Building a large-scale surface gravity network in Colombia using highly redundant measurements

2.1 The OSU field protocol

The Colombian gravity network was strictly surveyed using the “OSU protocol.” This protocol comprises four main steps: (1) a preliminary study based on the analysis of topographical maps, satellite images, road maps, seasonal precipitation and temperature outlooks, etc., to anticipate potential challenges, such as road closures, adverse weather conditions, safety hazards, and logistical difficulties, (2) a reconnaissance pass to be conducted weeks before each campaign to evaluate road conditions, locate survey markers, estimate travel times, and assess sky visibility for optimal GNSS positioning, (3) the forward-reverse gravity survey along gravity lines (Figure 1b) to ensure high observational redundancy, and (4) a GNSS survey to obtain accurate station coordinates at those sites lacking prior geodetic positioning.

The OSU methodology also requires the instruments to be serviced regularly and subjected to periodic calibration tests. During the project period in Colombia, we conducted two calibration surveys involving one gravity line between two AG stations in Bogotá and Honda (∼160 km), and a shorter line (∼50 km) covering three AG stations in the Bogotá area.

2.2 Two-step least-squares adjustment

The adjustment approach to produce the gravity solution consists of two sequential steps. The first step involves adjusting gravity lines individually for each gravimeter, using raw readings and measurement times. This step ensures consistent and redundant estimates of Δg values between consecutive stations along a gravity line. The adjusted Δg values serve as the primary input for the second stage of adjustment.

The network adjustment, or second-level adjustment, integrates the AG observations with the Δg values of the gravity lines. The AG values are introduced as constraints to resolve the rank deficiency inherent to relative gravimetry. In this step, we apply a weighting scheme based on gravimeter performance and an iterative reweighting procedure to mitigate the effects of outliers. Section 6 of Sobrero et al. (2024) provides a detailed explanation of the adjustment methodology, the weighting scheme, and the reweighting process.

2.3 Gravity stations

Most RG measurements were taken at existing topographic benchmarks from Colombia’s National Geodetic Network (Red Geodésica Nacional), primarily distributed along the country’s road system. Using existing monuments instead of building new ones reduced the overall project costs and minimized the need for additional GNSS surveys. The benchmarks’ coordinates were previously determined by IGAC through static GNSS occupations, processed using reference stations from Colombia’s Continuous GNSS Network (Red Activa GNSS) following IGAC’s guidelines (IGAC 2024).

To further ensure coordinate accuracy, we reprocessed the benchmarks’ raw GNSS data using three independent services: the Precise Point Positioning (PPP) service from Natural Resources Canada, CSRS-PPP, provided by the Canadian Geodetic Survey, and two online differential positioning services, AUSPOS, from Geoscience Australia, and OPUS (On-line Positioning User Service) provided by the National Oceanic and Atmospheric Administration (NOAA) – National Geodetic Survey (NGS). We assessed the consistency of the results as an indicator of coordinate reliability. The OSU protocol requires a height precision of 0.20 m for gravity stations. Benchmarks showing discrepancies beyond this threshold among the different solutions (PPP, online differential, and IGAC) were flagged for further investigation. If the source of the inconsistency remained unclear, we conducted new GNSS occupations lasting at least 2 h. This session length ensures the target precision in low-latitude regions when processed with online differential positioning services (Eckl et al. 2001; Soler et al. 2006) and post-processed PPP services (Diouf et al. 2023; Grinter and Janssen 2012; Kurtz et al. 2024; Shouny and Miky 2019).

3.1 Leveraging the strengths of automatic and manual instruments

Automatic gravimeters, such as the Scintrex CG-5 and CG-6, are among the most sensitive field gravity meters, offering advantages such as ease of use, high repeatability and stability, digital data logging, and rapid measurement acquisition. However, in high-noise environments – such as our study sites near heavy-traffic roads – background vibrations can severely degrade reading repeatability (Aly et al. 2020; Timmen et al. 2020). When disturbances are significant and persistent, even leveling the instrument may become challenging, or not possible at all. Hence, user manuals advise against using these instruments near such noise sources (Scintrex Limited 2012).

Another limitation under these conditions is that Scintrex gravimeters record measurements at fixed intervals (e.g., 1 Hz), limiting operator control over measurement timing. Conversely, manual gravimeters, such as the widely used LaCoste and Romberg (LCR), though less sensitive, tend to perform better in high-traffic areas since operators can time their measurements manually and wait for disturbances to pass before taking their readings (Figure 3). The OSU protocol’s 5 min timeframe for completing three LCR measurements (Section 4) allows operators to record readings at strategic intervals within this window, taking advantage of the brief moments between passing vehicles rather than requiring continuous quietness.

Figure 3

RG measurements at contrasting environments showing the effect of traffic-induced noise on instrument performance. Panel (a) shows boxplots of readings from three noisy stations (xc19, xc20, xc39) located 5–10 m from heavy-traffic roads. Panel (b) shows boxplots of readings from three ‘quiet’ stations (xc28, xc14, xc58), either located far from roads or occupied during periods of minimal traffic. All readings are shown after removing their respective average to enable the comparison across instruments and sites. Statistics are computed from 24 Scintrex and 9 LCR readings for panel (a), and 22 Scintrex and 9 LCR readings for panel (b). Boxplots show median (central mark), 25th and 75th percentiles (box edges), and extreme values excluding outliers (whiskers). Instruments: Scintrex CG6 #19100211 and LaCoste & Romberg (LCR) #268.

In Colombia, we employed a combination of automatic and manual gravimeters to leverage their strengths and create a complementary measurement system that optimized data collection across different site conditions. The simultaneous deployment of both instrument types provided valuable cross-validation capabilities and improved error detection. This approach was possible due to the flexibility of the OSU protocol and GRAVITAS, which support multiple gravimeter models. Over the course of 3 years, we employed a total of ten RG meters: eight LCR Model G units (#59, #171, #268, #710, #810, #845, #1024, and #1025), and two Scintrex CG-6 units (#19100211 and #23030503). Integrating both gravimeter types proved valuable, enhancing data reliability throughout the surveys.

3.2 Increasing instrumental redundancy

Detecting measurement errors with a single relative gravimeter requires care even when observing all stations in the forward and backward directions, and it is nearly impossible when using the more traditional occupation pattern. Without an alternative dataset to compare against, anomalous readings may be indistinguishable from accurate ones, and systematic errors may affect all measurements in a consistent but undetectable way. Using two gravimeters can reveal discrepancies, but determining which instrument is erroneous is often challenging. Therefore, increasing the number of gravimeters in a survey improves reliability by providing redundancy and enabling cross-validation. However, there is no single standard for the optimum number of gravimeters to be used in gravity surveys, and different agencies follow their own best-practice guidelines. For instance, Argentina’s first-order gravity network was measured entirely using three gravimeters (Antokoletz 2017) while lower-order lines employed as few as one. In Mexico, the Instituto Nacional de Estadística y Geografía (INEGI) requires two gravimeters for first-order lines (INEGI 2015), while NGS in the United States and the Instituto Brasileiro de Geografia e Estatística (IBGE) in Brazil recommend, but do not mandate, the use of three instruments for high-precision stations, and one for “densification stations” (FGCC 1984; IBGE 2017).

Since our surveys took place in high-traffic locations, we significantly increased the number of gravimeters used at every gravity line to produce a massive observational redundancy, complementing our strategy of diversifying instrument types (Section 3.1). Among the 117 gravity lines measured in Colombia, the majority (77%) were surveyed using four gravimeters, while 10% utilized five instruments, another 10% used three, and just 3% relied on two gravimeters (Figure 4). Notably, no lines were surveyed with just one instrument. This level of redundancy allowed us to identify reading blunders and systematic errors and mitigate the impacts of traffic-induced noise.

Figure 4

Map of the Colombian gravity network totaling 117 gravity lines, color-coded by the number of gravimeters used in each line. The bar plot in the bottom right corner indicates the number of lines surveyed with each gravimeter count.

4.1 RG measurements

All RG readings were recorded on GNSS-enabled tablets using the Android application Log4G, developed by OSU and made publicly available at https://github.com/lateral-search/Log4G. This app performs real-time line-closure checks and automatically captures timestamps from the tablet’s clock, expediting field data collection and minimizing the occurrence of errors from manual input and transcription.

The OSU protocol requires operators to take three RG readings, which are then averaged and corrected for calibration and tidal effects to produce one ‘reduced’ RG measurement (see Figure 5 in Sobrero et al. 2024). Data quality is assessed by evaluating the standard deviation of the readings at each site to detect and exclude blunders before computing the mean. For LCR meters, three readings were taken within a 5 min period. For the Scintrex CG-6 instruments, IGAC’s operation manual specifies six measurements (increased to ten measurements at high-noise locations) at 1 min intervals. To ensure compatibility with OSU’s gravity processing software GRAVITAS, which requires three input values, the Scintrex data were processed by sorting the measurements in ascending order, averaging the middle two values, and using these two values, along with their average, as input in GRAVITAS.

During the measurements, all instruments were located within 1.5 m of the station monument and operated nearly simultaneously. This maximum horizontal separation is in line with standards for microgravity surveys (ASTM International 2018; EPA 2016; Kennedy et al. 2021). Gravity variations over such short distances (Röder and Wenzel 1986) can be considered negligible relative to the expected measurement precision of 0.06 mGal for relative gravimeters operating in field conditions (i.e., vehicle transport on rough terrain, station separation >10 km, large gravity differences, and altitude variations). Following the OSU protocol, each gravimeter had a single designated operator throughout each measurement campaign. For a step-by-step description of the data collection process, the reader should refer to Section 4 of Sobrero et al. (2024).

4.2 AG measurements

In 1995, the US Defense Mapping Agency, in collaboration with IGAC, established three AG stations in Colombia, identified as Bogotá 9801, Honda 9802, and Cartagena 9803, and their respective eccentric stations, 9801-R1, 9802-R1, and 9803-R1. These stations were measured with an AXIS FG-5 gravimeter, achieving precisions of 2, 14, and 34 μGal at the main stations and 3, 15, and 35 μGal at their respective eccentric stations (IGAC 1998; Martínez et al. 1995). By 2021, when the OSU-IGAC partnership began, only the stations in Bogotá and Honda (both main and eccentric) remained in suitable condition to be incorporated into the new network. At that point, the eccentric stations were assigned new names: xc01 (formerly 9801-R1) and xb12 (formerly 9802-R1).

In 2022, IGAC expanded the AG network in collaboration with the Servicio Geológico Colombiano (SGC), the Géosciences Environnement Toulouse laboratory (GET), the Institut de Recherche pour le Développement (IRD), and the International Gravimetric Bureau (BGI), and renamed it as “Red de Gravedad Absoluta para Colombia” (RGAC). Over the course of 1 month, 25 new AG stations were established using an A10 absolute gravimeter (#014) with an average precision of 11 μGal (Matiz-León et al. 2022). The measurement procedure consisted of repeated sessions (sets) of multiple drops, ranging from 60 to 100, depending on noise levels. All measurements were processed using Micro-g LaCoste’s “g” software and corrected for the effects of Earth tides (ETGTAB model, Tamura 1987), ocean loading (Schwiderski model, Schwiderski 1980), atmospheric pressure, and variations in polar motion. Half of the stations were monumented with concrete blocks (60 cm × 60 cm × 60 cm, with 20 cm above the surface), featuring a stainless steel rod at its center and a stainless steel plate showing the station’s name. The remaining monuments consist of a nail embedded in a concrete surface with a stainless steel plate indicating the station’s name. Of the 25 new AG stations, 18 were incorporated into our gravity solution. The remaining seven stations are located in remote areas and have not yet been integrated into the RG network. Together with the four original stations (9801, 9802, xc01, and xb12) the gravity network presented in this work includes 22 AG stations (Figure 2). Because the four older stations were measured decades ago and might be detecting gravity changes, their uncertainties were conservatively set to 30 μGal in the network adjustment, three times that of the new AG stations. This increased uncertainty has the effect of reducing their weight in the network adjustment.

5.1 Validation and accuracy assessment

To evaluate the robustness of the network adjustment, we performed a leave-one-out cross-validation (LOOCV) test, as we did previously in Bolivia. This approach consists of sequentially removing each of the 22 AG constraints, one at a time, and re-adjusting the network using the remaining 21 constraints. The estimated gravity value at the excluded station is then compared with its known “true” value, producing a residual. Repeating this process across all AG constraints provides an unbiased assessment of the gravity solution.

The results presented in Figure 9 show that all LOOCV residuals are statistically indistinguishable from zero at the 95% confidence level, demonstrating the method’s capability to accurately predict AG values at stations surveyed using the OSU protocol. The standard deviation of the residuals (0.04 mGal) is a direct measure of the network’s accuracy. This value is consistent with the typical uncertainty level of the gravity solution (Figure 6), confirming that the adjustment uncertainty estimates are realistic. Furthermore, the mean residual of 0.008 mGal indicates minimal systematic bias in the method. This level of agreement between the predicted and true values demonstrates that massive observational redundancy and strict implementation of the OSU protocol yield a robust network solution with high internal consistency, as well as accurate gravity estimates.

Figure 9

LOOCV test results. Residuals correspond to the difference between the estimated gravity value at each station and its measured AG value. Estimates were obtained by re-adjusting the network with the constraint at the target station removed while keeping the constraints at all other AG stations. Error bars indicate uncertainties, calculated as the square root of the sum of the squared AG uncertainty and the squared estimated relative uncertainty, reported at a 95% confidence level. The dashed line represents the zero-residual baseline. The AG station locations are shown in Figure 7.

Among all stations, xe10 exhibits the largest residual and highest uncertainty. This can be attributed to its position at the end of a “hanging” line (i.e., a gravity line that is not part of a closed loop and does not end at an AG station), where random-walk-type errors accumulate along a chain of survey lines, allowing larger biases to develop. Moreover, as an edge station, its gravity estimate is inherently less constrained and more uncertain, underscoring the importance of strategically positioning AG stations to limit error propagation and enhance the stability of the network solution.