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Time-domain induced polarization forward modeling and an apparent spectral parameter solution based on the Weibull growth model
Geophysics ( IF 3.3 ) Pub Date : 2020-09-11 , DOI: 10.1190/geo2018-0693.1
Qingxin Meng 1 , Xiangyun Hu 2 , Heping Pan 2 , Huolin Ma 2 , Miao Luo 2
Affiliation  

The application of the Cole-Cole model within time-domain induced polarization (TDIP) forward field modeling shows that the model parameters can characterize time-varying states of the TDIP field and support observed data analysis. The Cole-Cole model contains real and imaginary parts, and it requires a frequency-to-time conversion for TDIP forward modeling. However, the TDIP field is usually expressed by a real number, and its intuitive time-varying states field intensity increases with charging time. Therefore, the forward model should be constructed in a simpler form. We have aimed to develop a forward model using mathematical functions not based on physical principles. The Weibull (WB) growth model, which is primarily used to describe the time-varying curve features in regression analysis, is introduced into the basic algorithm of the TDIP forward model. Subsequently, a forward expression of the TDIP effect is established. Based on the time-varying shape and scale parameters, this expression describes the time-varying rate and relaxation states of the TDIP fields. Furthermore, based on the extensively used conjugate gradient optimization, an apparent WB parameter scheme is initiated to calculate the spectral parameters that represent the relaxation and time-varying rate obtained from the multi-time-channel TDIP data. Finally, this scheme is applied to interpret the different simulated and actual TDIP data. The results demonstrate that the WB growth model can be used for the TDIP forward model without involving physical principles, the model parameters without specific physical significance can be used to represent the time-varying states of TDIP fields, and apparent WB parameters can be used to discern different TDIP observed data. The setting of the TDIP forward model and model parameters can actually be more flexible and diverse, so as to obtain simpler forward expressions and ensure a highly efficient inverse solution.

中文翻译:

基于威布尔生长模型的时域诱导极化正演建模和表观光谱参数解

Cole-Cole模型在时域感应极化(TDIP)前场建模中的应用表明,模型参数可以表征TDIP场的时变状态,并支持观测数据分析。Cole-Cole模型包含实部和虚部,并且需要时频转换以进行TDIP正向建模。但是,TDIP字段通常用实数表示,其直观的时变状态字段强度随充电时间而增加。因此,前向模型应以更简单的形式构造。我们旨在使用不基于物理原理的数学函数来开发正向模型。威布尔(WB)增长模型,主要用于描述回归分析中随时间变化的曲线特征,介绍了TDIP正向模型的基本算法。随后,建立TDIP效应的正向表达。基于时变形状和比例参数,此表达式描述了TDIP字段的时变速率和松弛状态。此外,基于广泛使用的共轭梯度优化,启动了表观WB参数方案以计算代表从多时信道TDIP数据获得的弛豫和时变速率的频谱参数。最后,该方案用于解释不同的模拟和实际TDIP数据。结果表明,WB增长模型可用于TDIP正向模型,而无需涉及物理原理,不具有特定物理意义的模型参数可用于表示TDIP字段的时变状态,而表观WB参数可用于识别不同的TDIP观测数据。TDIP正向模型和模型参数的设置实际上可以更加灵活和多样化,从而获得更简单的正向表达式并确保高效的逆解。
更新日期:2020-09-16
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