SciFigs: Curve Browser

Loading curves

Click on Load button

• Load a dispersion curve from a text file (e.g. Test_Rayeigh_2modes.disp). It is a theoretical curve computed using tutorial Computing a theoretical dispersion curve.

Note: you can load as many curve as you want. However, you MUST keep only the curves that you want to invert. PLEASE do not forget to REMOVE the Data Sets you do not want to be used in the Inversion.

Loading a curve

By pressing button Load a pop up window appears and you can select the ASCII file that has in a multi-column file format the Dispersion Curve information.

Accepting different information from the multi column a curve

After you select the file and press Open another window appears where you can define the type of information you have in each column. If it is necessary you can even skip a column. Through the same tool/window you can specify:

• Lines : the starting and ending line that you want to import. Additionally the Accept (not defined as a default) and Reject (# is the default descriptor) pattern.
• Columns : the delimiter (space is the default) for the different columns (Tab, Space or user specific) or specify the Width of each Column.
• Sections : a new section each time the parser encounters a pattern (# is the default), after reading a specific number of lines or/and columns or after you specify a pattern you find a number of matches in a column.

Finally one can specify to use the same parser for the next files when he has to import more files or Save the parser for later use by pressing the Load button.

Clearing curves

You can also associate a special color, pen and symbol to each curve with the Legend button. Naming curves with unique names might be also useful.

Averaging or merging curves

Once you have at least two curves loaded, you can select the following action to average or merge several curves. A dialog box lets you select the curve to average or merge. Merging applies to non-overlapping frequency ranges, average applies to overlapping ranges. Both actions are automatically performed. If more than two curves are selected, curves are averaged or merged one by one using the same process:

• Build a vector with X values from the two curves.
• Resample both curves with this common X sampling.
• For each X value and for both curves, we have mean, variance, and weight (number of values used to compute statistics)

${\begin{array}{ll}\mu ^{(1)},\sigma ^{(1)},w^{(1)}\\\mu ^{(2)},\sigma ^{(2)},w^{(2)}\end{array}}$

Where:

${\begin{array}{lll}\mu ^{(j)}&=&{\frac {\sum _{i=1}^{w^{(j)}}{s_{i}^{(j)}}}{w^{(j)}}}\\\sigma ^{(j)}&=&{\frac {\sum _{i=1}^{w^{(j)}}{(s_{i}^{(j)}-\mu ^{(j)})^{2}}}{w^{(j)}-1}}\\&=&{\frac {\sum _{i=1}^{w^{(j)}}{[(s_{i}^{(j)})^{2}+(\mu ^{(j)})^{2}-2s_{i}^{(j)}\mu ^{(j)}]}}{w^{(j)}-1}}\\&=&{\frac {\sum _{i=1}^{w^{(j)}}{(s_{i}^{(j)})^{2}}+w^{(j)}(\mu ^{(j)})^{2}-2\mu ^{(j)}\sum _{i=1}^{w^{(j)}}{s_{i}^{(j)}}}{w^{(j)}-1}}\\&=&{\frac {\sum _{i=1}^{w^{(j)}}{(s_{i}^{(j)})^{2}}+w^{(j)}(\mu ^{(j)})^{2}-2w^{(j)}(\mu ^{(j)})^{2}}{w^{(j)}-1}}\\&=&{\frac {\sum _{i=1}^{w^{(j)}}{(s_{i}^{(j)})^{2}}-w^{(j)}(\mu ^{(j)})^{2}}{w^{(j)}-1}}\end{array}}$

$w^{(j)}$ is the weight or equivalently the number of items in the statistical population used for the computation of $\mu ^{(j)}$ and $\sigma ^{(j)}$. $s_{i}^{(j)}$ is the ith item in population j.

The mean and variance computed over the whole population is then:

${\begin{array}{lll}\mu &=&{\frac {\sum _{i=1}^{w^{(1)}}{s_{i}^{(1)}}+\sum _{i=1}^{w^{(2)}}{s_{i}^{(2)}}}{w^{(1)}+w^{(2)}}}={\frac {w^{(1)}\mu ^{(1)}+w^{(2)}\mu ^{(2)}}{w^{(1)}+w^{(2)}}}\\\sigma &=&{\frac {\sum _{i=1}^{w^{(1)}}{(s_{i}^{(1)})^{2}}+\sum _{i=1}^{w^{(2)}}{(s_{i}^{(2)})^{2}}-(w^{(1)}+w^{(2)})\mu ^{2}}{w^{(1)}+w^{(2)}-1}}\\&=&{\frac {\sigma ^{(1)}(w^{(1)}-1)+w^{(1)}(\mu ^{(1)})^{2}+\sigma ^{(2)}(w^{(2)}-1)+w^{(2)}(\mu ^{(2)})^{2}-(w^{(1)}+w^{(2)})\mu ^{2}}{w^{(1)}+w^{(2)}-1}}\end{array}}$

Table with Curve data

Curve Browser

All curves loaded or created so far are displayed on the attached plot (right hand side). Only one curve is shown in the Table (gray frame) each time (left hand side). To change the active/shown curve, move the horizontal scroll bar above the Table entitled Curve Data. The title of the frame just below the scroll bar give the index and the total number of available curves. All items within this frame Curve 1 of 2 apply to the current curve:

• Values of each parameter are given in the table and you can define if set of values for any frequency is valid, to be used, or not
• The curve Name as defined from the Filename when we imported the ASCII data file
• Visible button that could be used to remove the line from the graph on the right hand side of the window. Be careful this does not exclude the curve from further calculations it is just a visualization trick, that is very handy. You need to use from Actions (see below) REMOVE to exclude the Data from the group of curves to be used
• menu Actions

Actions

List of available actions for the current curve

Save

Saves current curve to a text file made of 4 columns: frequency, slowness, standard deviation and weight. The log is save as comments before the curve samples.

Log

Shows a log of all actions performed on the current curve.

Remove

Removes the current curve from the plot

Resample

Reorganize sampling of the current curve. Samples can be distributed on a log, linear or curvilinear scale. You can define any frequency range even outside the current available range. In this later case, samples are extrapolated and set as invalid. If the defined range is smaller than the current range, outside samples are not affected. To remove them use Cut.

Cut

Removes all samples outside a defined frequency or period range.

Smooth

Smooths the curve... currently not implemented.

Manual editing

You can edit all values like in a usual work sheet.

If you want to set the same value to several rows:

• Selected the rows (by clicking on the left header to select the full row)
• Edit one cell of the selection
• Hit enter or move to another cell to validate
• A dialog box should pop up asking if you want to extend the edition to all other selected rows.