@article { author = {Jamie, Majid and Oskooi, Behrooz}, title = {Enhancing the resolving power of 2D least-squares inversion of magnetotelluric data}, journal = {Journal of the Earth and Space Physics}, volume = {38}, number = {4}, pages = {117-130}, year = {2013}, publisher = {Institute of Geophysics, University of Tehran}, issn = {2538-371X}, eissn = {2538-3906}, doi = {10.22059/jesphys.2013.30210}, abstract = {This paper presents results of applying a new approach on 2D inversion of Magnetotelluric (MT) data in order to enhance resolution and stability of the inversion results. Due to non-linearity and limited coverage of data acquisition in an MT field campaign, minimizing the error by linearization of the problem in least squares inversion usually leads to an ill-posed problem. In general, an inverse problem is unstable, ill-posed and is characterized by non-uniqueness (Tikhonov et al., 1998). The concept of ill-posed problems goes back to Hadamard (1923). He defined a problem to be ill-posed if the solution is not unique or if it is not a continuous function of the data i.e., arbitrarily small perturbations in the input data can cause great changes in the solution. Hence, in order to stabilize the problem and come to a stable solution, further information should be incorporated. In order to acquire reasonable geoelectrical models, regularization of the problem by imposing definite constraints is necessary. Determination of a suitable Lagrangian multiplier in order to balance minimization of error and model roughness could be a useful approach to achieve both the resolution and the stability in inversion. In order to achieve both the resolution and the stability in least-squares inverse modelling in our study, an intermediate value of the Lagrangian multiplier must be chosen. Too large or small Lagrangian multipliers yield to undesirable effects on resolution and stability. In this paper, the regularization parameter is set by a value from log-linear interpolation (Yi et al., 2003). Where, , and , are minimum and maximum for Lagrangian multipliers and spread function respectively. The regularization parameter can be set optimally by the spread function of the ith model parameter which is defined by the parameter resolution matrix R. The spread function shows how much the ith model parameter is not resolvable and is written as bellow: Where, M is the total number of inversion parameters, is a weighting factor defined by the spatial distance between the ith and jth model parameters, and is a factor which indicates whether the constraint or regularization is imposed on the ith parameter and its neighboring parameters. An alternative to varying the Lagrangian multiplier as the iterations proceed is to use the spatially varying Lagrangian multiplier (Sasaki, 1989). Hence, varying the Lagrangian multiplier by trial and error is preferred to get resolution and stability. Small regularization parameters mean higher resolvable inversion blocks in parameter resolution analysis sense (Menke, 1989). We tested the capability of the Active Constraint Balancing (ACB) approach (Yi et al., 2003) in enhancing the resolving power of least-squares inversion results by applying it on 2D synthetic MT data generated from forward modeling code of Geotools-MT for simple models of the earth and then on the field data. Using ACB approach, the rms error and data misfit is much less than the conventional approach with fixed Lagrangian multiplier, which leads to higher resolving power and the stability of the inversion results. The inversion code which was used in this paper (Lee et al., 2009) consists of finite element for computing 2D MT model responses, and smoothness-constrained least-squares inversion. By comparing the resistivity sections, the anomalous object can be seen much clearer and distinct in the case of ACB approach. This enhancement in the resolution could be well interpreted as the result of using varying Lagrangian multipliers in the smoothness-constrained least-squares inversion using ACB approach.}, keywords = {ACB,Lagrangian multiplier,Least-squares inversion,magnetotelluric,resolution,Stability}, title_fa = {ارتقاء تفکیک‌پذیری نتایج حاصل از برگردان دو‌بُعدی داده‌های مگنتوتلوریک}, abstract_fa = {هدف از این تحقیق ارتقاء تفکیک‌پذیری نتایج حاصل از برگردان به‌‌روش کمترین مربعات داده‌های دو‌بُعدی مگنتوتلوریک با استفاده از یک روش هموار‌سازی جدید است. این روش که متعادل‌سازی فعال نامیده می‌‌شود تلاش می‌‌کند تا با متعادل ساختن قیود در برگردادن به روش کمترین مربعات با توجه به حساسیت یک مسئله‌‌ خاص به ارتقا توان تفکیک و پایداری نتایج حاصل از برگردان بپردازد. برای این کار از یک برنام? از پیش نوشته شده در دو محیط برنامه‌نویسی فرترن و مَت‌لَب استفاده شده است و با ایجاد تغییرات تکمیلی در آن امکان مدل‌سازی داده‌های مگنتوتلوریک و ارزیابی الگوریتم متعادل‌سازی فعال فراهم شده است. با اِعمال الگوریتم برگردان داده‌های مصنوعی مگنتوتلوریک برای مدل‌‌های ساده‌‌ای از زمین و نیز داده‌های صحرایی و مقایسه نتایج حاصل با نتایج برنامه‌‌های برگردان موجود، ارزیابی‌‌های لازم صورت گرفته است. خطای rms و نبود تجانس ناچیز بین داده و مدل به‌دست آمده از این روش، در مقایسه با نتایج حاصل از روش برگردان مرسوم که از ضریب لاگرانژ ثابت در کل فرایند برگردان استفاده می‌‌کند، معلوم می‌‌شود که این روش رهیافتی مفید برای دستیابی به نتایجی با پایداری و تفکیک‌پذیری بیشتر است.}, keywords_fa = {ACB,Lagrangian multiplier,Least-squares inversion,magnetotelluric,resolution,Stability}, url = {https://jesphys.ut.ac.ir/article_30210.html}, eprint = {https://jesphys.ut.ac.ir/article_30210_926fd3964a0fd09939559150b418b968.pdf} }