## 2 Noise in Magnetotelluric Survey  
Aside from its many advantages, one of the crucial drawbacks of MT method is how it is prone to electromagnetic interference (EMI) or noise. The natural EM field recorded in the MT survey is quite weak and easily affected by noise. Many sources can contribute to noise perceived in the MT survey, but cultural or man-made noises are what cause severe distortion in the transfer function estimation. Cultural noise sources such as power lines, automobiles, transmission networks, mobile devices, and many other EM devices can severely affect the signal quality, thus affecting the MT impedance tensor estimation and potentially leading to unreliable results. Noise issues have been a long-standing concern of the MT community and have been extensively studied in previous research [27, 28], yet they continue to present challenges.  
Many MT surveys suffer from the presence of such EMI, and finding ideal MT sites in the environment where rapid urban development occurs is challenging. For example, the MT survey carried out in Pohang suffered near-field noise effects at their MT stations [29]. They set up far-remote reference stations, located 60-500 km from their observation sites to reduce the noise effect in their estimation. Another survey faced the same issue and explored various processing approaches to determine the parameters that are best suited for data processing. They also combined several other methods to denoise the data, including Remote Reference [30].  
To deal with the noise in our data, we also use the Remote Reference (RR) Method [31]. RR has been around for decades and remains the most widely used method in the industry as a way of minimizing the noise impact on MT data. Since its development, this method has been used by many researchers to support MT studies to this day [29, 30, 32]. The idea is to set up a station at a distance from the target station where the noise is assumed to be uncorrelated. The recording requires a synchronous recording of the remote site and the target site. The \(H\) of the remote reference station is then retrieved and used during the impedance tensor calculation as follows:  
\[Z_{xx} =\frac{\left(\overline{E_{x}H_{x}^{*}}\ \overline{H_{y}H_{yr}^{*}}- \overline{E_{x}H_{yr}^{*}}\ \overline{H_{y}H_{yr}^{*}}\right)}{D} \tag{7}\] \[Z_{xy} =\frac{\left(\overline{E_{x}H_{yr}^{*}}\ \overline{H_{x}H_{x}^{*}}- \overline{E_{x}H_{x}^{*}}\ \overline{H_{x}H_{yr}^{*}}\right)}{D}\] (8) \[Z_{yx} =\frac{\left(\overline{E_{y}H_{x}^{*}}\ \overline{H_{y}H_{yr}^{*}}- \overline{E_{y}H_{yr}^{*}}\ \overline{H_{yr}H_{yr}^{*}}\right)}{D}\] (9) \[Z_{yy} =\frac{\left(\overline{E_{y}H_{yr}^{*}}\ \overline{H_{x}H_{x}^{*}}- \overline{E_{y}H_{yr}^{*}}\ \overline{H_{x}H_{yr}^{*}}\right)}{D} \tag{10}\]  
where \(D\) is:  
\[D=\overline{E_{x}H_{x}^{*}}\ \overline{H_{y}H_{yr}^{*}}-\overline{E_{x}H_{yr}^{ *}}\ \overline{H_{y}H_{yr}^{*}} \tag{11}\]  
This will result in an unbiased impedance tensor as long as the noise between the local and remote sites is uncorrelated. \(H_{x}^{*}\) and \(H_{yr}^{*}\) are the complex conjugates of the remote site \(H\). In this study, remote reference processing is carried out using Bounded Influence Remote Reference Processing (BIRRP) through the open-source MT python toolbox MTPy [33, 34].