We corrected the gravity values collected in the Berkeley Hills for latitude variations using the WGS84 ellipsoidal gravity formula (45) to create latitude-corrected gravity anomalies. Furthermore, we corrected these gravity anomalies for the effects of terrain using a National Elevation Dataset 1–arc sec (~30 m) digital elevation model and the Plouff approach (46). The terrain correction was calculated in an annulus around a gravity station, with an inner radius of 50 m and an outer radius of 166.7 km, per standard practice. Most of the variability in the terrain correction among these stations arises from the terrain variability within 5 to 10 km of the stations. The local terrain is rougher at higher elevations in the Berkeley Hills than near their base, and local terrain effects always add to gravity (36). Hence, accounting for the terrain will yield a VGG that is smaller than the measured gradient and that can be used to estimate the density of the terrain via the Nettleton method (47). We first calculated terrain corrections using the standard density reduction value of 2.67 g/cm3 to modify the measured VGG. This terrain-corrected VGG implies a density of the Berkeley Hills to be about 2.0(2) g/cm3. Then, we recalculated the terrain corrections using that density to get a new terrain-corrected VGG that again implies a density value of 2.0(2) g/cm3.

To verify the measurement accuracy, we referenced to the gravity stations that were collected in 1998 by the USGS at 10 sites (37) along the same roads in the Berkeley Hills as our mobile atomic gravimeter. In (37), the 10 stations have the prefix of “98rp” and are numbered 094, 095, 096, 097, 149, 150, 151, 152, 161, and 162. The VGG and estimated terrain density values from these stations are 0.221(10) mGal/m and 2.1(2) g/cm3, respectively, which are equivalent within uncertainties to the values determined from the mobile atom gravimeter.

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