The direction–correction tilt test: an all-purpose tilt/fold test for paleomagnetic studies

The tilt or fold test in paleomagnetism is used to infer whether paleomagnetic remanence was acquired before or after tectonic tilting. While several tilt test formulations have been proposed, none fully satisfies the requirements of statistical validity, applicability to all bedding geometries, and ease of use. This paper introduces the direction–correction (DC) test, which examines the relationship between the paleomagnetic site mean directions and their corresponding bedding tilt corrections. The DC test is similar to McFadden’s correlation test because both test whether or not the site directions contain information about the bedding tilts, however the DC test gives greater weight to sites with greater counter-bedding. The DC test is similar to Watson’s numerical tilt tests because they determine the degree of untilting which gives optimal concentration of site directions, however the DC test uses analytical rather than numerical methods. Graphical output aids the researcher in recognizing problem sites. Using both real and simulated data, the DC test is demonstrated to be more discriminating than other tilt test formulations for all bedding geometries. The simulations show that the power of the tilt test is inversely proportional to the 95% confidence interval (α95) of the overall mean. As a rule of thumb, paleomagnetists should attempt to sample sufficient sites to obtain an α95 less than 1/6 of the bedding attitude difference.