GeoRes user´s manual:

Electric modelling for a stratified Earth in the iPhone-iPad language

Developed by: Angel Daniel Peralta Castro and

Marco Antonio Pérez Flores

Introduction:

This application is very useful for geophysicists that wants to find water in harvest areas and then to drill

water wells. There are so many applications for this tool. But it can also be applied inside the classroom

for teaching purposes in bachelor and graduate courses in electrical methods in geophysics.

In our Electrical methods course in 2014, we studied the case of modeling over a flat Earth and flat

horizontal multi-layers. When this problem is solved, the electric potential iso-lines are circular in the (x,

y) plane and not-circular in the (x, z). This shows a cylindrical geometry. We can says that electrical

potential has a cylindrical geometry, therefore we solve the Laplace equation for the scalar electrical

potential in cylindrical coordinates. When doing this, the Bessel functions appears. It is usual to solve the

differential equation applying the Hankel transform to the Laplace equation and get a general solution

for the electrical potential in the Hankel domain, then we apply the inverse Hankel transform in order to

get the potential in the spatial domain (original domain). For a multi-layer problem, we assume a

different Laplace equation in every layer. We get a general solutions for the electrical potential in every

layer. Some constants will appear. We got the expression of those constants by applying the boundary

conditions between the layers. For two layers, it can be solved analytically, but for a multi-layers

problem, it must be solved numerically. We applied the Pakeris´ recursive method for recovering the

kernel or the so called resistivity transform for the first layer.

Figure1. The more common arrays used on a layered Earth.

For a pole-pole array (one source-one receiver) the electrical potential is terms of just one invers Hankel

transform. This integral can be solved anyway, but we use the fastest and more accurate methods. We

use the Anderson´s filters that work for order 0 and 1 in the Bessel functions. We use the order 0.

For a tetra-polar arrays (two sources-two receivers), we get an electrical potential transform for every

pair of source and receiver. For the tetra-polar array, we get a combination of 4 potentials (equation 1):

∆� = ����� − ���� − ���� + ���

(1)

Every potential is expressed in terms of the invers Hankel transform of the Kernel � (equation 2). This

kernel is named the resistivity transform. This kernel has the information of the whole set of resistivities

and thicknesses of the layered model. The Bessel function has the information about the distance

between the point source and the point receiver (eg. ���). The variable � is the Hankel variable. It is a

radial spatial frequency.

∆� = � �2� �� � �����

������� −� � ������������

−� � �����

�������

+ � � �����

��������

(2)

The apparent resistivity � is computed after the solution of the four integrals.

� = 2� ∆�� !" (3)

I

A B

∆V

M

a a aN

Wenner

I

A B

∆V

MAB/2

N

Centro

Centro

Schlumberger

∆V

M N

I

A B

a na aCentro

Dipolo-Dipolo

! = # 1��� − 1

���% − # 1��� −1���%

Thanks to the symmetry in the schlumberger and wenner array, we can solve the problem with just two

Hankel transform and three for the dipole-dipole case. But for a non-symmetrical array a 4 Hankel

transform solution is needed. The program we made for the iPhone-iPad language is for non-

symmetrical arrays. So, we can use any known or invented tetrapolar array. The schlumberger case is

very usual for class or even at the field. But other arrays are used mainly in class. That is why, this

program is useful for schlumberger real field projects but also for other array purposes in class.

iPhone-iPad devices are very limited in their hard drive and RAM. However, we made the program so

efficient that the 4 transforms are solved in less than 2 seconds. iPhone-iPad manufacturers made them

in such a way that, we do not have a direct access to their hard drive in order to introduce field data

sets. We have to introduce the field data sets by mean of the Drope Box application.

To use this application you must download the free Drope box application and introduce your filed data

set in the Drope Box. Then you can download the GeoRes application directly from the Appstore. You

will need internet for the very first time to download the GeoRes application. Then, the program will be

installed in your iPhone-iPad hard drive and you will not need internet, unless you need to download a

new data set from your Drope Box.

For testing purposes, we computed the response from a 5 layers model in a program not made by us

and that runs in Matlab and in a desktop. We used that data set for testing the accurate of our

application. The resistivities and thicknesses were recovered. This data set is available in our homepage

http://geoinversion.cicese.mx/geores.

In our homepage you can download FOUR files with a 5 layers example and one field data set. The

example files are for schlumberger array and in the usual format AB/2, MN/2 and apparent resistivity

(file Schlumberger3.dat)

For other academic purposes, we have another data set in the format:

(xA, yA), (xb, yB), (xM, yM), (xN, yN), apparent resistivity (file Schlumberger9.dat). With this 9 columns

format you can use an arbitrary tetrapolar array over a multi-layer model. This is a schlumberger, but

declared as an arbitrary array. It is the same apparent resistivity as Schlumberger3.dat (3 columns

format).

To download the GeoRes program, you must go to the AppStore and type GeoRes in the Search option.

You can do it in any Apple device. The AppStore will show you a resume of the application. The purpose

of this manual is to explain more.

When you find the application in the AppStote, this is the information shown.

After downloading GeoRes, you will find the icon inside the screen of your Apple device, as shown:

Touch the icon once and the first image will appear for three second:

The next image will appear. Now the program is ready to receive instructions. The purpose of the

program is to find the resistivity and thickness of every layer by fitting an apparent resistivity curve. So,

we have first to read an apparent resistivity data set from a Drop Box. This screen shows a plot with the

y-axis as the logarithm (base 10) of the apparent resistivity and x-axis as the log10 (AB/2). In the case of

the schlumberger.

.

You can use your iPhone-iPad vertically, but we recommend to use it horizontally.

Push the DATA button and another screen will appears:

Push the DROPBOX button:

Type the name and your password for your Drop Box account:

You will see the many folders you have. Choose the folder where your data file is located. If you

downloaded the example files from our homepage. Choose your data file or our example file

SCHLUMBERGER3.DAT pushing twice and fast.

Now the data set will be moved thought internet to your iPhone-iPad hard drive. After here your will not

need internet anymore, unless you choose another file from your Drop Box. The information of your file

is shown on the screen. You do not need to specify how many data lines are. You do not need to smooth

the apparent resistivity curve by editing data in the AB/2 overlaps. You can introduce the crude data as

you got from the field. If you want, you can edit your data since your Drop Box.

The screen shows the (x, y) position for the four electrodes A, B, M, N and the apparent resistivity in

ohms-meter. (A, B) are the source electrodes, (M, N) are the receiver electrodes.

Push the GEORES button and you will get the plot of your apparent resistivity field data. This data set

was obtained from another modelling program for a five layer Earth. No error was added. We will try to

fit this curve by modeling.

Push MODEL button and another screen will be shown:

In this screen you will be able to type the resistivity in ohms-m and thickness in meters for the very first

layer. Remember that the procedure is beginning with the first layer, then the second, then the third

and so on.

The next screen will show you the data typed. In this case 10 is the apparent resistivity in ohm-m. The

thickness is stored but not shown, because if you introduce just one layer, the program assume a half-

space with infinite depth. If you introduce another layer, the thickness of the first layer will appear.

This is the fitness with just one layer. You can edit the first layer as many times as you want. The red line

is the response of an infinite depth half-space with 10 ohms-m. A flat red line.

The can declare another layer by pushing the MODEL button:

Now, you have reported in the screen one layer and one half-space. The second layer thickness is stored

but not shown. You can introduce the data for the other layers without looking the fitness, but it is not

recommended.

In this screen you can edit any layer. Just put your finger on the right side of the first row and drag it to

the left and the EDIT and DELETE buttons will appear. If you select EDIT, you can edit the resistivity

and/or the thickness. If DELETE, that layer will dessapear.

You can also edit the second layer.

Let’s continue. Push the GEORES button and you will see the fitness. The red line is the response for a

model with one layer and a half-space. Remember the axis are in base 10 logarithm.

Now we can declare the third layer by pushing the MODEL button.

The screen will show you the information for a model with two layers and one half-space. Again, the

third layer thickness is stored but not shown.

Here is the response for a model with two layer and one half-space.

We can introduce the layer four by pushing the MODEL button.

You get a report of your current model. In this screen you can edit any layer.

This is the response for a model with three layers and one half-space.

We can declare the layer number five.

The report and the opportunity to edit.

This is the fitness for a model with four layers and one half-space.

We have finish. The fifth layer thickness is assumed infinite. So the fifth layer thickness is not taken into

account for the model calculations. So any value can be introduced.

You can continue introducing more layers if you want, but this curve was already fitted.

When you push GEORES button, the four integrals are computed inside the RAM of your iPhone-iPad.

New iPhone-iPad versions will execute the calculations faster.

Fitting other arrays

This section is for fitting non-conventional arrays. We show you our Dropbox screen with the files

available for fitting.

The Sclumberger3.dat is a file that we made with a synthetic model of 5 layers in a desktop. It is the one

used for the example described before. Schlumberger9.dat is the same date set, but with the 9 columns

format; (xA, yA), (xb, yB), (xM, yM), (xN, yN), apparent resistivity. This format give us lots of flexibility. By

instance you can make the same procedure described before but with this data set. You will not see the

difference, only you see the file since the Dropbox.

Our schlumberger files are for AB=4MN. Some says that approximation works for AB>5MN. Our Wenner

file is designed for AB=3MN. That means that Wenner and Schlumberger curves should be very similar.

As you can see in the next picture (Schlumberger, black; Wenner, red).

Figure 2. Apparent resistivity logarithm vs. pseudo-depth logarithm for Schlumberger (black line),

Wenner (red line), dipole-dipolo (blue line) and dipole-dipolo in V (green line).

In our Dipolo-dipolo file, the dipoles are spreading away from the center (figure 3). We also makes that

dipole distance (a) be larger as distance from the center increases (blue line in figure 2).

Figure 3. Dipole-dipole array spreading away from the center. Value a increases with the distance.

We also are trying with a non-collinear array. We designed an array similar to dipole-dipole but

perpendicular and spreading away from in a V way from the center as shown in figure (4). Here we are

also increasing (a) as the distance from the center increases.

Figure 4. Dipole-dipole array spreading away in V from the center. Value a increases with the distance.

These four non-conventional arrays can be downloaded in your iPhone-iPad device and fitted layer by

layer. Always beginning with the first layer.