Geophysical correlation: global versus local perspectives

Abstract

AbstractRobust anomalies that point to the same buried features frequently occur in diverse data sets from multi‐method surveys [e.g. ground penetrating radar (GPR), magnetic gradiometry, electrical resistivity]. Relationships between such corresponding anomalies traditionally have been noted subjectively, through visual comparisons of mappings or overlays of geophysical results. These circumstances create a paradox because theory and correlational studies generally suggest largely independent dimensions, while mappings of geophysical results often illustrate parallel anomalies which suggest that robust correlations should exist. Through application of local Pearson's r in small neighbourhoods, with radii ranging from 0.71 to 1.6 m, a means is offered, and demonstrated, to quantify and map local correlations between two geophysical data sets. A case study examines relationships between apparent electrical resistivity, a GPR depth‐slice, and magnetic susceptibility data acquired at Army City, a Great War troop support town in Kansas, now obliterated except for subsurface remains. Intricate spatial patterns of positive and negative correlations between these modalities are illustrated that vary in complexity with neighbourhood size. Neighbourhoods of moderate size seem preferable because the spatial patterning of correlations is enhanced locally and region‐wide. With focus given to positive correlations that point to parallel anomalies, overlays of high correlation frequently correspond with robust anomalies observed in each data set and offer objective criteria for assessments of correlation. However, it is also demonstrated that mutually robust anomalies do not necessarily exhibit high correlation and that high correlations frequently exist in regions devoid of apparent anomalies. The issue of assessing jointly parallel correlations between three or more geophysical data sets is also confronted using a form of local principal components analysis. It is shown that high eigenvalues associated with first principal components that exhibit loadings in the same direction point to zones of mutually high parallel correlation.