ERT（Electrical Resistivity Tomography，电阻率层析成像），又称高密度电法，是一种基于介质电性差异的地球物理勘探方法。它通过在地表布设一系列电极，向地下供入人工电流，并测量不同位置的电势差，进而反演出地下介质的电阻率分布，形成二维或三维的”电性剖面”。

ERT (Electrical Resistivity Tomography) is a geophysical exploration method based on the electrical contrast of subsurface media. By laying out a series of electrodes on the surface, injecting artificial current into the ground, and measuring potential differences at various positions, it inverts the resistivity distribution of the subsurface to produce a 2D or 3D “electrical profile.”

由于地下水、孔隙流体、岩性界面与构造破碎带等都会显著改变介质的电阻率，ERT 成为探测地下结构最具性价比的手段之一。它起源于 20 世纪初的常规电阻率法，随着 20 世纪 80 年代后多电极自动采集与二维/三维反演算法的成熟，逐步发展为今天广泛使用的层析成像技术。

Because groundwater, pore fluids, lithologic interfaces, and fractured zones all significantly alter medium resistivity, ERT has become one of the most cost-effective means of investigating subsurface structure. It evolved from conventional resistivity surveying of the early 20th century, maturing into today’s tomographic technique after the development of multi-electrode automated acquisition and 2D/3D inversion algorithms in the 1980s.

ERT 的物理基础是欧姆定律与大地电阻率测量。在地下两点 A、B 供入电流 I，电流在地下建立稳定电场；再用另外两点 M、N 测量电势差 ΔV。对于均匀半空间，可由下式计算视电阻率 ρa：

The physical basis of ERT is Ohm’s law and earth resistivity measurement. Current I is injected via two electrodes A and B, establishing a steady electric field in the ground; the potential difference ΔV is measured at two other electrodes M and N. For a homogeneous half-space, the apparent resistivity ρa is:

其中 K 为装置系数（geometric factor），由四个电极的相对几何关系决定。实际地下并非均匀，故测得的是综合反映探测范围内介质电性的”视电阻率”。通过沿测线滚动、变换电极组合，可获得大量视电阻率观测，再经反演得到地下真实电阻率分布。

where K is the geometric factor determined by the relative geometry of the four electrodes. The real subsurface is not homogeneous, so the measured quantity is an “apparent resistivity” integrating the electrical properties within the investigation volume. By rolling along a profile and varying electrode combinations, a large set of apparent-resistivity observations is gathered and then inverted to obtain the true resistivity distribution.

四个电极（A、B 供电极，M、N 测量极）的相对排列方式称为装置类型。不同装置在水平分辨率、垂向探测深度与抗噪能力上各有侧重，实际工作中常组合使用。

The relative arrangement of four electrodes (A and B for current, M and N for potential) is called an array type. Different arrays emphasize horizontal resolution, vertical depth, or noise resistance, and are often combined in practice.

表1  常见 ERT 电极装置类型对比

Table 1  Common ERT electrode arrays compared

实际”高密度电法”系统通常沿测线布设 32~128 根电极，由采集主机自动切换 A、B、M、N 角色，一次布极即可获得数百至数千个观测点，大幅提高效率。

In practice, a “high-density” system lays 32–128 electrodes along a profile; an acquisition unit automatically switches the A/B/M/N roles, yielding hundreds to thousands of observations from a single layout.

一条典型 ERT 测线的作业流程如下：

A typical ERT profile workflow:

其中电极接地质量直接影响数据信噪比；在干燥或岩石出露区，常需浇水或使用盐水降低接地电阻。地形起伏显著的测线还需进行地形校正，否则反演结果会产生假异常。

Electrode contact quality directly affects data S/N; in dry or rocky areas, water or brine is used to reduce contact resistance. Profiles with significant topographic relief require topographic correction, otherwise inversion produces false anomalies.

ERT 反演是一个非线性最优化问题：给定观测的视电阻率数据，求解使正演响应与观测最佳拟合的地下电阻率模型。主流采用最小二乘光滑约束（如 Loke & Barker 的 Gauss-Newton 法），在数据拟合与模型平滑之间权衡，避免过拟合。

ERT inversion is a nonlinear optimization problem: given observed apparent resistivity, solve for a subsurface resistivity model whose forward response best fits the data. The mainstream approach uses least-squares smooth-constraint (e.g., Loke & Barker’s Gauss-Newton method), trading off data fit against model smoothness to avoid overfitting.

典型处理步骤包括：坏点剔除 → 地形校正 → 正演建模 → 迭代反演 → 模型评估（均方根误差 RMS）→ 地质解释。最终输出的电阻率剖面需结合钻孔或地质资料才能转化为可信的地质结论。

Typical steps: bad-point removal → topographic correction → forward modeling → iterative inversion → model evaluation (RMS error) → geological interpretation. The final resistivity section must be combined with borehole or geological data to yield reliable conclusions.

使用 Python 生态 pyGIMLi 进行 ERT 反演的示例：

Example of ERT inversion using the Python ecosystem pyGIMLi:

import pygimli as pg
import pygimli.meshtools as mt
from pygimli.physics import ert

# 1. 读取观测数据（含电极坐标与视电阻率）
data = ert.load("survey.dat")

# 2. 建立正演网格（带地形）
grid = mt.createParaMesh(data, quality=33.5)

# 3. 初始化反演管理器
mgr = ert.ERTManager(data)
mgr.invert(
    data="rhoa",         # 视电阻率列
    lam=10,               # 正则化参数，控制平滑度
    zweight=0.3,          # 垂向权重，影响深部分辨
    maxIter=20,
    verbose=True
)

# 4. 输出与可视化
print(f"RMS = {mgr.inv.chi2():.2f}")
mgr.showResult(cMin=10, cMax=1000, logScale=True)

理解电阻率量级差异是解释 ERT 剖面的基础。下表列出常见地质介质的典型电阻率范围：

Understanding resistivity magnitude is fundamental to interpreting ERT sections. Typical resistivity ranges of common media:

表2  常见地质介质典型电阻率范围（量级参考）

Table 2  Typical resistivity ranges of common geological media

优势：ERT 设备相对轻便、成本低于地震勘探、可同时获得较大探测深度与较高分辨率，并能用于时延动态监测；对不同含水条件敏感，特别适合水文与工程问题。

Strengths: ERT equipment is portable and lower-cost than seismic, offers good depth and resolution simultaneously, and supports time-lapse monitoring; it is sensitive to water content, suiting hydrology and engineering problems.

局限：分辨率随深度衰减（深部更模糊）、反演结果非唯一、在市区金属管线密集区受电磁干扰、高阻结晶岩区电流难以注入。对极低阻或极高阻屏蔽层下的目标探测能力有限。

Limits: Resolution decays with depth, inversion is non-unique, urban metallic infrastructure causes interference, and current injection is difficult in resistive crystalline rock. Targets beneath extreme low- or high-resistivity screening layers are hard to resolve.