IMPROVING THE QUALITY OF HVSR REGRESSION EQUATIONS

The horizontal-to-vertical spectral ratio (HVSR) passive seismic method has become a popular technique for determining thickness of unconsolidated sediments overlying bedrock. It has been successfully applied at sites with a high contrast in acoustic impedance between overburden and bedrock to depths of approximately 250 meters. Two formulas are used to compute sediment thickness, and both require determination of the resonance frequency (F_r) from passive seismic data. One formula uses average shear-wave velocity (Vs) whereby the overburden thickness (Z) is computed as Vs/4F_r. In this approach, Vs is assumed to be uniform with depth and location. The other approach involves constructing a power-law regression, Z = C F_r^-a, using a constant (C) that represents average velocity and a negative exponent (a) that controls the slope of the regression line. Using this formula, the Vs can vary with depth depending on the exponent. We propose using both formulas in parallel to help assess the quality of data points and improve the regression equation.

Including additional data-quality assessments after determining the resonance frequency can improve the quality of regression equations. We propose using calculated Vs at each “calibration site” with known depth to bedrock to remove Vs outliers. If the computed Vs for a given data-collection point is outside the expected range, based on other data or published results, the HVSR data should be reinterpreted or removed from the regression. Additionally, calibration points for the regression equation should cover the expected range of depths. Once a regression is constructed, it should make sense for the geologic setting. In most cases, Vs increases with increasing overburden thickness. We demonstrate how (1) the inclusion of a couple of low-quality points can adversely affect regression and computed overburden thickness, and (2) removing these points can improve regression and make better physical sense for a geologic setting.