The 23 August 2011 Mw 5.8 Mineral, Virginia, earthquake was the largest earthquake in the central and eastern United States in the past 100 years, and it was well recorded by strong motion and broadband seismometers, thus providing abundant ground‐motion data for earthquake ground‐motion studies. The largest recorded ground motion among Advanced National Seismic System stations was at station CBN, but the site effects at station CBN need to be understood because the strong motions recorded there do not represent bedrock site conditions. On the radial component of these recordings, the initial P wave is very weak, and is followed by a strong signal 0.3 s later, which is interpreted to be the S wave converted from the P wave (PS) at the interface between the sediments and bedrock. We first estimate the subsurface shear‐wave velocity by modeling the ratio of the radial to vertical components of the initial P waves, and then resolve the velocity structure and thickness of the unconsolidated sediments by modeling the PS wave. The subsurface shear‐wave velocity is found to be approximately 300 m/s, consistent with field survey results. The shear‐wave velocity at the bottom of the sediments is constrained to be in the range of 320∼780 m/s, from which the thickness of the layer is estimated to be 100∼230 m. The estimates of shear‐wave velocity structure and thickness of the sediments are further improved by modeling the oscillatory waveforms between the P and S waves. This study suggests that site characterization for the estimation of ground‐motion amplification at a site can be achieved inexpensively and noninvasively by modeling local P waveforms recorded at the site.