A proposal of optimum calculation settings of continuous wavelet transform in magnetotelluric data processing

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  • Ogawa Hiroki
    Graduate School of Creative Science and Engineering, Waseda University Nittetsu Mining Co., Ltd. Tono Geoscience Center, Japan Atomic Energy Agency (JAEA)
  • Hama Yuki
    Nittetsu Mining Co., Ltd.
  • Asamori Koichi
    Tono Geoscience Center, Japan Atomic Energy Agency (JAEA)
  • Ueda Takumi
    School of Creative Science and Engineering, Waseda University

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Other Title
  • MT法時系列データ処理における連続ウェーブレット変換の最適な計算設定の提案
  • MTホウ ジケイレツ データ ショリ ニ オケル レンゾク ウェーブレット ヘンカン ノ サイテキ ナ ケイサン セッテイ ノ テイアン

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Abstract

<p>　In the magnetotelluric (MT) method, so as to identify the subsurface resistivity structure, the apparent resistivity and phase profiles are calculated by transforming time-series data into spectral data. The continuous wavelet transform (CWT) is well known as a new method of time-frequency analysis instead of the short-time Fourier transform. The CWT is superior in processing non-stationary wideband signals like the MT signal by adjusting the size of the wavelet according to the value of frequency. However, the calculation settings of the CWT, such as the type of basis function and the wavelet parameter, are often determined empirically because of the arbitrariness of the shape of the wavelet. Although there might be differences between the calculated MT responses and the true responses due to improper settings of the CWT, there are no detailed studies considering the effect of numerical errors derived from spectral transforms on MT data. In this study, focusing on the frequency band between 0.001 Hz and 1 Hz, we examined the optimum calculation settings of the CWT in processing MT data in terms of suppressing the numerical errors caused by the spectral transform of time-series data. First, we investigated the effect of change in the resolutions of time and frequency on the apparent resistivity and phase profiles by altering the shape of the wavelet. Next, we examined the type of basis function and the range of the wavelet parameter which would provide high-quality MT responses with high continuity that may accurately reflect the subsurface information. Through these experiments, this study proposed the complex Morlet function including a sine wave component with its wavelet parameter k set to 6 ≤ k < 10 as the optimum calculation settings of the CWT. We also show the validity of the proposed calculation settings by applying the CWT to MT survey data of different types. Superiority of the CWT with proposed settings is suggested especially when the signal-to-noise ratio of observed data is low. Consequently, the proposed calculation settings were confirmed to strike a balance between the resolutions of the time and frequency domains well and will therefore be effective in obtaining reliable MT responses.</p>

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