Model Design for AMT Data Inversion

By analyzing the characters of the mainstream commercial magnetotelluric inversion softwares in dealing with audio magnetotelluric data, a dynamic model-making method for inversion has been developed based on the observed AMT data. This method focusing on model domain can adjust mesh’s scale and model’s dimension depending on the field data just with a few parameters. By this, it is convenient to study the geo-electrical anomalies variations of different scale or dimensional models. Applying such model-making technique into the known hardrock geological setting, it is easy to obtain a new geo-electrical model which agrees with the resistivity curves of core samples better than before. It is demonstrated that this can increase the recognition of the resistivity contrast and deserves studying further.


Introduction
Audio magnetotelluric method (AMT), with simple logistics and no transmitter required, became a key geophysical method accompanying with more kinds of commercial AMT instruments produced in the markets since the 1990s (Yao, 2012) [1]. In the past several decades, one of the sparkles of geophysical exploration is the forward and inversion techniques applied into the field. In the induction electromagnetic exploration field, there were several practicably EM 2D inversion methods applied vastly, such as NLCG, RRI, OCCAM and so on [2] [3] [4]. The hardware and software progress made AMT method to be applied to many fields, such as base metals [5] [6], uranium exploration [7] and so on.
As general geophysical exploration data process, there are mainly three steps to process AMT data. The first step is to convert each station's time serial data to the frequency domain before calculating the cross power spectrum. Then, the estimation of each station's impedance is followed by seeking a corresponding resistivity model which also satisfies a specified regularization function through inversion. However, many softwares to invert AMT data come from those focusing on MT data. Although the principle is identical for processing two types' data, the anomaly scale to be focused is much different because AMT exploration is about 2000 m depth underground and MT about the deeper and big scale anomalies. Moreover, some commercial software is bounded with several fixed models or will meet memory overflowing when inversing fine meshes. When studying the sand body anomaly among the weak resistivity contrast in uranium exploring by AMT data, an inversion process was outlined using different scale models with checking anomalies [8]. To meet such situations, a simple method of making different scale or dimensional model is required. The paper gives a way of making such models conveniently.
Here, a model-making method based on AMT field data is discussed specially and the main steps for programming are explained in detail. An example of AMT exploring in hardrock area using this model-making method showed that this method was conductive to detailed resistivity anomaly mining and these anomalies agreed with core sample resistivity curves. The paper aims at giving a method to make the model for detailed inversion based on field data, which makes it convenient to study resistivity anomalies variation of models.

Model Design
The paper here only focuses on the 2-D inversion problem of finding a 2-D electrical resistivity model that can fit the observed data in two mode's impedances (TE and TM). There are many papers on the fundamental equations for 2D modeling (e.g. Swift, et al., 1971;Zhdanov, et al., 1982;Wannamaker, et al., 1985) [9] [10] [11] so that they will not be re-counted here. The inversion process minimizes a regularized function as the trade-off between a structure penalty function and the data residual norm weighted with data variances (Rodi & Mackie, 2001) [2]. The inversion codes based on these or similar modeling schemes are also widely used (e.g. Sasaki, 1989 [12]. The paper employed the NLCG inversion scheme of Rodi & Mackie (2001) [2], and electric and magnetic fields are computed using a finite-difference scheme by network analogs to Maxwell's equations (Charles M. Swift, 1971;Madden 1972) [9] [13]. The modelled domain (a user-defined 2D mesh of resistivity blocks incorporating topography) is much larger than the actual region of interest to ensure that the model boundaries are sufficiently far away from resistivity anomalies in order to satisfy the boundary conditions.
There is a coherence relationship between resistivity anomaly scale and that of the model's cell. If the cell grid is too coarse, it may integrate the anomaly and host rock into one cell so that the anomaly is not identified or attenuated. On the contrary, if cell grid is smaller than the scale of the anomaly, it may delineate the boundary between the anomaly and the host rock in detail. However, if the cells are too close, it may produce overburden calculating resource and causes memory overflow sometimes. The problem is that the scale of the resistivity anomaly is unknown before inversion procedure without the prior information.
In order to make the inversion model coherent with the AMT data characteristics, this making model method based on the real field data has the following three steps: 1) To calculate detecting depth of each frequency in all station data of the area or one profile.
2) To configure cells' height. In general, the height of the cells above the minimum detecting depth is set as a constant. The heights of the cells between the minimum and maximum detecting depths are set to a geometric progression, whose first term is that constant height and whose common ratio is based on how much the model dimension to be built. Below the maximum detecting depth, the height distribution is also a geometric progression, but its common ration is at least 0.1 more than that common ration above.
3) To configure horizontal column allocation. Setting two columns in the modeled domain, three columns or more are inserted between neighborly stations based on the AMT observing station space and the model's dimension to be designed. In two lateral zones out of the domain, the spacing between columns distributes also as a geometric progression, whose first term is the spacing between the first and the second column in the domain and whose common ratio is always set as 1.5. For detecting depth is related to apparent resistivity of each frequency, this model-making method is different from that of only using hemi-sphere resistivity value as before and is corresponding to field data's detecting depth.

Hardrock Area Example
Due to the high resistivity value in the hardrock area and lack of significant resistivity contrast, it is more difficult to explore resistivity anomaly. However, in this situation, the weak resistivity contrast is related to some factors with many kinds of ore mineralization or safety so that it's significant to detect such anomalies. The following example is about exploring copper with AMT data in hardrock area, but the emphasis here is about how to mine detailed resistivity ano-malies varying using the making model method above.   sotropy with depths. Not only the resistivity, but also the chargeability is measured and will be discussed later.

Inversion Results Comparing
The geo-electrical models inverted from AMT data of D profile represent in  However, there are clear differences in Figure 3 where the model B gives new and more detailed information as following: The parts, where the two bidirectional arrows (C and D in Figure 3) point to, are the relative low resistivity areas in both models. However, the parts in model B are mixed with relative high resistivity blocks instead of the only relative low resistivity area. Especially for D pointing at part in the model B, there are three relatively low different value anomalies composed while for the corresponding part in model A there is only a block of relative low resistivity.
The inversion geo-electrical model B (in Figure 3) did not change the general electrical anomaly distribution of the model A, but there appeared detailed information which the model A did not show. By applying dynamic model-making method to the inversion procedure, the relatively low or high resistivity blocks are decomposed into several different anomalies and more small scale resistivity variances are probed.

Reliability Discussion
In the above discussion, the inversion result's reliability was not mentioned.
Here, the core sample resistivity curves will be used to discuss about the reliabil-

Conclusions
In hardrock area, especially in granite rock environment, its resistivity is always much higher and the geo-electrical contrast is not prominent. These facts make it difficult to detect the geo-electrical variations. Mining such electrical resistivity anomalies is significant because this kind of geo-electrical variations is usually related to some key problems such as safety factors, some favorable factors for forming ores, and so on.
During the studying period, the reason why the model A did not agree with the core sample resistivity curves was considered as the decreasing resolution ability with the increase of depth based on the principle of electromagnetic field diffusion. But with further study, it was found that using different scale model to be inverted might mine new information that did not appear before. After checking the new anomaly with the known information such as core sample resistivity curves, the dynamic model-making method based on field data for inversion proved to be a valuable study direction. Besides, the ability of detecting the deep anomaly can be improved if the related methods are used appropriately.