# Statistical Analysis of Synthetics

It is possible to analyse synthetics misties of the wells in the Synthetics Analysis Table.

This feature allows you to analyse the misties between the well synthetics and seismic synthetics in a table that displays attributes including Correlation Coefficient, Misfit, SNR, Shift, Phase, and Scale. The time range which the values are measured over is displayed in the table under the TWT Range column. You can adjust the time range by changing the default window of interest or specifying a window of interest for a particular well (see Default Window Of Interest and Overriding the Window of Interest).

You can also view the Correlation Coefficient (CC) vs Phase Rotation and CC vs Bulk Shift graphs for a range of phase rotations and bulk shifts. The graphs allow you to analyse the optimum phase rotation and bulk shift in synthetics.

## Analyse synthetics misties 1. In the Synthetics window, open the Synthetic tab.
2. Under the Analysis section, click Show Analysis Table. The Synthetics Analysis Table, the CC vs Phase Rotation and CC vs Bulk Shift graphs will be displayed.

Note: Alternatively, click on the View menu in Insight's Control Panel and select Synthetics Analysis Table.

As you adjust the wavelet parameters in the Wavelet tab in Insight’s Control Panel, other parameters in the Synthetic and Well tabs in the Synthetics window, and/or edit the checkshots as part of the quality checking measures, the Synthetics Analysis Table and the correlation coefficient graphs will be updated interactively.

At the bottom of the Synthetics Analysis Table, set the maximum shift to be displayed.

### Statistical Calculations (Table)

Correlation coefficient is:

• Calculated from the cross correlation of synthetic and seismic
• The values range between -1.0 and 1.0 whereby
• Correlation of 1.0 shows a perfect positive correlation
• Correlation of -1.0 shows a perfect negative correlation
• Correlation of 0 shows strong mismatch

Misfit is defined as:

• Misfit (%) = 100 * ( RMS(residual) / RMS(seismic trace) )
• The smaller the misfit value, the better is the match

SNR is defined as:

• SNR = 20 * log10(RMS(seismic) / RMS(residual))

Δ Shift (ms) is calculated as:

• The peak time of the envelope of the seismic-synthetic cross-correlation
• This is the suggested value to add to the wavelet lag in order get a good match

Δ Phase (°) is calculated as:

• The instantaneous phase of the seismic-synthetic cross-correlation at the current time-shift
• This is the suggested value to add to the wavelet phase in order get a good match

Δ Scale:

• This is the suggested value to multiply to the wavelet scale in order get a good match

## Well correlation graphs

These graphs show the correlation between the synthetic and seismic as different phase and time shifts are applied.

• Current Well: Select the well to evaluate. The synthetics window is updated to match the selection.
• Camera icon: Click to capture a screenshot of the window (see Taking Screen Captures).
• Green/amber circle: Click to hide or display the correlation curves for individual synthetic tests.
• Colour patch: Click to assign the line colour for a synthetic test.
• CC vs Phase shift graph: The graph peak correlation indicates the phase which must be added to the current wavelet, to optimise the seismic-synthetic tie, at the current wavelet / checkshot times.
• CC vs Time shift graph: The graph peak correlation indicates the time lag which must be added to the current wavelet, or bulk shift applied to the checkshots, to optimise the seismic-synthetic tie, at the current wavelet phase, over the current analysis window.

## Explanatory and QC notes

1. The phase and time shifts are that which are required to be added to the current wavelet, to optimise the tie. For example, a wavelet of phase -45 degrees from true, and lag/checkshots -10 ms from true, will indicate a delta-phase and delta-time of +45 degrees and +10 ms.
2. The optimum tie, from a phase/time perspective, should achieve:
1. Near zero delta phase and time values in the table
2. Peak of the phase and time correlations centred at zero and symmetrical about negative and positive lags in the graph

Naturally other considerations and QCs are essential, including : seismic processing / wavelet polarity, wireline log / wellbore integrity, checkshot/sonic drift and seismic/well marker match.

1. Due to the equivalence between phase and time shifts, the graph peak correlation will not necessarily match those values indicated in the table. Moreover, the table values are calculated instantaneously, at a coincident state, whereas the graphs phase and time shifts are demonstrated independently of each other.

## Example

Figure 1 shows an example of a wavelet extracted from a perfectly matched seismic to synthetic trace. The wavelet has 0 lag and 0 phase shift.

The table shows near zero delta time and phase. The graph shows a peak of time and phase centered at zero and a symmetrical graph.

Figure 2 shows the effect of wrongly introducing a 5 ms shift to the wavelet. Graph shows a 60 degree phase shift to optimise tie when a 5 ms time shift is introduced.

Figure 3 shows that when the timing is wrong, compensating the 60 degree phase shift in the wavelet can wrongly compensate the graph and is shown through the table. In addition, it will also show up in the time shift correlation graph as an asymmetrical shape.