Inferring Shallow Subsurface Density Structure from Surface and Underground Gravity Measurements: Calibrating Models for Relatively Undeformed Volcanic Strata at the Jemez Volcanic Field, New Mexico, USA

Abstract

Imaging shallow subsurface density structure is an important goal in a variety of applications, from hydrogeology to seismic and volcanic hazard assessment. We assess the effectiveness of surface and subsurface gravity measurements in estimating the density structure of a well-characterized rock volume: the mesa (a small, flat-topped plateau) upon which the town of Los Alamos, New Mexico, USA is located. Our gravity measurements were made on the mesa surface above a horizontal tunnel and underground, within the tunnel. We demonstrate that, in the absence of other geophysical data such as seismic data or muon attenuation, subsurface (tunnel) gravity measurements are critical to accurately recovering geologic structure. Without the tunnel data, our resolution is limited to roughly the surface gravity station spacing, but by including the tunnel data we can resolve structure to a depth of ~ 10 times the surface gravity station spacing. Densities were obtained using both forward modeling and a Bayesian inverse modeling approach, incorporating relevant constraints from geologic observations. We find that Bayesian inversion, with geologically relevant prior, is a superior approach to the forward models in terms of both robustness and efficiency and correctly predicts the orientation and elevation of important geologic features.

Appendix

Model discretization Our forward calculations utilize a very high-resolution model with 1.6 × 10⁵ rectangular prisms (each with area ~ 4² m² in the x–y plane and vertical height = elevation above the minimum elevation of 2089 m) over a region that is 1402.1 m (E–W) by 1909.5 m (N–S). We find that the model results are unchanged if a lower resolution discretization is used (~ 15–25 m horizontal linear dimension of prisms) but the predicted gravity at each station is quite sensitive to the lateral dimensions of the region considered.

For our inverse models, we discretize the terrain into cubical voxels (cells), but limited our calculations to a maximum of 10⁴ voxels to avoid inversion issues for large matrices in Matlab (in our formulation, the only matrix inverse we need to calculate is the inverse of the model covariance matrix, $C_{\text{m}}^{ - 1}$). We do not, however, wish to compromise on the accuracy of the forward-predicted gravity. To understand how best to decimate the LIDAR data (5 points/m²) and optimize the terrain specification for inversion, we explored a range of voxel dimensions and dimensions of the discretized region. Our optimized configuration produces the same predicted gravity at each station as our high-resolution forward calculations, but uses high resolution (16³ m³) in the region containing the stations and lower resolution (200 × 16 × 16 or 200 × 200 × 16 m³) at the edges (Fig. 9).

Fig. 9

Map view (a) and perspective view (b) of our optimized discretization used in the inverse models, where lower left voxel corner locations are indicated (black dots) in relation to station locations (red dots). The dashed red rectangle in (a) indicates the high-resolution part of the model, as depicted in Fig. 8

Fig. 10

Resolution tests for the 3D inverse models with “true” density structure given by a N–S and E–W sinusoidal variation (a–c), with wavelength as indicated (double arrows in a–c). Lower panels show the corresponding recovered density structure for each synthetic (d, e). Each column corresponds to varying spatial wavelength in the true structure but the (isotropic) spatial correlation length, λ, to smooth the model is fixed for all tests. The tests here are designed to illustrate the limitations given our station geometry (white dots = station locations)

Inverse model resolution test and prior We test the ability of the model to resolve lateral variations in density by prescribing a 2D sinusoidally varying density structure: $\rho \left( {x,y} \right) = \rho_{0} \left\{ {1 + A\left[ {sin\left( {\frac{2\pi x}{w}} \right) + sin\left( {\frac{2\pi y}{w}} \right)} \right]} \right\}$, with $\rho_{0}$ = 1400–2100 kg/m³, A = 0.1–0.5, w = 70–700 m.

Using the discretization above, we prescribe the layered prior with a three-layered density identical to the geologically relevant model used in our forward calculation: ρ ₃ = 1850 kg/m³ (uppermost layer, Qbt3); ρ ₂ = 2100 kg/m³ (middle layer, Qbt2); ρ ₁ = 1420 kg/m³ (lowest layer, Qbt1). The prescribed starting elevations of the (initially flat, planar) layer interfaces were: 2180–2200 m for the Qbt3-2 (upper) contact and 2090–2150 m for the Qbt2-1 (lower) contact; our results are insensitive to the starting layer elevations.