Finite Difference Algorithm on Non-Uniform Meshes for Modeling 2D Magnetotelluric Responses

Round  1

Reviewer 1 Report

This paper is very interesting, and can be accepted if the revision corresponding to the following comment is made.

More papers should be reviewed, as the problem it self should have deeper backgrounds and there would be a number of related publications.

Some stability analysis, either from theoretical or numerical viewpoints, should be carried out.

Author Response

Responses：

(1)We have added some related publications about 2D magnetotelluric modeling.

(2) The accuracy of the FD calculation for the magnetotelluric responses, including the apparent resistivity and the impedance phase, depends on the vertical grid spacing size near the surface. At the highest frequency, the vertical grid spacing size at earth’s surface must be small enough so that the linear approximation of the electric field is reasonably close to the exponential decay of the electromagnetic fields. Through the numerical calculation in some examples, we introduce that the first vertical mesh size should be satisfied approximately 1/3 of the shortest skin depth of the top layer.

Reviewer 2 Report

In the submitted manuscript the authors present a finite-difference algorithm to solve the Maxwell’s equations for modeling the 2D magnetotelluric response on Earth surface. The algorithm is clear and also accurate by comparing the results from an analytical solution and a finite-element method. The referee believes that this manuscript can be accepted for publication in the journal.

However, before the acceptance, the authors should revise the manuscript according to the following comments:

1.     Describe the condition of the numerical stability.

2.     Derive the analytical result and provide its reference.

3.     Improve the quality of the English writing and check the grammar in the manuscript. For example, a sentence from the abstract “Then we compared to the analytical solutions for the two-layered model, the relative errors of the apparent resistivity and the impedance phase were both increased when the frequency was increased.” does not show the significance of the model; it is not correct in grammar, neither.

Author Response

Responses：

(1) The accuracy of the FD calculation for the magnetotelluric responses, including the apparent resistivity and the impedance phase, depends on the vertical grid spacing size near the surface. At the highest frequency, the vertical grid spacing size at earth’s surface must be small enough so that the linear approximation of the electric field is reasonably close to the exponential decay of the electromagnetic fields. Through the numerical calculation in some examples, we introduce that the first vertical mesh size should be satisfied approximately 1/3 of the shortest skin depth of the top layer.

(2) The analytical result can see magnetotelluric book or reference [14].

(3) We have rewrite some sentances in our revised manuscript.

Round  2

Reviewer 1 Report

The authors addressed good revision of the paper.

The paper can be now accepted.