A Geophysical Gravity Survey Of The Durham Area: Analysing The Butterknowle Fault

Abstract

The Butterknowle fault does not provide a sufficient anomaly to account for that which was observed in the survey. The large gravity anomaly cannot have been caused by the fault alone and as such further subsurface structures must be present. Through direct and indirect methods of interpretation, we suggest that a thickening of the Carboniferous limestone succession to the south of the fault, potentially also with a step in the basement structure, is the most probable cause of a gravity anomaly on the scale of the one we observed.

1. Introduction

The aim of this study is to establish whether the Butterknowle fault could create a sufficient gravity anomaly to explain the data collected. If not, then an alternate hypothesis will be formed to try and explain the observations.

1.1 Geological Setting

Carboniferous limestones make up the majority of the uppermost succession north of the Butterknowle fault, then Permian limestones form the upper succession to the south. (fig. 1). Early borehole data, along with outcropping basement rocks suggest a basement formed from Ordovician Skiddaw Slate (Bott, 1961). The near-surface geology consists of numerous small basins of drift that sit on the surface, for the purpose of this study these will be largely ignored.

1.2 Tectonic History

The Durham region “lies within the tectonic framework of the Iapetus Suture Zone” (Beamish and Smythe, 1986; Soper et al., 1992). Subsequently, the area has “experienced a number of extensional, compressional and wrench tectonic events” (Austin et al,. 2009). This complex tectonic history has resulted in rifting and subsidence throughout many of the formations, especially the Carboniferous successions.

2. Methodology

2.1 Data Acquisition

A Lacoste-Romberg gravimeter was used to measure relative gravity from station to station. To start the survey, a base station with a known absolute value of gravity is required. In this survey the IGSN station at the Department of Earth Sciences, Durham, was used, with an absolute value of 981475.76 ± 0.02 mGal. Subsequent stations were then visited at intervals of several hundred metres. The stations were located along a roughly linear profile from the Department of Earth Sciences, to Sedgefield. In order to obtain enough data, measurements were split over two separate mornings, a week apart. Longitude and latitude were recorded via a Reach RS+ GPS, a single-band RTK GNSS receiver. The field data from 09/10/2019 is presented in Table 1.0.

2.2 Data Reduction

The full gravity survey was undertaken by a group of 20 students, split into two groups of 10, one for each week. The reduction calculations were subsequently conducted by smaller teams, who focussed on an individual station. This paper focuses on station 1A (Table 2.0). A condensed summary of the calculations is shown in Table 3.0, accompanied by individual errors. For more information on the errors calculated in this paper, refer to (Hughes & Hase, 2010)

Drift Correction

When conducting a gravity survey, it’s crucial to accommodating mechanical and tidal drift problems. This is done through repeat readings at the base station over the course of the readings. In this survey only two measurements were taken at the base station, as such it is assumed that the drift is linear with relation to time. As station 1A is also the base station in this survey, there is no required drift correction.

Instrument Calibration

Using the calibration tables supplied in the Lacoste-Romberg manual (Lacoste & Romberg, 2004), the raw data for both base station measurements are converted to mGal. Standard deviation is calculated for both sets of data then converted to standard error.

Furthermore, an estimated error of ± 0.01 mGal was added to accommodate for any interference, such as people walking down the stairs directly above where the measurements were being taken. The calibrated gravity readings for the first base station (g1A) and second base station were 5318.84 ± 0.03 mGal and 5318.82 ± 0.04 mGal.

Absolute Gravity

The absolute gravity (gobs) at station 1A will simply be that of the absolute value provided by the IGSN, i.e. 981475.76 ± 0.02 mGal.

Latitude Correction

Due to the varying radius of the Earth, and hence varying centrifugal force due to the Earth’s rotation, gravity varies with latitude. As such, “latitude correction estimated by the International Gravity Formula (3) and the height correction is designed to remove the gravity effects due to an ellipsoid of revolution” (Li & Götze, 2001). (3)

The calculated error is so small compared to previously calculated errors that its effect will be negligible and as such will be ignored hereafter.

Free Air Correction

The free air correction “accounts for the fact that the measurement was not made at sea level” and compensates for the “Earths shape by applying the free-air gravity gradient, the derivative of g with respect to h” (4) (Chapin, 1996)

Subsequently, the free air correction is simply the free-air gravity gradient multiplied by height.

For station 1A, the height, above sea level, was 60m, as such the free air correction was calculated as 18.516 ± 0.04 mGal.

Bouguer Correction

The free air correction assumes “that there is nothing but air between the observation point and sea level” (Chapin, 1996). Clearly this is not true, as such a further correction, the Bouguer correction, is needed. The Bouguer correction accounts for the effect of rock layers between sea level and station 1A. By approximating the rock layer as an infinite horizontal slab of uniform thickness equal to the elevation of station 1A, the correction can be made.

Assuming an underlying mixture of primarily late Permian limestone and Pennine coal measures (Bott & Masson-Smith, 1957), an average density of 2550 ± 100 kg m-3 can be determined from (Kimbell et al., 2010). Hence, the Bouguer correction for station 1A is calculated to be 6.41 ± 0.04 mGal.

Terrain Correction

The terrain corrections were applied via 3 methods. The B and C sections were completed by eye during the collection of data, the sections D-F were attained through the use of a Hammer chart (fig. 2) overlain onto a topographic map of the area and comparing to the terrain correction chart supplied by (Hammer, 1939) (fig. 3). Finally, the outermost regions, G-M, were attained using a computer code (HAMXYZ2) alongside a digital elevation map downloaded from EDINA. The total terrain correction for zone 1A was ≈ 0.5 ± 0.15 mGal

Free Air Anomaly

The free air anomaly can be simply calculated by

This must be done before calculating the complete Bouguer anomaly. For station 1A the free air anomaly comes out as 6.63 ± 0.05 mGal.

Bouguer Anomaly

With the reduced data, the complete Bouguer anomaly can be derived.

For station 1A the Bouguer anomaly is 0.81 ± 0.1 mGal. The Bouguer anomaly for all the stations along the profile is illustrated in figure 3, with all the values displayed in Table 4.0

3. Interpretation

3.1 Direct Methods

3.1.1 Creating a cross-section to estimate the throw of the fault

“Geological studies indicate that the succession (from top-down) is: 100 – 200 m of Permian limestone (density 2400 kg m-3) overlying 1000-1200 m of Carboniferous sandstone and limestone (density 2550 kg m-3), overlying a basement of Ordovician Skiddaw Slate (density 2700 kg m-3)” (Hobbs 2019). The Permian limestone is only significantly present south of the Butterknowle fault and as such, the thickness has been hypothesized to give an indication of the overall throw of the fault, in this case 150 ± 50m. From this information, a simple cross-section has been drawn (fig. 4), providing the basis upon which further interpretations will be made.

3.1.2 Bouguer Anomalies

The Bouguer anomalies calculated were plotted on figure 2 as a gravity profile, illustrating the change in anomaly as it moves along the profile.

3.1.3 Estimating the effect of the fault

There is geological evidence to suggest that the Butterknowle fault is responsible for a displacement of the Permian limestone succession of somewhere in the region of 100-200m. Using the slab formula (9) it’s possible to estimate the produced gravity anomaly caused by this displacement. Rock density values are sourced from (Kimbell et al., 2010).

3.1.4 Estimating the required displacement to produce a sufficient anomaly

Through rearrangement of the slab formula (9) to make height the subject, the required displacement between the two successions to produce a Δg value of 12.36 x10-5 can be determined.

3.1.5 Estimating depth of the structure

Assuming the observed anomaly is caused by the Butterknowle fault, the depth to the top of the structure can be determined using the formula

Where d is the depth, Amax is the maximum relative anomaly, and A’max is the maximum gradient of the anomaly (Kearey & Brooks, 2013).

3.1.6 Estimating a thickening in the Carboniferous limestone succession

A potential source of the observed anomaly could be a thickening of the Carboniferous succession. Using the rearranged slab formula (10) it can be estimated that a 2000m thickening of the Carboniferous limestones could produce the observed anomaly.

3.2 Direct Methods

Using the software IX2D-GM, we used our gravity data to try and create models that could potentially provide a solution to the observed anomaly. In the end two models were created (fig.5 and fig. 6), both creating an anomaly plot similar to that which we observed, yet with different subsurface structures being responsible for it. Figure 5 illustrates a thickening of the Carboniferous succession alone, whereas figure 6 models a step in the basement with subsequent thickening afterward. This second model was based upon an image in (Fielding & Johnson, 1987) (fig. 7) and is thus based on more than just the gravity survey we undertook. For both models, the depth of the Permian limestone is taken to be 200m to the south of the fault and the Carboniferous limestone kept at 1200m thickness north of the fault. The depth and shape of the Carboniferous limestone were changed along with the angle of the fault to get the best fit for the observed anomaly.

4. Discussion

4.1 Gravity anomaly of the Butterknowle fault

The estimated anomaly effect resulting from the known subsidence of a slab to a depth of 200m was only 1.26 mGal, far smaller than the observed 12.36 mGal. We know that the densities, despite being a rough average for large successions, are not going to be a factor of 10 out, and hence couldn’t be a substantial enough error in the calculation. Therefore, for the fault to be the only source of the anomaly, it would take a structure roughly 2km deep and a displacement of the Permian and Carboniferous successions of 2km. We know this isn’t possible as there are confirmed coal deposits across the Durham area thus making it impossible for the Permian succession to be 2km deep. Furthermore, borehole data proves that this is not the case and furthermore a fault of this size is highly improbable from a geological perspective. Whilst the Butterknowle fault undoubtedly contributes to the observed anomaly, it’s not possible for it to be the only cause.

4.2 Changes in the Carboniferous limestones basement topography

Having shown that that the Butterknowle fault cannot be wholly responsible for the observed gravity anomaly, an alternate hypothesis must be formed to account for the anomaly. Use of the rearranged slab formula (10) with the densities of the Carboniferous and Ordovician successions indicate that thickening of around 2000m could produce a sufficient anomaly. (Fielding & Johnson, 1987) suggest the presence of a sedimentary basin in the basement structure of the Westphalian Coal Measures, which could help explain a potential thickening of the Carboniferous succession south of the fault. The IX2D-GM model (fig. 5) suggests an overall thickening of about 2200m, similar to the earlier estimate. Whilst this model appears to provide a strongly correlating gravity anomaly, (Fielding & Johnson, 1987) suggest the presence of a step in the basement. Figure 6 attempts to model this, the formed gravity anomaly does not appear to fit as well as simply thickening, yet this could be a result of the limited data in this survey.

4.3 Limitations

The use of gravity data to understand subsurface geology is inherently indistinct, a whole range of models can produce results that appear to match the data. This was shown in the study through the two IX2D-GM models (figs. 5 and 6) which illustrated two different solutions to the problem, both of which provided a reasonable answer to the anomaly. This ambiguity makes it almost impossible to confidently predict the subsurface geology through a gravity survey alone. In a future study it would be necessary to acquire further information about the area, such as magnetic and seismic data, to help build a clearer picture of the subsurface. Another major flaw in this study was the use of an arbitrary fault line when attempting to form the models. Using a fault of any random angle could have a significant effect on the overall results. It’s also important to note that a fundamental assumption of 2D modeling is that the fault has an infinite strike away from the profile, which inherently cannot be true. Two more major assumptions are made when calculating the Bouguer correction (Chapin, 1996):

1. That we can fill in the elevation difference with a simple infinite slab.
2. That the “till” has a reasonable mass (density) distribution, to allow an average density to be reasonably used.

In this survey, the second point is very important, as it was assumed that the Carboniferous succession had an average density of 2550 kgm-3, yet in reality, its density varies from top to bottom, according to (Kimbell et al., 2010) it varies from 2550 kgm-3 to 2700 kgm-3 as you move from top to bottom.

5. Conclusion

The Butterknowle fault cannot account for an anomaly large enough to match that which was observed. As such it is likely to be another subsurface structure which is accounting for the observations. Both simply a thickening of the Carboniferous succession by roughly 2200m or a step of around 2000m could be the cause of the anomaly and provided satisfactory models to support this. Yet the uncertainties involved in gravity surveying, particularly in a survey like this, makes a confident conclusion difficult to achieve. As such, further analysis of the subsurface is needed in any future surveys to achieve a more reliable understanding of the structures responsible.