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2024 Vol.27, Issue 4 Preview Page

Research Article

2D Resistivity Inversion Using Spectral Parameterization

주파수 매개변수화에 의한 2차원 전기비저항 역산

Hannuree Jang1
,
Changsoo Shin12*
,
Dongkweon Lee1
,
Hangilro Jang1
장 한누리1
,
신 창수12*
,
이 동권1
,
장 한길로1
1BOMIN GLOBAL Co., Ltd.
2Department of Energy Resources Engineering, Seoul National University
1보민글로벌㈜
2서울대학교 에너지자원공학과
*Corresponding Author
30 November 2024. pp. 224-232
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Abstract

In this study, we have introduced a novel 2D electrical resistivity inversion method based on spectral parameterization that uses a complex Fourier series to image subsurface resistivity. Decomposing the resistivity into frequency components enables the efficient computation of stiffness and sensitivity matrices, which are crucial for electric field modeling and inversion. We defined a virtual current source at every model grid point to calculate the partial differentiation of the electric potential during inversion. The inversion process uses the Gauss-Newton method to update the Fourier coefficients iteratively, with a sensitivity-based weighting scheme that dynamically adjust the influence of each data point. This ensures greater resolution in high-sensitivity areas while maintaining stability in less sensitive regions. To validate the method, synthetic numerical experiments were conducted to compare it with traditional block parameterization. This simplifies the model by dividing the subsurface into homogeneous blocks. Although block parameterization offers computational efficiency, the spectral method has superior resolution and convergence in complex geological environments.

Keywords
Resistivity
Inversion
Spectral
Complex Fourier Series
Gauss-Newton

이 연구에서는 복소 푸리에 급수를 활용한 공간 파수 매개변수화를 기반으로 한 새로운 2차원 전기비저항 역산 알고리즘을 개발하였다. 이 기법은 전기비저항 분포를 공간 파수 구성 요소로 분해할 수 있어 전기장 모델링에서 강성 행렬과 감도 행렬을 효율적으로 계산할 수 있게 한다. 또한, 역산에서 전위차의 편미분을 계산하기 위한 가상 전류원은 모든 모델의 격자점에서 정의된다. 역산 과정에서는 푸리에 계수를 반복적으로 갱신하기 위해 가우스-뉴턴 방법을 사용하며, 민감도 기반 가중치 기법을 통해 각 자료의 영향을 동적으로 조정한다. 이 방법은 감도가 높은 영역의 해상도를 향상시키는 동시에 감도가 낮은 영역의 수치적 안정성을 보장한다. 합성 자료의 수치 실험을 이용하여 역산 알고리듬의 적용성을 검증하였다. 민감도 기반 가중치 역산은 연속적인 전기비저항 분포를 영상화하여 보다 세밀하고 정확한 모델을 제공할 수 있다. 수치실험을 통해 푸리에 급수 기반 전기비저항 역산이 지하의 이상체 및 지질구조 해석에 효과적으로 활용될 수 있음을 확인하였다.

키워드
전기비저항
역산
주파수
복소 푸리에 급수
가우스-뉴턴
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Information
  • Publisher :Korean Society of Earth and Exploration Geophysicists
  • Publisher(Ko) :한국지구물리물리탐사학회
  • Journal Title :Geophysics and Geophysical Exploration
  • Journal Title(Ko) :지구물리와 물리탐사
  • Volume : 27
  • No :4
  • Pages :224-232
  • Received Date : 2024-11-18
  • Revised Date : 2024-11-25
  • Accepted Date : 2024-11-28
  • DOI :https://doi.org/10.7582/GGE.2024.27.4.224
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