# Partial coherence¶

The bivariate coherence between inputs H_{x} and H_{y} and output E_{x} is given by:

When there is a strong linear relationship between the inputs H_{x} and H_{y} and output E_{x}, this ratio is close to 1. However, when there is no such relationship, this ratio is closer to 0.

Simarly, for E_{y}, the equation is:

The value can be interpreted in a similar way.

In general, good magnetotelluric data follows a strong linear relationship such that bivar_{x} and bivar_{y} should both be close to 1.

Partial coherences measure the linear relationship between two signals after the influence of a third signal has been removed. For example, to find the partial coherence E_{x} H_{y}, the inluence of H_{x} needs to be removed. This is done as follows:

Where coherence_{xx} is the standard coherence between E_{x} and H_{x}.

Here, the influence of H_{x} on the linear relationship between E_{x} and H_{y} is being removed. However, in most situations, the coherence between E_{x} and H_{x} is small due to induction of perpendicular currents. Therefore, partial coherences for magnetotellurics tend to give similar results to bivariate coherence and even standard coherence.

Important

The resistics name for the parital coherence statistic is: **partialCoherence**.

The components of the partial coherence statistic are:

bivar E

_{x}bivar E

_{y}par E

_{x}H_{x}par E

_{x}H_{y}par E

_{y}H_{x}par E

_{y}H_{y}

An example of bivariate and partial coherence statistics are shown below. The values plotted here suggest a noisy measurement.

The same plots are shown below for another measurement sampled at 128 Hz. Here, the bivariate and partial coherences suggest good data quality in the evenings, after 16:00. However, even after this time, there is still scatter that could be removed using masks.