Investigation of the correlation of fracture frequency and electric resistivity in impact craters in crystalline rocks

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NVESTIGATION OF THE CORRELATION OF FRACTURE FREQUENCY AND ELECTRIC RESISTIVITY IN IMPACT

CRATERS IN CRYSTALLINE ROCKS

Ann Bäckström

April 2004

TRITA-LWR.LIC 2019 ISSN 1650-8629

ISRN KTH/LWR/LIC 2019-SE ISBN 91-7283-708-X

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Ann Bäckström TRITA-LWR.LIC 2019

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ABSTRACT

Impact craters are formed when a large meteorite or comet hits the Earth. At the impact a shock wave is released causing abundant fracturing in the surrounding bedrock. This type of fracturing is intense and occurs throughout a very large volume (> 100 km³) of the bedrock. Fractures of this type have been observed in deep drilling, to 5 km depth, in the Puchezh-Katunki Impact Crater. At these depths the ambient temperature is high. Thus, impact structures are candidates for potential heat-exchange sources for extraction of geothermal energy.

There is a relation between fracture intensity and electric resistivity in bedrock predominated by impact-generated fractures. In crystalline bedrock changes in electric resistivity is mainly due to fracturing which is the main source of porosity in these rocks. Electric resistivity methods are highly sensitivity to porosity. Furthermore high fracture-intensities have generally been associated with low electric resistivity. Electro-magnetic methods like Very Low Frequency Resistivity (VLF-R) and Magnetotellurics (MT) can indirectly measure electric resistivity to relatively large depths in the bedrock.

This study will quantify the relationship between fracture intensity and electric resistivity which can be used as a prospecting tool for geothermal energy resources at large depth.

To meet that end, a method for fracture mapping on outcrops in Swedish terrain and a method to calculate the three-dimensional fracture frequency from two-dimensional fracture data has been developed. The fracture traces measured in two dimensions on outcrops are assumed to represent a vertical surface and must be converted to a three-dimensional measure of the fracture frequency per unit volume. Spacing, dip and trace length of fractures have been accounted for.

The biases associated with the mapping method have also been accounted for (II).

The correlation between impact-induced fracturing and electric resistivity in crystalline rocks in the Lockne Area shows that the extent of impact fracturing in crystalline rocks can be measured with electro-magnetic or electric techniques. In addition the electric resistivity of crystalline basement and impact generated Tandsby Breccia from the Lockne Crater were determined (I).

The relation between fracture frequency and electric resistivity in fresh water conditions using the VLF-R method is established from data collected from both two drill holes and from numerous outcrops in the Björkö region. A preliminary quantification of the fracture frequency has been made. The MT resistivity models, related to the two drill holes, show that porosity and mineral- conductivity variations of the bedrock affect this relation more than the salinity variations in the bore-hole fluid. Further research is needed to establish a firm relation between fracture frequency, salinity of rock fluid, conductivity and porosity in order to validate the MT resistivity models (III).

Keywords: Electric resistivity, Fracture frequency, Impact generated fractures, Electro-magnetic techniques, VLF-R method, MT method, Window-mapping technique, Three-dimensional frac- ture calculations, heat-exchange structure, geothermal energy.

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PREFACE

This licentiate thesis has been carried out at the Department of Land and Water Resources Engi- neering at the Royal Institute of Technology (KTH). Funding for this licentiate thesis has been provided by the Swedish Energy Agency (STEM) within the Björkö Energy Project.

The steering committee of the Björkö Energy Project is:

Coordinator of the project Assoc. Prof. Herbert Henkel, Royal Inst. of Technology. Stockholm, Dept. Land and Water resources management, , Prof. Leif Bjelm, Lund Inst. of Technology, Prof. Emeritus Maurits Lindström, Stockholm University, Prof. Ove Stephansson, GeoFor- schungsZentrum, Potsdam, Germany and Civ.Eng. Börje Bergman, Scandinavian Water Envi- ronment Council (SWEC).

The scientific advisory board for this project is:

Civ. Eng. Lennart Frise, Fortum, Stockholm, Tekn. Dr. Peter Rohlin, Swedish Energy Agency, Eskilstuna, Assoc. Prof. Thomas Wallroth, Chalmers University of Technology, Göteborg, Dr.

André Gerard, representative of the HDR Project in Soultz, Rock Eng. Anders H. Lindén, Svensk Geofysik AB, Falun, Civ. Eng. Lars Hammar, Sydkraft Värme AB, Malmö, Ragnar Jans- son, County Administrative board of Stockholm, Civ.Eng. Erik Thurner, SKB.

Ann Bäckström Stockholm, April 2004

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LIST OF PAPERS

This thesis is based on the following papers, which are referred to by their Roman numerals. The papers are appended at the end of the thesis.

I Bäckström, A. 2004: A study of impact fracturing and electric resistivity related to the Lockne impact structure, Sweden. Reviewed by referees, to be published in Koeberl, Ch.

and Henkel, H. (eds), Impact Tectonics, Proceedings of the 8^th Workshop of the ESF program IMPACT. Springer Verlag.

II Bäckström, A., Grünfeld K. and Johansson M., 2004: Fracture mapping of rock outcrops from the Björkö structure. Björkö Energy program, Report, 34 p.

III Bäckström, A. and Henkel, H., 2004: Electric resistivity and fracture frequency- the Björkö case. Manuscript.

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ACKNOWLEDGEMENT

This work is a part of the Björkö Energy Project initiated with funding from the Swedish Energy Agency (STEM).

I would like to direct a special thanks to my supervisor Assoc. Prof. Herbert Henkel (Royal Inst.

of Technology Stockholm) for his ideas and guidance during this work. I am also thankful to, the soon to be, Dr. Behrooz Oskoii (Uppsala University) for the work with the MT resistivity models and for his nice company during fieldwork. Other field workers and friend I am grateful to are;

Pauline Eggebratt, Ulrika Lindberg and Malin Johansson (Stockholm University) without whom there would have been much more rain.

I wish to thank Lutz Kübler (Swedish Geological Survey) for the laboratory measurements of the core samples. For interesting information of the distribution of the Mälaren sandstone in lake Mälaren I wish to thank Assoc. Prof. Tom Flodén and Dr. Monica Bjerkéus from Stockholm University. I also would like to thank Anja Olsson and Maria Viksten for a great work on the sandstone core. I would like to express my gratitude to Kirlna Skeppström for help with the fracture mapping of the crystalline core.

I am grateful to Prof. John Hudson (Imperial college, London), Assoc. Prof. Lanru Jing and, the soon to be, Dr. Ki-Bok Min, (Royal Inst. of Technology Stockholm) for rewarding discussions on the subject of Fracture frequency, two or three-dimensional. The calculations of the orientations of fractures could never have been made without the help of Dr. John Stokes, the soon to be, Dr. Tomofumi Koyama (Royal Inst. of Technology Stockholm) and Henrik Meijer.

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Table of Contents Page

INTRODUCTION... 1

BA C K G R O U N D... 1

Locations ... 1

OB J E C T I V E S... 2

HY P O T H E S I S... 2

LI M I T A T I O N S... 2

DI S P O S I T I O N O F T H E T H E S I S... 3

ELECTRIC RESISTIVITY ...4

ME T H O D S F O R T H E M E A S U R E M E N T S O F E L E C T R I C R E S I S T I V I T Y... 4

Very Low Frequency Resistivity VLF-R ... 4

Magnetotellurics ... 5

FRACTURES...5

MA P P I N G M E T H O D S ... 6

Lockne ... 6

Björkö ... 6

THREE-DIMENSIONAL FRACTURE FREQUENCY ...7

CA L C U L A T I O N I N D I F F E R E N T A P P L I C A T I O N S... 7

Drill cores... 7

Outcrop surfaces ... 7

RE S U L T S... 8

RELATION BETWEEN ELECTRIC RESISTIVITY AND FRACTURE FREQUENCY ... 10

DA T A A C Q U I S I T I O N... 10

RE S U L T S... 10

DISCUSSION AND CONCLUSIONS ... 14

Relation between electric resistivity and fracture frequency... 16

CO N C L U S I O N S... 17

PR O P O S A L F O R C O N T I N U E D R E S E A R C H... 18

REFERENCES ... 19

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INTRODUCTION

This licentiate thesis is a part of a project that started in the beginning of the year 2001 and is planned to be finished by the end of year 2004.

Background

The work presented in this thesis is a part of the results of the first two years of research.

The object of the project was to investigate an impact structure and the applicability of the structure as a reservoir for geothermal energy. As a part of this project the investigation of the correlation between electric resistivity and fracture frequency of crystalline rocks was being tested. This is then used to asses methods for remote characterization of crystalline rock masses. Electric resistivity methods are useful to investigate the fracturing of the bedrock. It is known that the electric resistivity in fractured crystalline rock has rather low values (Eriksson, 1980; Hen- kel, 1988). This is known from studies using Slingram and VLF electromagnetic techniques to map fracture zones and for ore prospecting in shield areas. Studies have also been made in connection with site selection for radioactive waste disposal. Typical values are around 2000 ohm-m in fractured rocks, while normal crystalline rock resistivities are

>10 000 Ωm. Even lower values are found for fault gouge, down to 30 Ωm (Henkel, 1988). However, no quantitative assessment of the fracture frequency using electric resistivity methods has so far been made in impact structures. This is the first step in such an attempt.

Locations

Two impact craters have been the object of investigations: The Lockne impact structure located close to Östersund in Jämtland, Sweden and the Björkö structure west of Stockholm.

The Lockne structure is located in Jämtland, Sweden at 63º N and 14.5º E Fig.

1, just east of the Caledonian thrust front in

an area with autochonous Lower Palaeozoic sedimentary sequences on Proterozoic crystalline basement. The structure is now ex- posed on land allowing detailed studies of the impact-induced effects to be made.

The structure has been covered by Caledo- nian thrust nappes of at least 3 km thickness (Karis and Strömberg 1998) and was preserved from erosion for a long time. The cover rocks are now eroded, and the front of the thrust complex is located about 1 km NW of the suggested margin of the structure.

The Björkö structure is located 15 km west of Stockholm in the eastern part of lake Mälaren, Fig. 2, at 59.2º N and 17.5º E.

Lake Mälaren is the third biggest fresh water lake in Sweden, which drains eastwards through Stockholm into the Baltic. The lake covers large areas of the Björkö structure.

The structure was proposed as an impact structure by Flodén et al. (1993). The central uplift of the proposed impact crater is located at the southern part of the Björkö Is- land. The diameter of the structure is about 10 km. Remains of rim terraces can vaguely be seen at Rasta on Ekerö, southern Adelsö and on the southern shores of Mälaren within the study area.

South of Mälaren the Sörmland horst domi- nates the morphology, rising over 100 m above sea level with pronounced west-east striking steps in the terrain.

The older rocks in the area are from mid- Proterozoic time about 2 Ga old. These rocks are strongly deformed crystalline gneisses, intruded by granites and dyke rocks and overlain by a mid to late Proterozoic undeformed sandstone cover, the Mälar sandstone, remains of which are preserved locally. The youngest rock unit in the area is the sandstone. The age of the lower parts of the Mälar sandstone is about 1.2 Ga (Flodén et al. 1993). During and after the last glacia- tion that ended about 10 400 years ago, a thin cover of sediments was deposited on top of the eroded crystalline basement and its remains of cover rocks.

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-

t -

i

Figure 1. Location of the Lockne structure in Sweden and two major deformation zones, the Stora Handsjön ductile zone (SEDZ) and the Hassela Shear zone (HSZ) (after Högdahl 2000). The light gray areas show the extent of Tandsby breccia (after Lindström e al. 1996). The sites for frac ture frequency and electr c resistivity measurements are marked with dots. The large box (broken lines) at section B shows the transition zone. The step in fracture frequency / electric resistivity is marked by the narrow box. The direction to the GBR radio transmitter in southern England is to the SW. Coordinates refer to the Swedish nat onal grid. Thick lines indicate the sections A and B on which the measurements are projected.

Objectives

The objectives of this thesis are:

1. To evaluate the effect of water filled fractures in crystalline rocks on the electric resistivity.

2. To describe impact crater structures and the extent of the impact-generated brec- ciation by applying electric and electro- magnetic methods.

3. To develop a tool for geothermal energy prospecting.

Hypothesis

The volume amount of fracturing in crystalline rocks can be estimated from measurements of their electric resistivity. Several

properties of the rock complicate this relation like the electric conductive minerals in the rock mass or in the fractures, the porosity, and the salinity of the fluid in the rock.

The basis for this thesis is that these different properties and their influence on the electric resistivity models of the MT-method can be identified by the pattern they induce on the model.

Limitations

The main limitation to this investigation has been the lack of accessibility to perform fracture mapping. A large part of the studied area is covered with water (lake Mälaren).

Areas with bare crystalline rock where the fracture frequency is high are difficult to

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Fittja

Igelsta

5 km N

The Sörmland horst Jotnian sandstone

District heating plants Björkö structure Central uplift

Drill holes

Ekerön

Södertälje

r

find. Fracture zones are generally more prone to erosion than surrounding rocks.

They constitute valleys in the terrain, which are filled with sediments from the latest gla- ciation. The geological structures most suit- able for this study are meteorite impact sites in crystalline rocks.

A further limitation is the representation of the three-dimensional fracture frequency calculated from the measurements of two- dimensional fracture frequency.

Fracture frequency is easiest assessed on drill cores but the costs of drill holes limits the amount of drill core data. Core sections with low integrity cannot be used in this study, as it is essential to re-assemble the core to quantify fracture frequency and orientation.

Disposition of the thesis

This thesis contains two parts, the first is the basis for and general outline of my work, and the second is a collection of papers pro- duced from this work. The first part is divided into chapters and a short description of each chapter is given below.

Chapter 2 contains a fundamental description of electric resistivity and the methods used to measure this property of the rock mass. The possibilities and limitations of each method for this investigation are presented here.

Chapter 3 is a general description of fractures and the fracture mapping methods developed.

Chapter 4 introduces the definition of fracture frequency as it is used in this investigation. In this chapter the detailed calculations and results of the fracture frequency from different data sets are presented.

Chapter 5 presents the results found between electric resistivity and fracture frequency as preliminary results so far in the investigation.

Chapter 6 includes the discussion and conclusions of the relations so far in the investigation and some pro- posals of further research.

Hässelby

Svartsjölandet

Stockholm Björkö

Munsön Adelsön

Figure 2. Left: Location of the study a ea in Sweden. Right: the location of the Björkö structure west of Stockholm.

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ELECTRIC RESISTIVITY

Electric currents are transported through rocks using different primary mechanisms like the electric conductivity (charge transport) and dielectric polarization (charge separation). The rate of change in the primary mechanisms are determined by several secondary effects with parameters like the frequency, temperature etc (Carmichael, 1989). In geophysical applications the recip- rocal value of the conductivity (σ), the electric resistivity (ρ), has traditionally been used with the unit Ωm. It is a measure of the in- ability or resistivity of a material to transport an electric current. The electric resistivity of rocks is dependant of the amount of conductive minerals, the porosity of the rock and the salinity of the fluids contained within the rock pores. A high content of conductive minerals, high porosity and high salinity all reduce the electric resistivity. The resistivity depends in addition on the way in which the water is distributed in the rock.

Other components are the rock forming minerals and conductive accessory minerals.

In crystalline rocks the porosity is almost entirely depending on the amount of fractures in the rock.

Different rock types have different electric resistivity signatures due to the mentioned properties.

For example:

Granite (low porosity (< 0.5 %) and no conductive minerals) > 10 000 Ωm Limestone (generally with high porosity) 300-1000 Ωm

Shale (rich in conductive minerals) 80- 100 Ωm

Depending on the salinity of the pore-fluid, porous rocks have a range of resistivities.

Methods for the measurements of elec- tric resistivity

The electrical resistivity of rock masses, the apparent resistivity (ρ_a), can indirectly be measured using different methods. The electromagnetic methods used are the Very Low Frequency Resistivity (VLF-R) and Mag-

netotellurics (MT), using frequencies in the range 15-25 kHz and 1 Hz to 250 kHz, respectively. These methods have different depth penetration. VLF-R reaches a few hundred meters down at certain resistivities.

The MT method has a depth penetration range down to ca 10 km. For the analysis of the MT data, interactive modelling software and optimisation algorithms are used. Sev- eral studies have shown that fracture zones result in significant VLF anomalies (Eriks- son 1980) caused by currents induced by the EM-field of distant radio transmitters.

Very Low Frequency Resistivity VLF-R As the earth is not a perfect conductor, the electric vector of electromagnetic (EM) - field is tilted near the earth’s surface thus also having a horizontal component. This tilt is measured by the phase angle (ϕ), and represents the vertical anisotropy of the resistivity within the penetration depth. The apparent resistivity (ρ_a) is also measured.

This method is used for mapping of apparent lateral resistivity variations down to moderate depths. The penetration depth depends on the local apparent resistivity and the transmitter frequency. The penetration depth for a frequency of 15 kHz is 60 m at 200 Ω m resistivity, 200 m at 2000 Ω m, and 600 m at 20 000 Ωm, respectively. Two radio-transmitters of the electro-magnetic signals were used, one is located in southern England, called GBR, with a frequency of 16.0 kHz and the other located in northeast USA, called NAA, with a frequency of 17.8 kHz.

The measurements were made with the instrument, Geonics EM16R, (Geonics, 1979). It is a VLF receiver for electromagnetic signals equipped with a 10 m reference antenna, measuring the phase angle and apparent resistivity. From the ratio of the horizontal electric and magnetic field, the apparent resistivity is obtained, in Ωm.

The instrument is calibrated to read the apparent resistivity directly. The antenna is placed on the ground and aligned in the direction of the transmitter to measures the horizontal electric field. The electric signal is

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compared to the magnetic field that is induced in the EM16R reference coil.

When modelling the results, a two-layer model was applied, to estimate the overburden thickness, overburden resistivity and the bedrock resistivity. One of these three model parameters must however be assumed. This procedure is put into practical form in the two-layer nomograms constructed by Geonics (1979).

If the subsurface has constant electrical resistivity at least down to the penetration depth, the material is isotropic and results in a phase angle of 45°.

A limitation to the method is that the model is restricted to two layers. In a situation of a multi-layered earth, a two-layered model will blur the different resistivities. The modeller assumes the electric resistivity of the upper layer in the model. When a nearby conductive vertical structure, like a fault zone, has a strike direction parallel to the VLF-R antenna, the phase angle measurements give a false and too high value. The problem can be avoided by measuring perpendicular over the structure. Above thick conductors, the resistivity can be estimated but the depth indication is unreliable (Hjelt et al., 1985).

The benefit of this method is that it is easy to handle during field work. With this method a fast survey can be made giving an overview of a larger area.

Magnetotellurics

Magnetotelluric (MT) measurements are a method to assess electric resistivity using natural electromagnetic fields. Source currents in the ionosphere and lightning currents in the atmosphere distribute these fields. The corresponding induced current systems in the Earth generally flow in all horizontal directions if integrated over a suf- ficiently long time. The frequencies of the signals used ranges from 0.001 Hz to 1 kHz representing a depth penetration of up to 10 km. By measuring the horizontal components of the natural electromagnetic field, the variations of the subsurface electric conductivity at a given measurement site, the impedance tensor, is constructed (Berdi- chevsky and Dmitriev, 1976). The deter-

mined average impedance tensor, also called the effective impedance (Z_DET), is defined as:

yx xy yy xx

DET z z z z

Z = − (1)

The apparent resistivity and phase angle are calculated from the impedance tensor in these measurements using the following relation:

2 0

1

i

a Z

ω

ρ = µ i =xx, xy ,yx, yy (2) )

( _i

i = phase Z

ϕ (3)

where µ₀is the permeability of free space and ω is the angular frequency.

Numerous inverse and forward modelling techniques using the apparent resistivity and phase for 1-D, 2-D and 3-D have been developed for deep Earth studies (Constable et al, 1987; Fischer et al, 1981; Wu et al, 1993;

Zhdanov & Fang, 1997).

F^RACTURES

The hydraulic and mechanical behaviour of a fractured medium is affected by the presence of discontinuities and their geometric pattern. A fracture is a type of discontinuity in rock with low shear strength, negligible ten- sile strength and high fluid conductivity compared with the surrounding rock materi- als (Priest, 1993). This definition refers to open fractures. Fractures can however be open, partially open along their length, or closed. The closed fractures are filled with minerals in their entire width, allowing no fluid to pass. Internal stresses in the rock volume may also close the fractures, again decreasing the fluid conductivity. An open fracture can contain minerals growing on its two surfaces but still allowing for hydraulic conductivity. In a drill core a fracture is considered to be open when the two core parts on either side of the fracture are separated from each other. Artificial fractures created during core retrieval and subsequent han- dling is considered to be distinguishable by their fresh rough surfaces and the lack of mineral coating and weathering. A fracture has two surfaces and in the calculations of the fracture area it is obtained by multiplying the area of a fracture by two. The surface

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area of fractures is of interest for the heat exchange efficiency in a fractured rock mass.

The outcrops for fracture mapping have been selected with respect to their location with respect to the structure studied, accessibility and size. The mapping areas of the selected outcrops were digitally photographed for subsequent image analysis.

Eight drill core sections from southern Björkö were used for a detailed study of fracture orientations. For the rest of the cores, the fracture frequency was estimated based on photographs of the individual core boxes. Sections for the manual mapping were selected with respect to the photo- graphic interpretation results, depths and lithologic variations.

Mapping methods

Each crystalline rock outcrop was investi- gated using the window-mapping technique to estimate its fracture frequency.

Lockne

The fracture frequency measurements were made within an 8 km wide area between two large shear zones in the area, Fig. 1. The study was made on outcrops along two for- est-roads. A total of 28 outcrops were measured.

The numbers of fractures were counted in- dependent of their length and the sides of individual clast were considered to be fractures. The measurements on each site were divided into two sets, one for large fractures and one for small fractures. The area on which the large fractures were counted was the entire outcrop whereas the small fractures were counted in a window <1 m². The maximum distance between large fractures was restricted to about 5 meters by the average size of an outcrop. The fractures with large spacing were counted and their frequency normalized to 1 m².

The study area for small fractures had to be limited to 0.25 m² due to the large number of fractures. The minimum trace length of fractures was set to two centimetres. Frac- tures smaller than that were too difficult to distinguish from the rock structure. All frac-

tures within the window were counted and the frequency normalized to 1 m². Small fractures were often not larger than a few cm in length and the amount of them (sometimes more than 2000/m²) required a sampling area restricted to ca 0.25 m².

The total number of small- and large fractures per unit area is the fracture frequency presented in the study of the Lockne structure.

Björkö

The method used for mapping fractures on outcrops in this area is a window sampling technique described in Priest (1993), modi- fied to meet the demands for mapping fractures of 0.05 to 10 m trace length both for orientation and fracture frequency. The fractures with a trace length between about 0.01 m and 0.05 m were counted in a smaller test window to estimate the fracture frequency separately.

The fractures of an outcrop were divided into three categories based on their trace length: Trace lengths from 3 to 10 m, trace lengths from 0.05 to 3 m and trace lengths from about 0.01 to 0.05 m. The mapping technique is different for these categories although they are mapped in the same local coordinate system (Fig. 3).

The first category has been measured on the outcrop and in the vicinity of the outcrop in

N N

N

Long fractures Whole outcrop

*

Intermediate fractures Sampling area

**

Short fractures Test area

***

Fracture surface

Azimuth and distance to fracture Trace length

*

**

***

Strike, dip, aperture and fracture mineral measured Digitally photographed

Number of fractures counted

Outcrop area

Figure 3. Reference system for the fracture sampling on outcrops in the Björkö area.

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an area about 50 m wide. These fractures are visible in the terrain as scarps and were measured for the orientation and trace length. The mapping window was adjusted to the estimated fracture frequency by enlarging the area from 1 to 9 square meters when the fracture frequency was low. This could be estimated before the mapping commenced.

To measure the strike and trace length of the second category, the window technique was used. Digital photographs were taken of the outcrop and then analysed using image analysis computer programs. Methods for the image analysis are described in more de- tail later in the report.

For category three the area of sampling was a fraction of the sampling area for category two due to the large amount of fractures with a trace length between 0.01-0.05 m on an outcrop. The number of fractures with this trace length was counted to estimate the fracture frequency.

THREE-DIMENSIONAL FRACTURE FREQUENCY

The three-dimensional fracture frequency is how much fracture area there are within a certain volume of rock mass. There are several ways to map the fracture frequency, in one-dimension, two-dimensions and three- dimensions. The one-dimensional fracture frequency can be mapped from scan-line surveys or drill core mapping. This technique achieves the number of fractures per length unit. The two-dimensional fracture frequency is commonly used in mapping for tunnelling. A common method used is the window technique in which the fracture trace length per surface area is assessed. At- tempts to measure the three-dimensional fracture frequency have been made by Hud- son and Priest (1983) using the scan-line method in several directions. This is not possible on the typical flat outcrops of the study area.

The three-dimensional fracture frequency is therefore estimated from the two- dimensional fracture frequency with several parameters like fracture trace length, orienta-

tion, and spacing. Assumptions related to the shape and orientation distribution of the fracture are needed.

Calculation in different applications Drill cores

The information obtained from mapping of fractures in cores lacks the information about the trace length of the fracture, which forces us to limit the area of the fracture to a disc through the core volume. From the fracture mapping with the cores the information of the number of fractures per meter is obtained. As the distribution of the dip of the fractures has >10 different directions within 5 to 6 m of the core, the dip was assumed to be an average dip of 45^ºfor the fractures when calculating the fracture area.

The under sampling of vertical fractures in the core sections is compensated by multi- plying the fracture area with 1.17 (i.e. the part of a uniform dip distribution that would make up the interval 0-15° from vertical). By multiplying the results by two the two surfaces of the fracture is accounted for in the calculation of the total fracture area.

The 3-dimensional fracture frequency F is then calculated by dividing the total fracture area A with the volume V of the mapped core section:

CN v

F cos

17 1 . 1

2⋅ ⋅ ⋅

= (4)

where N is the number of fractures per me- ter, v is the average dip angle of the fractures (set to 45°), C is the length of the mapped core section.

Outcrop surfaces

The window-mapping technique was used when mapping fractures on outcrops in the area. Trace length, strike, and spacing was assessed.

The under sampling of fractures with an orientation close to horizontal was compensated from observations made in the drill core. The outcrop window was oriented as close to horizontal as possible. These fractures were accounted for by multiplying the

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area of fractures with 1.17 (i.e. the part of a uniform dip distribution that would make up the interval 0-15° from vertical).

The square shape was chosen as an ap- proximation in this study. A comparison of the difference in fracture area due to shape where the trace length represents the side of a square, the mean secant of a circle, and a half circle, respectively, are seen in Fig. 4.

The area that the fracture describes in the rock volume was calculated as the square of the length of the individual fractures.

The mean trace length L is calculated as the average of the natural logarithm of the length distribution. The fractures with a short trace length are assumed to have a larger number in a volume than fractures with long trace lengths. To account for this the distribution function with the best fit to the trace length distributions of all mapped surfaces was studied (Fig. 5) The function with the lowest RMS is f = e^-8.8L.

Another factor describing the distribution of fractures is their spacing within the sampling area. It was calculated by the square root of the area divided with the number of fractures within the area. The relation between spacing and trace length does not follow a linear trend. It is approximated with a 3^rd power function passing through zero (Fig.

6). The function with the lowest RMS is used.

The non-linear relation between spacing and mean trace length has been accounted for by introducing the factor 1+y, where y is the difference between the 3^rd power law function to the linear trend. Combining the fac- tors, the 3-dimensional fracture frequency

for window-mapped fractures is calculated as:

3 8 .

8 1

2

) 1

(

) 1 ( 17 . 1 2

s e

F y_L

n

i i

⋅

− +

⋅

= ⋅ ₋

∑

⁼ ^λ ₍₅₎

where the factor 1+y, is the correction for the spacing distribution where y is the difference between the 3^rd power function between spacing and mean trace length of the sampling surfaces with the lowest RMS, λ_i is the trace length of the i^th fracture, The func- tion f = 1- e^-8.8L is derived from the mean trace length distributions from all sampled are- as, where L is the mean trace length of the location and s is the side length of the samp- ling surface.

The area selected for estimates of the number of small fractures was adapted to the conditions at the location, but a commonly used size was 0.25x0.25 m. The general length of the feldspar crystals was noted and no fractures shorter than that length were included to avoid any interference from the striation of minerals. For the calculation of the fracture frequency of short fractures the estimated mean length L of the fractures was calculated by dividing the difference between the largest length (5 cm) and the local feldspar crystal length with two.

The mean length of the short fractures was then used to calculate the fracture frequency F of small fractures in the rock volume as:

∑

=

− −

⋅

+

⋅

= ⋅ ⁿ

L i L

e s

F y

1 2 8

. 8

3 (1 )

) 1 ( 17 . 1

2 (6)

where y is the difference between the linear function and the 3^rd power function between spacing and mean trace length of the sam- pling surfaces with the lowest RMS. L is the mean trace length of the fractures, s is the side length of the test surface, usually 0.25 m.

Results

0 5 10 15 20 25 30 35 40 45 50

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Location number Total fractur area (m2 )

square circle half circle

Figure 4. The total fracture area of the dif- ferent outcrops calculated for different frac- ture shape.

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i i

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5

0 1 2 3 4

Trace length (m)

Frequency (%)

Location 1 Location 2 Location 3 Location 4 Location 5 Location 6 Location 7 Location 8 Location 9 Location 10 Location 11 Location 12 Location 13 Location 14 Location 15 Location 16 Location 17 Location 18 Location 19 f=e-8.8L

Figure 5. Trace length distribution of window sampled outcrops in the Björkö area. The distr bu- tion is negative exponential and the average function describ ng all distributions is f= e^-8.8L.

The three-dimensional fracture distribution of the Björkö area is presented in Fig. 7. The

fracture frequencies of the intermediate and short fractures on outcrops are presented together with the fracture frequencies of the drill core sections. The distributions of the fracture frequency of the intermediate and the short fractures are bi-modal. The first peak for intermediate fractures has a mode of 4 m²/m³ and the second at about 45 m²/m³. The first peak for short fractures has

a mode of 45 m²/m³ and the second at about 240 m²/m³. The drill core sections have a peak at about 45 m²/m³, which coin- cides with the second peak of the intermediate fractures and the first peak of the short fractures on the outcrops (Fig. 7). The spatial distributions of the fracture frequency of the intermediate fractures can be seen in Fig.

8 and the individual fracture frequency of each location can be seen in Table 1.

0 0,1 0,2 0,3 0,4 0,5 0,6

0 0,1 0,2 0,3 0,4

Mean trace length (m)

Spacing (m)

The fracture frequency estimated from the drill cores (Tab. 2) is about 10 times higher than that at outcrop locations in the external region. The highest fracture frequency calculated from mapping of eight drill core sections is 20 times higher than that of the outcrop mapping results in the exterior area.

Figure 6. The relation between spacing and mean trace length of the widow sampled outcrops. The linear trend applies when length and spacing is equal. A trend line with a 3^rd degree function (14x³) represents the observations.

The fracture frequency estimated in photographs of the drill core boxes has similar values as obtained from the manual mapping of the drill core sections. The highest fracture frequency is about 110 m²/m³, which is about 26 times higher than the fracture frequency of the outcrop mapping results in the exterior region.

The most fractured sections of the core could not be used for manual mapping as

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Table 1. The fracture frequency of the different outcrops in the area. 11v is a vertical surface at location 11.

Location 1 2 3 4 5 6 7 8 9 10

Fracture frequency (m²/m³) 3.0 3.7 1.5 2.8 5.2 4.8 5.8 6.6 28 50

Location 11 11v 12 13 14 15 16 17 18 19

Fracture frequency (m²/m³) 51 72 37 42 12 26 13 4.3 3.1 3.1

the reconstruction in these sections is virtu- ally impossible. From Table 2 it can be seen that the fracture frequency from photograph interpretations is overestimated by about 8

%. An underestimation is seen at two inter- vals. Here the contrast between fractures and rock mass was very weak

RELATION BETWEEN ELECTRIC RESISTIVITY AND FRACTURE FREQUENCY

Data acquisition

Several datasets from the Björkö area are used as a basis for an evaluation of the relation between electric resistivity and fracture frequency.

Datasets of fracture frequency have been obtained from outcrops, selected sections of the drill cores from drill hole BJO-01, and es- timates from photographs of the drill cores from drill holes BJO-01 and MID-01, respectively. These three sets of fracture fre-

quency data are compared with three datasets of electric resistivity related to the same material as the fracture frequency data. The resistivity datasets are from very low fre- quency VLF-R measurements on outcrops, drill hole loggings, and models derived from Magnetotelluric (MT) measurements close to the drill holes on the islands Björkö and Midsommar, respectively. In the drill hole BJO-01, crystalline rocks (granites and gneisses) occur. The drill hole MID-01 on Midsommar is entirely within sandstone.

Table 2. Orientations of poles of fractures from drill core measurements on eight sections.

Fracture frequency

(m²/m³) Dominating poles Rotation

Depth interval

(m) Core Photography

Number of poles

(%) Strike (°) Dip (°) (°)

1.9-7.5 30 35 16 12 2 88 350

51-57 58 32 16 10 210 40 350

193-199 39 56 10 10 210 40 355

316-321 20 32 14 12

(1) 10 (2) 538

(1) 40 (2) 45

(1) 70

(2) 10

366-371 68 38 15 6 195 40 110

525-529 38 39 12 16 315 70 55

826-832 28 28 13 18 35 50 310

883-887 30 41 19 8 170 50 190

As electric conductive minerals will interfere with the resistivity measurements, only sections devoid of such minerals are selected for this correlation. Zones with conductive minerals are detected from the induced polarization (IP) measurements in the drill hole wall.

Results

The electric resistivity of the outcrops in the Björkö area was measured with a VLF-R

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0 10 20 30 40 50 60

0 1 2 3

Fracture frequency (m²/m³)

Frequency (%)

Drillcore

Intermediate fractures Short fractures

11 1010 100 10001000

t

Figure 7. Fracture frequency distribution for the differen sampling methods. The class width is10^0.25m²/m³.

instrument and has been modelled using a two-layer concept, (paper III; Tab. 2, Fig. 7).

In a bivariate plot of electric resistivity and fracture frequency the data tend to group into clusters. The approximate locations of the cluster centres are listed in Tab. 3. The different clusters have different properties shown by their location in the diagrams. The Björkö measurements cluster into 4 different clusters (1 to 4 in Tab. 3).

When the measurements of electric resistivity and fracture frequency from the Björkö structure are combined with the measurements from the Lockne structure, the range of fracture frequency is increased towards the low end (paper III; Fig. 8). The trend seen in the Lockne data can also be seen in the Björkö data. Cluster 3 from the Björkö data plots on an intermediate position, re- ducing the gap in the trend of the Lockne data. The Lockne data are represented by clusters 5 and 6 and make up the two ex- tremes in the fracture frequency and electric resistivity trend.

For the data from the drill hole BJO-01 two clusters are determined. Cluster 7 shows quite low electric resistivity and corresponding high fracture frequency whereas cluster 8, which is quite, elongated on the electric resistivity scale, and shows a consistent high fracture frequency.

The data from MID-01 plot in three areas of the bivariate diagram (paper III; Fig. 11) referred to as cluster 9, 10 and 11 in Tab. 3.

They are high fracture frequency and low electric resistivity (cluster 9), low fracture frequency and high electric resistivity (cluster 10) and high fracture frequency and relative high electric resistivity (cluster 11).

The equations for the relations between the electric resistivity and fracture frequency, in the different data sets are listed in Tab. 4. A negative trend between fracture frequency and electric resistivity can be envisaged in the combined Lockne and Björkö data when cluster 1+2 and 5 are combined with clusters 3 and 6.

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i -

0 1 5 km

3.1 3.1 4.3

13 1242

28 5.2 5.8

4.8 1,5

3.7 3

2.8

6.6

50

51 37 42

Ekerön Björkö

Munsön

Adelsön

Rasta

E R

N

Fracture frequency 4.3

Brecciated outcrops

E,R,

C Crater regions

C

Figure 8. Spatial distr butions of the fracture frequency of the intermediate fractures. The num bers represents the calculated 3-dimensional fracture frequency estimated, in m²/m³. Estimated extent of the Björkö structure is represented by the large circle. The small circle represents the central uplift area.

From data from BJO-01 the bivariate plot shows a weak negative trend between fracture frequency and electric resistivity (Tab.

4). The data in the lower range of the electric resistivity (cluster 7) are located close to the trend found in the combined Lockne and

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