ESTIMATING THE UNCERTAINTY OF PASSIVE SEISMIC DATA FOR A DEPTH TO BEDROCK MAP IN BAYFIELD COUNTY WI

The passive seismic method is an effective method for estimating depth to bedrock for water-resources and other geological studies in the Midwestern United States. This method, often called the HVSR (horizontal-to-vertical-spectral-ratio) method, relies on an empirical relationship between the resonant frequency of ground vibrations and sediment thickness. Current investigations in northern Wisconsin provide an opportunity to estimate the uncertainty in depth-to-bedrock measurements using the HVSR technique.

With funding from Bayfield County, the Wisconsin Geological and Natural History Survey is undertaking a county-wide characterization of groundwater resources and contaminant susceptibility. The products of the study include a 1:100,000 depth-to bedrock map. The HVSR method was chosen to aid in this effort because data acquisition is fast, low cost, and has the necessary accuracy for this project. In order to calibrate the HVSR method to the sediment in Bayfield County, 14 measurements were taken within 100 meters of wells with records of depth to bedrock from driller’s well construction reports. Control locations were intentionally selected to encompass a range of depth to bedrock, from 2 to 114 meters. HVSR peak frequencies were plotted against the driller’s records of sediment thickness. A power curve fit to this data identified a relationship between resonant frequency and sediment thickness for the setting in Bayfield County, depth = a (peak frequency) ^b where a = 131.3 and b = -1.236. The error between the power curve fit and the data appear log-normally distributed with an R² value of 0.9028. Confidence intervals based on standard error of this log-normal distribution show that the accuracy of the HSVR method decreases with increasing sediment thickness. At a HVSR peak frequency of 12 Hz, for example, the model calculates depth to bedrock at 6 meters with the 68% confidence interval from 4 to 9 m. At a peak frequency of 2 Hz, the model yields a depth to bedrock of 56 m, with the 68% confidence range between 39 and 81 m. Providing an estimate of error in the observations is useful during map development, in communicating with project stakeholders, and improving the design of other projects that use the HSVR method.