نوع مقاله : مقاله تحقیقی (پژوهشی)
1 مؤسسه ژئوفیزیک، دانشگاه تهران، ایران
2 دانشگاه اپسالا، سوئد
عنوان مقاله [English]
There is a set of variables affecting the results of an inversion process. Some effects are negligible while others are significant. It is important to know these essential variables to set them appropriately. In this study, the effect of change in the number and the thickness of the layers, the trade-off parameter, the number of frequencies and frequency content of the signals used for the inversion are studied. Occam’s inversion is employed to reconstruct the resistivity and/or conductivity of the assumed layers.
The thickness and number of layers can affect the recovered model. The best way to choose the number of layers is to increase it until the fitness error flattens. The error decreases, significantly with the inclusion of the first additional layer then in increasingly lesser degrees with subsequent additions, until it reaches a relatively constant level. The number of layers at which it first reaches this constant level is assumed to be the best number. As the number of layers is increased, the original model is modified slightly. On the other hand, the EM signal strength drops exponentially with distance. Hence, it is better to increase the thickness of the lower layers to overcome this decrease. Experience shows that logarithmically increasing thicknesses result in better models. However, if the sufficient number of layers has been chosen, the change in thickness cannot affect the recovered model significantly because a thick layer can be estimated as a sum of thinner layers.
The trade-off parameter has a critical effect on model parameters. It controls whether more weight is given to minimize the norm of the data misfit or model norm. When this parameter is large, the inversion process tends to produce a smoother model and the data misfit becomes less important. On the other hand, when it is small, the data misfit takes over regardless of a priori information. Generally speaking, the best trade-off parameter is considered to be that at which the data fit is satisfying. The results of this paper show that the effect of the changes on the trade-off parameter is significant and if one chooses it inappropriately, the estimated model will fail to represent the true model.
It is clear that the inversion response depends on the number of data used. The more data used, the better the model produced. The values of frequencies used are also important because high frequency data can have information only about surface layers while low frequency data have more information from deeper layers. The effect of the number and values of the frequencies was studied by changing or removing high/low frequency. The results show that the change in frequency content causes a considerable effect on the resolution of inversion.
We also studied the effect of the changes of these parameters on the results of inverting a real data set and the results confirm the effects described in the models recovered.
In brief, we can say that the effects due to changes in the number and the thickness of layers are negligible, but the effects of changes in the trade-off parameter and the number of frequencies are significant.