- Full paper
- Open Access

# Monitoring hydraulic stimulation using telluric sounding

- Nigel Rees
^{1}Email authorView ORCID ID profile, - Graham Heinson
^{2}and - Dennis Conway
^{2}

**Received:**27 April 2017**Accepted:**19 December 2017**Published:**11 January 2018

## Abstract

## Keywords

- Telluric sounding
- Hydraulic stimulation
- Monitoring
- Transfer functions

## Introduction

**E**) at different sites (Berdičevskij and Keller 1965; Yungul 1966). The measured

**E**can be affected by galvanic distortion, which is caused by gradients in electrical conductivity associated with near-surface heterogeneities (Chave and Smith 1994). The accumulation of charge at conductivity boundaries strongly alters

**E**(Groom and Bailey 1989). This local distortion of

**E**can be described by a real-valued second-rank tensor

**D**that relates the electric field measured at a local (

**E**\(_M\)) and regional (

**E**\(_B\)) site according to (Chave and Jones 2012)

**D**is relative to axes

*X*and

*Y*, typically north and east. Introducing a rotation matrix

**R**(\(\theta\)),

**D**relative to axes \(X^\prime\) and \(Y^\prime\) (which are rotated \(\theta ^\prime\) clockwise from north and east) is given by the matrix

**D**\(^\prime\) (Lilley 2015)

**E**along and across strike.

Targets for hydraulic stimulation are generally in sedimentary basins that are laterally extensive, and for most of the bandwidth the responses are 1D. The injection of conductive fluids into the subsurface will alter the telluric distortion matrix which can be mapped to show the lateral constraints of fluid migration. Lilley (2015) proposed the application of both eigenvalue analysis (EA) and singular value decomposition (SVD) on the telluric distortion matrix, with Mohr diagrams introduced as a versatile way of visualising properties of the matrix. These diagrams can be used to determine the extent to which the matrix is diagnostic of 1D, 2D or 3D geological structure as well as determining a strike direction (with \(90^\circ\) ambiguity) and a relative amplitude change. Grids of Mohr circles can show where the greater amplitude changes occur at depth and may be used to determine the extent to which fluid has migrated from the injection point.

**E**\(_M\) for which the change in

**E**\(_B\) is in the same direction, with the eigenvalue of the direction giving the gain of the process. When real eigenvectors exist, the characteristic equation for

**D**,

**D**\(^\prime\). Figure 1a shows an example of such a Mohr diagram, where P represents the observed point, H and J mark the EA positions and C represents the centre of the circle. The eigenvalues are the \(D^{\prime }_{xx}\) axis values of H and J.

The SVD of **D** produces a rotation for the axes at the regional site B and a different rotation for the axes at local site M. Therefore, a change in **E** at rotated site B produces a change in **E** along the corresponding but differently rotated axis at site M, with the change generally amplified or attenuated (Lilley 2015). This rotation of the local and regional axes reduces the telluric distortion tensor to an ideal 2D form. The results of SVD can also be displayed on a Mohr diagram as shown in Fig. 1b. Here, OG and OF represent the greater and lesser singular values, P is the observed point and C is the centre. Grids of SVD Mohr circles can show the magnitudes and directions of the injected near surface anomaly. For a detailed explanation on the theory of EA, SVD and Mohr diagrams related to the telluric distortion matrix, the reader is referred to Lilley (1993, 2012, 2015).

The goal of this study is to test the viability of utilising the TS method for monitoring hydraulic stimulation at depth. Ideally we would like to be able to constrain the spatial and temporal dimensions of resistivity changes. Spatial changes can be constrained laterally from using multiple sites, and depths can be estimated given resistivity data to map periods to depths. One advantage of the TS method is that it is relatively easy to measure **E** with many dipoles and multi-channel systems and therefore **E** arrays could be deployed for continuous monitoring. Additionally, hydraulic stimulation targets are generally laterally extensive sedimentary basins where **E** transfer functions are essentially the identity matrix. Therefore, monitoring would involve plotting deviations relative to the identity matrix, with static shift appearing as a galvanic multiplier at all periods. The impedance on the other hand has real and imaginary components that vary with frequency. Finally, the TS method is relatively low cost when compared with traditional magnetotelluric measurements and may prove a simple and favourable method for monitoring fluid movement.

## 3D feasibility study

**D**

**D**is a \(2 \times 2\) matrix. If we multiply both sides by a regional and uniform

**B**field (i.e. \({\mathbf {B}} _B = {\mathbf {B}} _M\)), then

Figures 3, 4, 5 and 6 show each component of the resultant transfer functions (\(D_{xx}\), \(D_{xy}\), \(D_{yx}\), \(D_{yy}\); here the first subscript represents the local site and the second the reference site) between the **E**\(_B\) and **E**\(_M\) sites for the six lines in the synthetic grid.

Changes in transfer functions (and hence telluric distortion matrices) can be analysed using SVD and EA and plotted onto Mohr circles grids [see Lilley (2015)]. Such a grid is shown in Fig. 7, where SVD analysis was performed on telluric distortion matrices comparing \({{\mathbf{E }}}_B\) and \({{\mathbf{E }}}_M\) along Line 3 during stimulation. The grey vertical and horizontal lines represent the \(D^{\prime }_{xx}\) and \(D^{\prime }_{xy}\) axes, respectively. The black radius interacts with the red circle at the observed point. The Mohr circles increase in diameter for stations surrounding the 1 \(\Omega\)m conductive body (stations 32–34) at periods of 3 s and greater. The size of the Mohr circles progressively become smaller and approach the identity matrix moving further east from station 34. Similar grids can be plotted using EA as shown in Fig. 8. Here the dashed red lines are the \(D^{\prime }_{yy}\) axis and the two black radii represent the eigenvalues. Notice that for the sites surrounding the conductive zone, the eigenvalues are real and different and the eigenvectors are orthogonal which is a representation of the 2D case [see Fig. 4 from Lilley (2015) for a detailed explanation on Mohr diagram eigenanalysis using different matrices as examples].

This synthetic study demonstrates different techniques for mapping changes in transfer functions resulting from changes in electric fields caused by hydraulic stimulation. The changes in transfer functions were observed to be in the order of 1–2%, and occurred in \(D_{xx}\) and \(D_{yy}\). The changes in \(D_{xy}\) and \(D_{yx}\) were generally less than 1%. The resultant telluric distortion matrix changes can be analysed using SVD and EA and mapped onto Mohr circle grids. The Mohr circles were found to increase in diameter at periods and areas associated with the conductive anomaly. In order to sufficiently monitor hydraulic stimulation, surveys should be designed such that lines of instruments extend sufficiently beyond the stimulation zone in both horizontal and (especially) vertical directions. Interpretations regarding the extent of the stimulation should be conservative and take into account the lack of cross-line constraint. In general, changes in telluric distortion resulting from hydraulic fracturing are small and for a real survey it may be difficult to see such changes due to noise in **E**\(_B\) and **E**\(_M\).

## Example from Paralana, South Australia

In July 2011, Peacock et al. (2013) conducted a magnetotelluric (MT) survey in Paralana, South Australia, with the aim of continuously monitoring changes in MT responses associated with the introduction of saline hydraulic fracturing fluids at depth. The test site was a geothermal reservoir containing hot granites, with the heat source coming from radiogenic elements within the Paleoproterozoic to Mesoproterozoic gneiss, granites and metasediments of the Mount Painter Domain that underlay the Flinders Rangers (McLaren et al. 2003; Brugger et al. 2005). 3.1 million litres of saline water (resistivity of 0.3 \(\Omega\)m) was injected at a depth of 3680 m, with the injection beginning on day 193 at 0400 universal time (UT) and taking 4 days to complete (Peacock et al. 2012). The survey layout is shown in Fig. 10, with the microseismic cloud visible in the bottom right corner.

Phase tensor (PT) and resistivity tensor (RT) residuals were used as a diagnostic tool for determining directional fluid migration. The changes observed in residual PT and RT were interpreted as fracturing fluids migrating towards the northeast of the injection well along an existing fault system trending north-northeast. This section attempts to analyse the impedance matrix **D** (calculated from the electric fields) from the Paralana experiment to determine whether electric fields alone can be used to monitor hydraulic stimulation at depth.

For this study, station 04 is used as the measured electric field (**E**\(_M\)) and stations 13 and 27 as the base electric fields (**E**\(_B\)). Each station recorded responses during the hydraulic stimulation from days 193–197 (see Additional File 1. Note that day 195 was excluded as the signal strength was low and hence the responses are dominated by noise). Transfer functions comparing stations 13 (**E**\(_B\)) and 04 (**E**\(_M\)) over the stimulation time interval are shown in Fig. 11. The grey shaded area represents the MT dead band, where signal power is naturally low, especially from 2009 to 2011 (Peacock et al. 2013). The blue horizontal lines represent the theoretical baseline transfer functions, with the pink shaded area representing a 1% noise uncertainty. Note that only the real components of the transfer functions are plotted. \(D_{yy}\) shows similar behaviour to the feasibility study, where increases of approximately 2% above the noise window occur from 5 s and continue to longer periods for all days. \(D_{yx}\) is mostly within the \({\pm } 1\)% noise window for all days. \(D_{xy}\) shows an almost 5% increase on day 194, with the other days mostly within the noise window. Finally, \(D_{xx}\) decreases by \(<1\)% on days 193 and 196.

Transfer functions comparing stations 27 (**E**\(_B\)) and 04 (**E**\(_M\)) over the same time interval are shown in Fig. 12. Similar trends to Fig. 11 are observed, where an increase in \(D_{yy}\) exists in the order of 5% from 5 s to longer periods for all days. \(D_{xy}\) shows a 2% increase over a similar period range to \(D_{yy}\). Both \(D_{xx}\) and \(D_{xy}\) are within the noise windows for most days.

SVD and EA is performed on the telluric distortion matrices for the four days, with the results plotted onto Mohr circle grids as shown in Figs. 13 and 14, respectively. Although the site noise and dead band add complexities to the analysis, the general trend shows the Mohr circles increase in diameter for periods greater than 5 s. When comparing stations 04 and 27, an interesting trend exists for periods between 2 and 14 s, where the Mohr circles progressively increase in diameter over the length of the pumping interval. EA shows eigenvalues that are real and different, with eigenvectors trending orthogonally indicating the telluric distortion matrix is close to 2D. This differs when comparing stations 04 and 13 where the eigenvectors are real but not orthogonal, which may be indicative of a general 3D structure.

## Discussion and conclusion

We have designed and conducted a feasibility study to determine the potential for using the TS method to monitor changes in resistivity structure of the Earth resulting from hydraulic stimulation. Three-dimensional forward modelling of our base and stimulation resistivity structures showed changes in **D** of between 1 and 2% as a result of introducing a 3 \(\times\) 1 \(\times\) 0.4 km conductive body at 3.6 km depth. The transfer functions were mapped onto a grid by comparing each measured station to a reference (or base) station. Eigenanalysis and singular value decomposition were performed on the telluric distortion matrices from each station at various periods, and plotted onto Mohr circle grids. The resultant grids showed circles increasing in diameter at sites and periods associated with the conductive body. Moving away from the conductive body, the circles progressively approach the identity matrix indicating no telluric distortion had occurred.

The Paralana electric field data were relatively noisy and affected by the dead band making interpretations difficult. \(D_{xx}\) and \(D_{yx}\) components showed little change from the theoretical transfer functions. \(D_{xy}\) and \(D_{yy}\) were increasing by 2–5% for periods greater than 5 s. Changes in the *y*-direction are significant but in the *x*-direction are not, suggesting the response is more complex and possibly anisotropic (MacFarlane et al. 2014). Mohr circle grids visualised these changes in transfer function, with the circle diameters increasing at periods greater than 5 s.

This study has shown some potential for utilising the TS method for monitoring subsurface fluid movement. The advantage of this technique is that electric fields are relatively cheap and easy to measure when compared with traditional magnetotelluric surveys. Additionally, this technique can be used for near real-time monitoring from a remote location. However, electric fields are more complex and noisier than magnetics making interpretation more challenging. The impedance matrix transfer functions are largely real rather than being complex numbers and, in principal for a 1D Earth, are the identity matrix at all periods (± static shift). Therefore changes in the earth resulting from the introduction of conductive bodies can be associated with deviations away from the identity matrix. SVD and EA can reduce the complexity of the telluric distortion matrix to simpler parameters that can be visualised in the form of Mohr circles. Grids of Mohr circles may be a useful diagnostic tool for understanding the extent of fluid movement resulting from hydraulic stimulation at depth. However, deep monitoring is always going to be marginal and for depths in the order of 4 km, changes in transfer functions are small. Therefore, in order to have meaningful interpretations, electric field data need to be of a high quality with low levels of site noise. Additionally, the dead band affects the transfer functions significantly so a controlled source may be useful for monitoring at depths incorporating dead band periods. Real data examples from depths shallower than the dead band may prove more suitable for determining distinguishable changes in the telluric distortion matrix resulting from the introduction of conductive fluids.

## Declarations

### Authors’ contributions

All authors were involved in the design of the study and development of the methodology. NR wrote the manuscript. All authors read and approved the final manuscript.

### Acknowledgements

We would like to acknowledge Jared Peacock for his assistance working with the Paralana dataset.

### Competing interests

The authors declare that they have no competing interests.

### Availability of data and materials

Included in Additional file.

### Consent for publication

Not applicable.

### Ethics approval and consent to participate

Not applicable.

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

## References

- Berdičevskij MN, Keller GV (1965) Electrical prospecting with the telluric current method. Colorado School of Mines, ColoradoGoogle Scholar
- Brugger J, Long N, McPhail D, Plimer I (2005) An active amagmatic hydrothermal system: the Paralana hot springs, northern flinders ranges, South Australia. Chem Geol 222:35–64View ArticleGoogle Scholar
- Chave AD, Jones AG (2012) The magnetotelluric method: theory and practice. Cambridge University Press, CambridgeView ArticleGoogle Scholar
- Chave AD, Smith JT (1994) On electric and magnetic galvanic distortion tensor decompositions. J Geophys Res Solid Earth 99:4669–4682View ArticleGoogle Scholar
- Groom RW, Bailey RC (1989) Decomposition of magnetotelluric impedance tensors in the presence of local three-dimensional galvanic distortion. J Geophys Res Solid Earth 94:1913–1925View ArticleGoogle Scholar
- Lilley F (1993) Magnetotelluric analysis using Mohr circles. Geophysics 58:1498–1506View ArticleGoogle Scholar
- Lilley F (2012) Magnetotelluric tensor decomposition: insights from linear algebra and Mohr diagrams. In: Lim HS (ed) New achievements in geoscience. InTech Open Science, Rijeka, pp 81–106Google Scholar
- Lilley F (2015) The distortion tensor of magnetotellurics: a tutorial on some properties. Explor Geophys 47:85–99View ArticleGoogle Scholar
- MacFarlane J, Thiel S, Pek J, Peacock J, Heinson G (2014) Characterisation of induced fracture networks within an enhanced geothermal system using anisotropic electromagnetic modelling. J Volcanol Geotherm Res 288:1–7View ArticleGoogle Scholar
- Mackie RL, Madden TR, Wannamaker PE (1993) Three-dimensional magnetotelluric modeling using difference equations-theory and comparisons to integral equation solutions. Geophysics 58:215–226View ArticleGoogle Scholar
- McLaren S, Sandiford M, Hand M, Neumann N, Wyborn L, Bastrakova I (2003) The hot southern continent: heat flow and heat production in Australian Proterozoic terranes. Geol Soc Am Spec Papers 372:157–167Google Scholar
- Peacock J, Thiel S, Reid P, Heinson G (2012) Magnetotelluric monitoring of a fluid injection: example from an enhanced geothermal system. Geophys Res Lett 39:L18403. https://doi.org/10.1029/2012GL053080 View ArticleGoogle Scholar
- Peacock JR, Thiel S, Heinson GS, Reid P (2013) Time-lapse magnetotelluric monitoring of an enhanced geothermal system. Geophysics 78:B121–B130View ArticleGoogle Scholar
- Yungul S (1966) Telluric sounding—a magnetotelluric method without magnetic measurements. Geophysics 31:185–191View ArticleGoogle Scholar