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7 Additivity check statistics

Additivity checks

An additivity check is a repeat demagnetization step to test the validity of Thellier's law of additivity (Krása et al., 2003). In the course of a paleointensity experiment, a pTRM at temperature $T_j$ is imparted, pTRM($T_j$, $T_0$), where $T_0$ is room temperature. An additivity check demagnetizes pTRM($T_j$, $T_0$) by heating to $T_i$, where $T_i < T_j$. The remaining pTRM (pTRM($T_j$, $T_i$)) is subtracted from the previous pTRM acquisition step, pTRM($T_j$, $T_0$), to estimate pTRM$^*$($T_i$, $T_0$). That is $$pTRM^*(T_i, T_0)=pTRM(T_j, T_0)-pTRM(T_j, T_i)$$ where * denotes an estimated value. This estimated value can be compared with a previously observed value of pTRM($T_i$, $T_0$) that was measured earlier in the experiment. The difference between the estimated and observed pTRMs is a measure of the violation of additivity between $T_i$ and $T_0$. The additivity check difference ($AC_{i,j}$) is the scalar intensity difference between the two pTRMs: $$AC_{i,j}=pTRM^*(T_i, T_0)-pTRM(T_i, T_0).$$ For an additivity check to be included in the analysis, both $T_i$ and $T_j$ must be less than or equal to $T_{max}$.

 

Statistic: $n_{Add}$

The number of additivity checks used to analyze the best-fit segment on the Arai plot (i.e., the number of $AC_{i,j}$ with $T_i \leq T_{max}$ and $T_j \leq T_{max}$).

 

Statistic: $\delta{AC}$
Report to 1 d.p.

The maximum absolute additivity check difference normalized by the total TRM (obtained from the intersection of the best-fit line and the x-axis on an Arai plot; Leonhardt et al., 2004a). $$\delta{AC}=\frac{\max{ \left\{ \left| AC_{i,j} \right| \right\} }_{i \leq end \textbf{ and } j \leq end}}{\left|X_{Int.}\right|}\times{100}.$$