电阻率调查时，这种近似可能不再适用，常规反演可能会产生错误结果。本研究通过三维高堤坝模型的正演和反演建模，探讨了高堤坝地形对电阻率测量的影响。结果表明，路面测量线的二维近似显著增加了高堤坝深度范围内的视电阻率。路肩和中线测量线的最大相对误差分别达到 21%和 11%。偏差的视电阻率导致反演电阻率高于真实值，尽管电阻率对比仍能识别层间界面。通过几何因子校正偏差的视电阻率，消除了高堤坝地形效应。 校正后的视电阻率反演结果与正演模型吻合良好。该方法随后通过现场应用得到验证。在青藏高原多年冻土区高路堤上采集的现场数据，其视电阻率在反演前进行了校正。通过钻孔温度验证了反演电阻率得出的多年冻土上限。这些发现表明，高路堤地形对电阻率测量的影响应予以考虑。对视电阻率的校正是反演电阻率定量解释不可或缺的步骤。

Keywords: permafrost table; ground deformation; ground resistivity tomography; topographical effect; road embankment; Qinghai-Tibet Plateau
关键词：多年冻土表；地面变形；地面电阻率层析成像；地形效应；路基；青藏高原

1. Introduction
1. 引言

Since soil electrical resistivity is closely related to soil texture, moisture, and freeze-thaw conditions, the resistivity tomography method has been successfully used to explore the movements of seasonal wetting and drying fronts ^1,2, the presence and spatial extent of soft clay ³, and the stratigraphy and permafrost conditions ⁴ in railway and highway embankments. Uncertainty of this method frequently resulted from data acquisition scheme and inversion method, which may impact the interpretation of inverted resistivity. Unreasonable 2-dimensional (2D) approximation over a complex topography is a common source of error. Understanding the influence of a high embankment on the resistivity investigation provides a basis for the successful application of the resistivity investigation method for evaluating the risk and causes of embankment failure ⁵
由于土壤电阻率与土壤质地、湿度和冻融条件密切相关，电阻率层析成像法已成功用于探索季节性湿润和干燥锋面的移动 ^1,2 、软粘土的存在及空间分布 ³ ，以及铁路和公路路堤中的地层和永久冻土条件 ⁴ 。该方法的不确定性常源于数据采集方案和反演方法，这些因素可能影响反演电阻率的解释。在复杂地形上不合理的二维（2D）近似是常见的误差来源。了解高路堤对电阻率调查的影响，为成功应用电阻率调查方法评估路堤破坏的风险和原因提供了基础 ⁵ 。.

High embankments are frequently designed in low-lying and waterlogging areas and are also common in permafrost regions, e.g., the Qinghai-Tibet Plateau (QTP). Permafrost is a ground that remains at or below 0℃ for at least two consecutive years ⁶. In these conditions, massive ground ice grows due to the repeated segregation of ground ice under seasonal freeze-thaw cycles ⁷. The disturbances by engineering constructions and climate warming tend to thaw the massive ground ice, causing damage to highways and railways ^8,9. High embankments are common countermeasures that retard permafrost degradation under the subgrade ⁹
高路堤常设计于低洼和易涝地区，在多年冻土区域如青藏高原（QTP）也颇为常见。多年冻土是指至少连续两年保持在 0℃或以下的地面 ⁶ 。在此条件下，由于季节性冻融循环中地下冰的反复分凝作用，大量地下冰得以形成 ⁷ 。工程建设和气候变暖的干扰往往导致这些大规模地下冰融化，进而对公路和铁路造成损害 ^8,9 。高路堤作为减缓路基下多年冻土退化的常见对策被广泛应用 ⁹ 。.

The 2-dimensional (2D) approximation is reasonable for a resistivity survey line along the cross-section of a high embankment. Yet this data acquisition mode is inefficient for large-scale investigation. If a conventional galvanic coupling instrument is used, the traffic must be stopped, apart from the time-consuming setting up of steel electrodes and cables. The recently developed capacitively coupled resistivity (CCR) instrument allows for a more rapid data acquisition than the conventional galvanic coupling instrument ^10,11. The cables (line antennas) of the CCR and the earth form a capacitor that AC current can pass through. An AC current generated at a transmitter will be injected into the ground, and the ground current will generate an AC voltage at the receiver; in this way, the apparent resistivity of the ground can be measured ¹⁰. The collected apparent resistivities are equivalent to those obtained using the conventional galvanic coupling instrument, and the interpretation schemes of the galvanic coupling method are applicable ¹². The line antenna of this equipment should be kept close to the ground surface to ensure data accuracy ¹³. At the same time, a gap is inevitable because of the topographic relief across a high embankment.
二维（2D）近似对于沿高路堤横截面的电阻率调查线是合理的。然而，这种数据采集模式在大规模调查中效率低下。如果使用传统的电耦合仪器，除了耗时的钢电极和电缆设置外，还必须停止交通。最近开发的电容耦合电阻率（CCR）仪器比传统的电耦合仪器允许更快的数据采集 ^10,11 。CCR 的电缆（线天线）与大地形成一个电容器，交流电流可以通过。发射器产生的交流电流将被注入地面，地面电流将在接收器处产生交流电压；通过这种方式可以测量地面的视电阻率 ¹⁰ 。收集到的视电阻率与使用传统电耦合仪器获得的视电阻率相当，并且电耦合方法的解释方案也适用 ¹² 。 该设备的线天线应靠近地面以确保数据准确性 ¹³ 。同时，由于高路堤的地形起伏，间隙是不可避免的。

A survey line parallel to the strike of the embankment may not need to disrupt traffic and is suitable for large-scale investigation. However, this line arrangement on a high embankment may violate the 2D assumption that can significantly distort the measured apparent resistivity of complex terrains. The numerical simulations indicate that the apparent resistivity is 3 to 4 times higher or lower than the actual value if the terrain is ignored ¹⁴. Similarly, the 2D assumption for the resistivity measurement along the crest of dam embankments leads to 3 to 7 times the apparent resistivity deviation ¹⁵. The inversion of apparent resistivity ignoring the topography of a mound is unstable and results in unrealistic resistivity values. The inversion process may become stable if a numerical simulated geometric factor, including the true topography, is used to cope with the topography effect. However, local artifacts may be induced because the topography is not involved in the parametrization ¹⁴
与堤坝走向平行的测线可能无需中断交通，适合大规模调查。然而，在高堤坝上采用这种测线布置可能违反二维假设，这会显著扭曲复杂地形下的视电阻率测量结果。数值模拟表明，若忽略地形，视电阻率可能比实际值高出或低出 3 至 4 倍 ¹⁴ 。同样，沿坝顶进行电阻率测量时的二维假设会导致视电阻率偏差达到 3 至 7 倍 ¹⁵ 。忽略地形起伏的视电阻率反演不稳定，会导致不切实际的电阻率值。如果使用包含真实地形的数值模拟几何因子来应对地形效应，反演过程可能会变得稳定。然而，由于地形未纳入参数化，可能会引发局部伪影 ¹⁴ 。.

To obtain a stable and reliable inversion resistivity model, 3D data collection and inversion are indispensable for electrical resistivity investigations on a complex terrain ^2,15. However, 3D data acquisition on a high embankment is frequently unavailable because it is time-consuming and not suitable for a large-scale survey.
为了获得稳定可靠的反演电阻率模型，在复杂地形上进行电阻率调查时，三维数据采集和反演是不可或缺的 ^2,15 然而，在高堤上进行三维数据采集往往不可行，因为它耗时且不适合大规模调查。

For the resistivity investigation along the strike direction of a road, the topographical effect of a high embankment has seldom been addressed. Since the topography of an embankment is simpler than that of a mound, the terrain along the survey line is basically flat and symmetric to the midline of the road. In this case, a 2D assumption of the inversion model may reduce the parametrization error, and the correction of the topographical effect using the simulated geometrical factor seems promising. Hence, the aims of this study were: to 1) explore the topographical effect of a high embankment on the resistivity measurements; 2) to assess the effects of the topography correction on the inverted model; and 3) to verify the topography correction method to a field resistivity measurement on a high embankment in permafrost regions on the QTP
针对沿道路走向的电阻率调查，高路堤的地形效应鲜有涉及。由于路堤地形较之土丘更为简单，沿线地形基本平坦且对道路中线对称。在此情况下，反演模型的二维假设可能减少参数化误差，而利用模拟几何因子进行地形效应校正显得颇具前景。因此，本研究旨在：1) 探究高路堤对电阻率测量的地形效应；2) 评估地形校正对反演模型的影响；3) 在青藏高原多年冻土区的高路堤上，验证地形校正方法于现场电阻率测量的适用性。.

2. Methods
2. 方法

An open-source library for modeling and inversion of various geophysical methods (pyGIMLi) was used to explore the influence of the topographical effects of the high embankment on the resistivity investigation ¹⁶. The library enables the creation of flexible 3D geometries and mesh, which can be generated by Python Scripting, FreeCAD, and Gmsh. The forward modeling and inversion algorithms are described by Rücker et al. (2006) and Günther et al. (2006) ^14,17
使用了一个开源库（pyGIMLi）来建模和反演多种地球物理方法，以探索高路堤地形效应对电阻率调查的影响 ¹⁶ 。该库能够创建灵活的三维几何体和网格，这些可以通过 Python 脚本、FreeCAD 和 Gmsh 生成。正演建模和反演算法由 Rücker 等人（2006 年）和 Günther 等人（2006 年）描述 ^14,17 。.

A 3D resistivity model was built to represent the high embankments built over the permafrost layer on the QTP (Figure 1a). In this model, the lower resistivity represented the unfrozen embankment fills and the active layer soil, and the high resistivity indicated the underneath permafrost layer. Since the commonly used coarse-grained fillings have a lower water content, we gave the high embankment fill a relatively higher resistivity than the active layer. The resistivity of the roadbed fill, active layer, and lower permafrost were assigned as 500, 300, and 1000 Ωm, respectively, according to the reported values in a field study on the QTP ¹⁸. The active layer thickness was set to 3 m for the natural field and 6 m below the crest of the embankment, which is generally consistent with the measured value on the QTP ^19,20. The depth of the permafrost table under the embankment is frequently deeper below the sunny slope. The asymmetrical depth of the permafrost table can also influence the calculated apparent resistivity. In order to exclude this impact, the asymmetrical depth of the permafrost table was ignored in the forward model to explore the topographic effect of the raised embankment only. The height of the embankment was 3 m, and the width of the road was 13 m, representing the common embankment configurations on the QTP ²¹. The depth of the permafrost table below the embankment is closely related to the embankment's settlement and attracts extensive attention ²². The investigation target in the forward model is the depth of the permafrost table, which is usually obtained by drilling and ground temperature monitoring
构建了一个三维电阻率模型来代表青藏高原（QTP）上多年冻土层上建造的高路堤（图 1a）。在该模型中，较低的电阻率代表未冻结的路堤填料和活动层土壤，而较高的电阻率则指示下方的多年冻土层。由于常用的粗粒填料含水量较低，我们赋予高路堤填料比活动层相对较高的电阻率。根据青藏高原现场研究报告的数值，路基填料、活动层及下层多年冻土的电阻率分别设定为 500、300 和 1000 Ωm ¹⁸ 。自然场地下的活动层厚度设为 3 米，路堤顶部下方则为 6 米，这与青藏高原上的实测值基本一致 ^19,20 。路堤下多年冻土层的深度在阳坡一侧通常更深。多年冻土层深度的不对称性也会影响计算得到的视电阻率。 为了排除这一影响，在正演模型中忽略了冻土表的不对称深度，仅探讨了高路基的地形效应。路基高度为 3 米，道路宽度为 13 米，代表了青藏高原上常见的路基配置 ²¹ 。路基下方冻土表的深度与路基沉降密切相关，并引起了广泛关注 ²² 。前向模型中的调查目标是多年冻土表的深度，通常通过钻探和地温监测获得.

The length of the embankment was 100 m. The data collection was designed to cover 50 m along the strike direction of the road. Two survey lines were arranged to assess the differences in topographical effects in the light of their different distances away from the slope break. One was on the road shoulder 0.5 m from the slope break, and the other was along the pavement’s centerline (the red and yellow lines in Figure 1a)
堤坝长度为 100 米。数据收集设计为沿道路走向方向覆盖 50 米。布置了两条测线，以评估因距坡折点距离不同而导致的地形效应差异。一条位于距坡折点 0.5 米的路肩上，另一条沿路面中心线布置（图 1a 中的红线和黄线）。.

Figure 1 Synthetic resistivity model (a) and mesh used for the forward modeling (b). The red and yellow lines in (a) represent the survey lines on the road shoulder and centerline. The 3-D mesh in (b) is refined around the electrodes.
图 1 合成电阻率模型(a)及用于正演模拟的网格(b)。(a)中的红色和黄色线条分别代表路肩和中心线上的测线。(b)中的三维网格在电极周围进行了细化。

The dipole-dipole array was used to simulate the apparent resistivity along the two survey lines on the road surface, as it is the commonly used configuration for a CCR instrument ¹⁰ and has better imaging resolution ²³. The numerical simulations also explored the influence of electrode separation, as the electrode spacing is closely related to the distribution and interface of inverted resistivity ²⁴. A profile length of 50 m was generated with two relatively small electrode separations (0.5 and 1.0 m). We found that a large electrode spacing results in poor accuracy for the inverted resistivity and interfaces ²⁴, therefore, dense electrode layouts were set to avoid the influence of electrode spacing and focus on the topographical effect of a high embankment.
偶极-偶极阵列用于模拟路面上两条测线的视电阻率，因为这是 CCR 仪器 ¹⁰ 常用的配置，并具有更好的成像分辨率 ²³ 。数值模拟还探讨了电极间距的影响，因为电极间距与反演电阻率的分布和界面密切相关 ²⁴ 。生成了 50 米的剖面长度，采用两个相对较小的电极间距（0.5 米和 1.0 米）。我们发现，较大的电极间距会导致反演电阻率和界面的精度较差 ²⁴ ；因此，设置了密集的电极布局，以避免电极间距的影响，并专注于高路堤的地形效应。

The model domain was meshed with tetrahedral elements. The model domain was meshed with tetrahedral elements. The maximum cell size was less than 5 m3 to improve the numerical accuracy, and the mesh was refined around the electrodes (Figure 1b). A Neumann-type boundary condition was assigned to the surface boundary of the model domain, and mixed boundary conditions were assigned to the surrounding and bottom boundaries ¹⁷
模型域被划分为四面体单元网格。为了提高数值精度，最大单元尺寸小于 5 立方米，并在电极周围进行了网格细化（图 1b）。模型域的表面边界被赋予了 Neumann 型边界条件，而周围和底部边界则被赋予了混合边界条件 ¹⁷ 。.

The topographical effect of the high embankments was assessed using the method described by Rücker et al. (2006) ¹⁷. The apparent resistivity () was calculated through the geomertic factor (k), injected current () and measured potential () related in the formula:
高路堤的地形效应采用 Rücker 等人（2006）描述的方法进行了评估 ¹⁷ 。视电阻率（ ）通过几何因子（k）、注入电流（ ）和测量电位（ ）在公式中相关计算得出：

The apparent resistivity was first calculated using a half-space approximation, ignoring the influence of the high embankment. In this case, the geometry factor () of a dipole-dipole array is expressed by the analytic formula:
首先使用半空间近似计算视电阻率，忽略高路堤的影响。在这种情况下，偶极-偶极阵列的几何因子（ ）由解析公式表示：

where (a) is the electrode spacing and (n) is the dipole separation factor. A homogenous resistivity of 1 Ωm was first assigned to the model to calculate the electrical potential. Since the must equal 1 Ωm in this condition, the actual geometric factor can be obtained by . The apparent resistivity including the effect of the high embankment was then derived using the actual geometric factor. Following the definition of Rücker et al. (2006) ¹⁷, the topography effect was calculated by
其中(a)为电极间距，(n)为偶极分离因子。首先为模型分配 1 Ωm 的均匀电阻率以计算电势。由于在此条件下 必须等于 1 Ωm，因此可以通过 获得实际几何因子。然后使用实际几何因子推导出包括高路堤效应在内的视电阻率。根据 Rücker 等人(2006) ¹⁷ 的定义，地形效应通过 计算得出。.

3 Results
3 结果

3.1 Numerical simulation results
3.1 数值模拟结果

3.1.1 Topographical effects along the road shoulder and centerline profiles
31.1 沿路肩和中心线剖面的地形效应

The apparent resistivities obtained using the half-space geometric factor and actual topography are shown in Figure 2. The two apparent resistivity pseudosections showed similar spatial distribution characteristics. Overall, the half-space geometric factor led to a higher mean apparent resistivity. The half-space approximation made a negligible difference in apparent resistivity near the ground surface. A significant difference appeared from 0.5 to 4 m depth of the apparent resistivity pseudosections, and the maximum difference reached 21% (Figure 2b). For example, the apparent resistivity calculated using the real topography was about 500 Ωm in the shallow ground, equaling the resistivity of embankment in the forward model, while the apparent resistivity obtained using the half-space geometric factor approached 600 Ωm. The difference in the apparent resistivity pseudosection indicates a significant topographical effect along the profile on the road shoulder.
使用半空间几何因子和实际地形获得的视电阻率如图 2 所示。两个视电阻率伪剖面显示出相似的空间分布特征。总体而言，半空间几何因子导致平均视电阻率较高。半空间近似在地表附近的视电阻率差异可以忽略不计。在 0.5 至 4 米深度的视电阻率伪剖面中出现了显著差异，最大差异达到 21%（图 2b）。例如，使用实际地形计算的浅层地面视电阻率约为 500 Ωm，等于正演模型中的路堤电阻率，而使用半空间几何因子获得的视电阻率接近 600 Ωm。视电阻率伪剖面的差异表明沿路肩剖面的地形效应显著。

Figure 2. Apparent resistivity and topographic effect along the road shoulder profile. (a) Apparent resistivity obtained using the half-space geometric factor, (b) topographic effect, (c) apparent resistivity calculated including the high embankment.
图 2. 沿路肩剖面的视电阻率与地形效应。(a) 使用半空间几何因子获得的视电阻率，(b) 地形效应，(c) 包含高路堤计算的视电阻率。

Along the centerline profile, the two apparent resistivity pseudosections were closer (Figure 3). The half-space geometric factor resulted in a slightly higher resistivity than the geometric factor, including the actual topography. The difference in resistivity increased and then decreased with depth, and the maximum difference was more than 10% at about 8 m depth in the apparent resistivity pseudosections
沿中心线剖面，两个视电阻率拟断面较为接近（图 3）。半空间几何因子导致的电阻率略高于包含实际地形的几何因子。电阻率差异随深度先增大后减小，在视电阻率拟断面中，约 8 米深度处的最大差异超过 10%。.

Figure 3. Apparent resistivity and topographic effect along the centerline profile. (a) Apparent resistivity obtained using the half-space geometric factor, (b) topographic effect, (c) apparent resistivity calculated including the high embankment.
图 3 沿中心线剖面的视电阻率及地形效应。(a) 使用半空间几何因子获得的视电阻率，(b) 地形效应，(c) 包含高路堤计算的视电阻率。

3.1.2 Topographical effect of the profiles with different electrode spacings
3.1.2 不同电极间距剖面的地形效应

The topographical effect of the large electrode spacing profile over the road shoulder (Figure 4) showed a similar pattern to the small electrode spacing profile. The relative error of the half-space approximation peaked in the shallow depth and decreased with depth. The maximum relative error of the larger electrode spacing (1.0 m) profile reached 21%, identical to that of the small electrode spacing. The minimum relative error was about 8% near the ground surface. This indicates that for a larger electrode spacing, the minimal investigation depth of the dipole-dipole array (spacing factor equals 1) can cause a sensible error if the half-space geometric factor is used
大电极间距剖面在路肩上的地形效应（图 4）显示出与小电极间距剖面相似的模式。半空间近似的相对误差在浅层达到峰值，并随深度增加而减小。较大电极间距（1.0 米）剖面的最大相对误差达到 21%，与小电极间距相同。最小相对误差在地表附近约为 8%。这表明，对于较大的电极间距，如果使用半空间几何因子，偶极-偶极阵列（间距因子等于 1）的最小探测深度可能会引起显著误差。.

Figure 4. Topographical effect along road shoulder profile. The profile has 51 electrodes and an electrode spacing of 1.0 m
图 4. 沿路肩剖面的地形效应。该剖面有 51 个电极，电极间距为 1.0 米。.

3.1.3 Inversion results of the apparent resistivities
3.1.3 视电阻率反演结果

According to the previous forward modeling, the half-space approximation caused similar spatial distribution but a significant relative error in apparent resistivity. The apparent resistivity derived from half-space and real topography geometric factors were inverted with identical parameter options to explore the influence of the biased apparent resistivity on the inversion result. For the half-space approximation apparent resistivity, the inverted resistivities of the embankment soil and active layer were significantly higher than the forward resistivity model (Figure 5). In contrast, the inversion results of the real topography apparent resistivity showed comparable resistivity with that in the forward model. In the two inverted resistivity models, the resistivity of the permafrost layer is higher than the true value because the accuracy of the investigation decreases with depth, and the collected apparent resistivity imposes little constraints on the deeper part of the inverted model ²⁵
根据之前的正演模拟，半空间近似导致了相似的空间分布，但在视电阻率上产生了显著的相对误差。为了探讨偏差视电阻率对反演结果的影响，使用相同的参数选项对半空间和真实地形几何因子导出的视电阻率进行了反演。对于半空间近似的视电阻率，反演得到的堤坝土壤和活动层的电阻率显著高于正演电阻率模型（图 5）。相比之下，真实地形视电阻率的反演结果显示出与正演模型相当的电阻率。在两个反演电阻率模型中，永久冻土层的电阻率高于真实值，因为调查的精度随深度降低，且收集的视电阻率对反演模型较深部分的约束较小 ²⁵ 。.

Figure 5. Inversion result using the calculated apparent resistivities with half-space approximation (a) and actual topography (b). The apparent resistivities were calculated for 51 electrodes at an interval of 0.5 m on the road shoulder
图 5 使用半空间近似（a）和实际地形（b）计算的视电阻率反演结果。视电阻率是在路肩上以 0.5 米间隔布置的 51 个电极上计算的。.

3.2 Field application
3.2 现场应用

The numerical simulations indicated that the half-space approximation impacted the apparent resistivity and the inversion results of resistivity measurement over a high embankment. The geometric factor considering the topography can be obtained numerically by building a 3-D embankment model. The method was applied to the field data collected on an experimental demonstration expressway (Figure 6).
数值模拟表明，半空间近似影响了高路堤上电阻率测量的视电阻率和反演结果。通过建立三维路堤模型，可以数值计算得到考虑地形的几何因子。该方法已应用于实验示范高速公路（图 6）上采集的现场数据。

Figure 6. Photo of the experimental demonstration expressway sections in the permafrost regions on the QTP. The permafrost distribution on the QTP is modified from ²⁶. Section I is the conventional embankment, section Ⅱ is the embankment with hollow concrete brick revetment and crushed rock base, and section Ⅲ is the embankment installed with ventilation tube and crushed rock base. The length of each section is 30 m. The B1~B3 indicates the position of ground temperature monitoring boreholes The apparent resistivity data are collected along the red dashed line using CCR.
图 6. 青藏高原多年冻土区实验示范路段照片。青藏高原多年冻土分布图根据 ²⁶ 修改。I 段为常规路堤，II 段为空心混凝土砖护岸与碎石基层路堤，III 段为安装通风管与碎石基层的路堤。每段长度均为 30 米。B1~B3 表示地温监测钻孔的位置。视电阻率数据沿红色虚线使用 CCR 采集。

The experimental demonstration expressway was built in the Beiluhe Basin (QTP), where continuous warm and ice-rich permafrost has been recognized ²¹. Considering that the heat absorption of the asphalt pavement tends to thaw the underlying permafrost, thus inducing embankment settlement and destabilization of infrastructures, mitigative techniques, including reducing solar radiation and altering heat conduction and convection within the embankment, were proposed ⁹. A section of the conventional embankment (Figure 7a) was designed for comparison with the embankments based on crushed rock, revested with hollow concrete bricks (Figure 7b) and installed with ventilation tubes (Figure 7c), measures that modify the convection within the embankment body (Figure 7b). To analyze the thermal regime in embankments with different mitigative measures, ground temperatures were measured with thermistor sensors pre-installed in each section (B1~B3 in Figure 6). The surrounding terrain was relatively flat, and the embankments were built with a height of 3 m and a width of 13 m (Figure 7).
实验示范高速公路建于北麓河盆地（QTP），该地区已被确认为连续温暖且富含冰的多年冻土区 ²¹ 。考虑到沥青路面的吸热倾向会融化下伏的多年冻土，从而引发路基沉降和基础设施失稳，提出了包括减少太阳辐射、改变路基内热传导和对流的缓解技术 ⁹ 。为进行比较，设计了一段常规路基（图 7a），与基于碎石、铺设空心混凝土砖（图 7b）及安装通风管（图 7c）的路基相对照，这些措施旨在改变路基体内的对流（图 7b）。为分析采用不同缓解措施的路基热状况，通过预埋在各段（图 6 中 B1~B3）的热敏电阻传感器测量地温。周边地形相对平坦，路基建设高度为 3 米，宽度为 13 米（图 7）。

Figure 7. Sketch map of the conventional embankment (a), embankments with hollow concrete brick revetment and crushed rock base (b), and embankment installed with ventilation tube and crushed rock base (c). The width and height of the road surface are 13 m and 3m, respectively. The side slope grade is 1:1.5.
图 7. 常规路堤示意图（a）、空心混凝土砖护坡与碎石基层路堤（b）以及安装通风管与碎石基层路堤（c）。路面宽度和高度分别为 13 米和 3 米。边坡坡度为 1:1.5。

We used the TRN OhmMapper CCR system to collect data, as the conventional instruments' steel electrodes are difficult to place on asphalt and concrete pavements. ¹¹. The antennas were dragged over the road surface and worked by capacitively coupling ^12,27. The purpose of the CCR investigation was to delineate the depth of the permafrost table under the embankment and analyze the cooling effects of the mitigative measures. The CCR investigation was conducted along the road shoulder surface in October 2018 (Figure 7). One transmitter and four receivers were used with an antenna length of 5 m and a minimum transmitter-receiver spacing of 5 m.
我们使用 TRN OhmMapper CCR 系统收集数据，因为传统仪器的钢电极难以放置在沥青和混凝土路面上。 ¹¹ 。天线被拖过路面并通过电容耦合工作 ^12,27 。CCR 调查的目的是划定路基下永久冻土层的深度，并分析缓解措施的冷却效果。CCR 调查于 2018 年 10 月沿路肩表面进行（图 7）。使用了一个发射器和四个接收器，天线长度为 5 米，发射器与接收器之间的最小间距为 5 米。

The raw apparent resistivity data were firstly de-spiked and low-pass filtered and then averaged over half of the antenna length (Figure 8a). Similar to the synthetic simulations, a 3D model was built according to the configuration of the embankment and surrounding topography. Based on the derived topographical effect ratio from the 3D modeling, the apparent resistivities were then corrected, as shown in Figure 8b. The corrected apparent resistivity showed an overall similar resistivity distribution with the original pseudosection. Specifically, the decrease of the shallow apparent resistivity was more significant than in the deeper layer
原始视电阻率数据首先进行了去尖峰和低通滤波处理，然后在天线长度的一半范围内进行了平均（图 8a）。与合成模拟类似，根据堤坝及周围地形的配置构建了一个三维模型。基于三维建模得出的地形效应比，对视电阻率进行了校正，如图 8b 所示。校正后的视电阻率显示出与原始伪剖面总体相似的电阻率分布。具体而言，浅层视电阻率的下降比深层更为显著。.

Figure 8. Apparent resistivity pseudosection collected on the road shoulder of the experimental demonstration expressway section on the QTP. (a) Apparent resistivity calculated with half-space geometric factor, (b) calculated with real topography geometrical factor.
图 8. 青藏高原实验示范高速公路路段路肩采集的视电阻率拟断面图。(a) 使用半空间几何因子计算的视电阻率；(b) 使用实际地形几何因子计算的视电阻率。

The inverted model of the corrected apparent resistivity is shown in Figure 9. Under the conventional embankment (0~30 m), a low-resistivity abnormality was observed. Under the section with hollow concrete brick revetment and crushed rock base (30~60m) and the one installed with a ventilation tube and a crushed rock base (60~90m), much higher resistivity appeared in deeper depth.
校正后的视电阻率反演模型如图 9 所示。在常规路堤（0~30 米）下方，观测到了低电阻率异常。在空心混凝土砖护岸和碎石基层路段（30~60 米）以及安装有通风管和碎石基层的路段（60~90 米）下方，较深处出现了更高的电阻率。

Figure 9. Inversion results of the apparent resistivity derived from the actual topography geometrical factor. The magenta boxes indicate the depth of the permafrost table revealed by the ground temperature monitoring.
图 9 由实际地形几何因子得出的视电阻率反演结果。洋红色框表示地温监测揭示的多年冻土上限深度。

According to the ground temperature measurements under the three embankment sections (Figure 10), the depth of the permafrost table was derived and overlaid in the inverted resistivity model (Figure 9). In section Ⅰ, the depth of the permafrost table was about 9 m. Thus, the low resistivity indicated the thawed active layer. The depth of the permafrost table cannot be identified since the depth should exceed the investigation depth of the CCR survey. In section Ⅱ and Ⅲ, the depth of the permafrost table corresponded well with the interface with sharp resistivity contrasts. The comparison suggested that the permafrost table under embankments can be reliably identified from the inverted models of corrected apparent resistivity.
根据三个路基段的地温测量结果（图 10），得出了多年冻土上限的深度，并将其叠加在反演电阻率模型中（图 9）。在第Ⅰ段，多年冻土上限的深度约为 9 米。因此，低电阻率表明该层为融化活动层。由于深度可能超过了 CCR 调查的探测深度，无法确定多年冻土上限的深度。在第Ⅱ段和第Ⅲ段，多年冻土上限的深度与电阻率急剧变化的界面吻合良好。比较表明，可以从校正视电阻率的反演模型中可靠地识别出路基下的多年冻土上限。

Figure 10. Ground temperature measured on 15 October 2018 at the three boreholes.
图 10 2018 年 10 月 15 日在三个钻孔处测量的地温。

4. Discussion
4. 讨论

The numerical simulation of the 3D high embankment model indicated that the influence of high embankment on the apparent resistivity was significant. In many cases, the influence of the topographical effect from an irregular topography is challenging to be inferred intuitively ¹⁴. As the topography of the embankment is relatively simple, the topographical influence of the high embankment is predictable. The topographical effect induces mainly higher apparent resistivity within the depth range of the embankment. For the configuration of the embankment model, the maximum relative errors of the apparent resistivity were about 21% and 11% for the survey lines along the road shoulder and midline, respectively.
三维高路堤模型的数值模拟表明，高路堤对视电阻率的影响显著。在许多情况下，不规则地形引起的地形效应难以直观推断 ¹⁴ 。由于路堤地形相对简单，高路堤的地形影响是可预测的。地形效应主要导致路堤深度范围内的视电阻率升高。对于路堤模型的配置，沿路肩和中线测量线的视电阻率最大相对误差分别约为 21%和 11%。

The inversion process may be unstable or divergent if a complex topography is not included ¹⁴. In this case, the inversion of the apparent resistivity ignoring the high embankment was stable, and the solutions generally made sense. The interfaces could be identified with equivalent accuracy by the resistivity contrasts. However, the topographical effects resulted in significantly higher resistivity than that in the forward model. The inversion results of the corrected apparent resistivity agreed well with the forward model, indicating the method’s effectiveness. The influence of the topographical effect is insignificant if the investigation purpose is to identify the interfaces qualitatively. However, the correcting of the apparent resistivity is essential if quantitative information, such as the soil moisture content, needs to be calculated from the inverted resistivity
如果未包含复杂地形，反演过程可能不稳定或发散 ¹⁴ 。在这种情况下，忽略高路堤的视电阻率反演是稳定的，且解通常合理。通过电阻率对比，界面可以以相当的精度识别。然而，地形效应导致电阻率显著高于正演模型中的值。校正后的视电阻率反演结果与正演模型吻合良好，表明该方法的有效性。如果调查目的是定性识别界面，地形效应的影响不大。但如果需要从反演电阻率中计算定量信息（如土壤含水量），则校正视电阻率至关重要。.

Moreover, the actual topography is often more complex than the conceptual model. The topographical relief may differ significantly on the both sides of the embankment, which can change the spatial distribution of apparent resistivity. In this case, the interfaces among geological layers may be distorted, and artificial interfaces may be induced if the topography effect is ignored
此外，实际地形往往比概念模型更为复杂。堤坝两侧的地形起伏可能差异显著，这会改变视电阻率的空间分布。在这种情况下，若忽略地形效应，地质层之间的界面可能会发生扭曲，甚至可能诱发人为界面。.

It should be noted that the correction of apparent resistivity can only eliminate the influence of the topography surrounding the embankment. The inhomogeneous soil moisture and texture distribution can cause remarkable resistivity differences around the embankment. The offline resistivity anomaly may also distort the measured apparent resistivity, such as the water level fluctuation around a dam embankment changing the apparent resistivity ¹⁵. This distortion can only be eliminated by three-dimensional data collection and inversion.
需要注意的是，视电阻率的校正仅能消除堤坝周围地形的影响。土壤水分和质地分布的不均匀性可能导致堤坝周围显著的电阻率差异。离线电阻率异常也可能扭曲测量的视电阻率，例如堤坝周围水位的波动会改变视电阻率 ¹⁵ 。这种扭曲只能通过三维数据采集和反演来消除。

5. Conclusions
5. 结论

This study investigates the influence of a high embankment on the resistivity measurement when a 2D survey line is measured along the strike direction of the embankment by forward and inverse modeling of a 3D embankment model and field verification. The main findings are summarized in the following
本研究通过三维堤坝模型的正反演模拟及现场验证，探讨了高堤坝对沿堤坝走向方向进行二维测线电阻率测量时的影响。主要发现总结如下：.

The half-space approximation of the 2D survey lines brought about significant errors in apparent resistivity. The maximum relative errors reached 21% and 10% for the road shoulder and midline survey lines, respectively. The part of the biased resistivity mainly appeared within the depth of the high embankment.
二维测线的半空间近似导致了显著的视电阻率误差。对于路肩和中线测线，最大相对误差分别达到了 21%和 10%。偏差电阻率主要出现在高路堤深度范围内。

The inversion of the biased apparent resistivity resulted in a noteworthy higher resistivity than the true value, although the interfaces among layers could be identified. Provided a calculated actual topography geometric factor, the inversion result of the corrected apparent resistivity agreed well with the true value.
偏置视电阻率的反演结果比真实值显著偏高，尽管各层之间的界面可以被识别。在提供了计算的实际地形几何因子后，校正后的视电阻率反演结果与真实值吻合良好。

The correction of apparent resistivity was successfully applied to the field data collected on an experimental demonstration expressway in the permafrost regions on the QTP. The depth of the permafrost table was delineated from the inversion results and verified by ground temperature monitoring
视电阻率校正成功应用于青藏高原多年冻土区试验示范高速公路现场采集数据。多年冻土上限深度通过反演结果划定，并得到地温监测验证。.

These findings indicate that the topographical influence of high embankments on the resistivity measurement should be considered if a 2D approximation is adopted. A correction of the apparent resistivity or 3D data collection and inversion is essential for quantitative interpretation of the inverted resistivity.
这些发现表明，如果采用二维近似方法，则应考虑高路堤地形对电阻率测量的影响。对于反演电阻率的定量解释，视电阻率的校正或三维数据采集与反演至关重要。

Acknowledgments
致谢

Thanks for the two anonymous reviewers for their thoughtful suggestions that have helped improve this paper. This work was supported by the National Natural Science Funds of China [Grant No. 42071095], the Key Research Program of Frontier Sciences, CAS [Grant No. ZDBS-LY-DQC026], the foundation of the State Key Laboratory of Frozen Soil Engineering [Grant No. SKLFSE-ZT-202106], Science and Technology Research Project, CCSHCC [Grant No. KJFZ-2019 - 041], and Youth Science and Technology Innovation Project, CCCC [Grant No. 2021-ZJKJ-QNCX16]
感谢两位匿名审稿人提出的宝贵建议，这些建议有助于改进本文。本研究得到了国家自然科学基金[项目编号：42071095]、中国科学院前沿科学重点研究计划[项目编号：ZDBS-LY-DQC026]、冻土工程国家重点实验室基金[项目编号：SKLFSE-ZT-202106]、中国铁建科技研究项目[项目编号：KJFZ-2019-041]以及中国交建青年科技创新项目[项目编号：2021-ZJKJ-QNCX16]的支持。.

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