Luis Guarracino
email: luisg@fcaglp.unlp.edu.ar

Damien Jougnot

A fractal model for effective excess charge density in variably saturated fractured rocks

A conceptual model is proposed to describe effective excess charge density in fractured media • The model is based on physical principles and a fractal description of fracture networks • Model expressions in terms of hydraulic variables are identical to those obtained for classic porous media

The streaming potential is the contribution of the self-potential signal that is generated by fluid flow. One of the first experimental evidences of the electrokinetic potential generated in fractured rocks is associated with earthquakes. Anomalous variations of self potential have been observed prior to the occurrence of earthquakes [START_REF] Sobolev | Application of electric method to the tentative short-term forecast of kamchatka earthquakes[END_REF][START_REF] Corwin | Self-potential variations preceding earthquakes in central california[END_REF]. [START_REF] Mizutani | Electrokinetic phenomena associated with earthquakes[END_REF] proposed an electrokinetic mechanism for these variations induced by diffusion of groundwater into the dilatant focal region.

Then, [START_REF] Yoshida | Electric potential changes prior to shear fracture in dry and saturated rocks[END_REF] provided strong evidences of an electrokinetic origin by demonstrating that self-potential markedly changes prior to rupture in saturated basalt specimens, whereas no signal is detected in dry basalts. More recently, researches have shown the interest of in situ streaming potential to detect flow in fractured groundwater reservoirs (e.g., [START_REF] Fagerlund | Detecting subsurface groundwater flow in fractured rock using self-potential (sp) methods[END_REF][START_REF] Maineult | Anomalies of noble gases and self-potential associated with fractures and fluid dynamics in a horizontal borehole, mont terri underground rock laboratory[END_REF], identify the orientation of hydraulically active fracture [START_REF] Wishart | Self potential improves characterization of hydraulically-active fractures from azimuthal geoelectrical measurements[END_REF][START_REF] Wishart | Fracture anisotropy characterization in crystalline bedrock using field-scale azimuthal self potential gradient[END_REF][START_REF] Roubinet | Streaming potential modeling in fractured rock: Insights into the identification of hydraulically active fractures[END_REF], or to localize water leakage resulting from hydraulic fracturing [START_REF] Revil | Passive electrical monitoring and localization of fluid leakages from wells[END_REF].

The aim of this study is to develop a fractal-based model to describe the electrokinetic coupling phenomena in fractured media using the effective excess charge approach (e.g., [START_REF] Revil | The self-potential method: Theory and applications in environmental geosciences[END_REF][START_REF] Jougnot | Modeling streaming potential in porous and fractured media, description and benefits of the effective excess charge density approach[END_REF]. This is a key parameter to calculate streaming potential, that is, the contribution to the self-potential signal due to the drag of electrical charge by water flow inside fractures. The fracture surfaces are usually electrically charged and form electrical double layer (EDL) at the solid-water interface (e.g., Leroy & Revil, 2004). This layer contains an excess of charge in water that compensates the charge deficiency of the fracture surface. The EDL can be decomposed into the Stern and diffuse layers. The Stern layer is very thin and contains only counterions that cover the mineral surface. The diffuse layer contains an unbalanced amount of counterions with a net excess charge. The streaming current is generated by water flow inside fractures that drags a fraction of this excess charge. Following the approach originally proposed by [START_REF] Sill | Self-potential modeling from primary flows[END_REF] and modified by [START_REF] Kormiltsev | Three-dimensional modeling of electric and magnetic fields induced by the fluid flow movement in porous media[END_REF] and [START_REF] Revil | Electrokinetic coupling in unsaturated porous media[END_REF], the electrical potential φ (V) distribution and the Darcy velocity v D (m s -1 ) are related through the following macroscopic equation:

∇ • (σ∇φ) = ∇ • Qv v D (1)
where, Qv is the effective excess charge density (C m -3 ) and σ is the electrical conductivity (S m -1 ). The streaming potential SP (V) is then the electrical potential difference between the electrical potential at a given point φ i and the one at the reference φ ref :

SP = φ i -φ ref .
An alternative approach to quantify the streaming potential is based on the coupling coefficient C c , a petrophysical property that relates fluid pressure (P ) and electrical potential gradients: C c = ∆φ/∆P [START_REF] Helmholtz | Studien über electrische grenzschichten[END_REF][START_REF] Smoluchowski | Contribution à la theórie de l'endosmose électrique et de quelques phenomènes corrélatifs[END_REF]. The cou-

pling coefficient C c (V Pa -1
) is related to Qv through the following relation (e.g., Revil & Leroy, 2004;[START_REF] Jougnot | Derivation of soil-specific streaming potential electrical parameters from hydrodynamic characteristics of partially saturated soils[END_REF][START_REF] Jougnot | Modeling streaming potential in porous and fractured media, description and benefits of the effective excess charge density approach[END_REF]:

C c = - Qv k ση (2)
where k (m 2 ) is the permeability of the medium and η (Pa s) the fluid dynamic viscosity.

The main assumption of the proposed electrokinetic model is that the fracture network has a fractal pattern. Fractal objects display self-similarity in their geometry, this means that the pattern observed in a small portion of the object is a replica of the whole at a larger scale. In nature, fractures exist over a wide range of scales, from microns to thousands of kilometers, and fractal patterns have been reported by many researchers (e.g., [START_REF] Bonnet | Scaling of fracture systems in geological media[END_REF][START_REF] Okubo | Fractal geometry in the san andreas fault system[END_REF]. In this study, the fracture pattern is described by a Sierpinski carpet, which is a plane fractal that contains a self-similar geometric pattern of holes. This specific fractal pattern has been detected in fractured coal samples using micro X-ray tomography [START_REF] Zhou | Characterization of porefracture networks and their evolution at various measurement scales in coal samples using x-ray ct and a fractal method[END_REF][START_REF] Wu | Imaged based fractal characterization of micro-fracture structure in coal[END_REF], and successfully used to derive constitutive models for variably saturated flow in fractured rocks (e.g., [START_REF] Guarracino | A fractal constitutive model for unsaturated flow in fractured hard rocks[END_REF][START_REF] Monachesi | A fractal model for predicting water and air permeabilities of unsaturated fractured rocks[END_REF][START_REF] Wang | A fractal model for gas apparent permeability in microfractures of tight/shale reservoirs[END_REF].

The equivalent medium theory is used to estimate the effective excess charge for fractured media, following the flux-averaging approach proposed by [START_REF] Jougnot | Derivation of soil-specific streaming potential electrical parameters from hydrodynamic characteristics of partially saturated soils[END_REF].

First, the effective excess charge in a single fracture is calculated from the spatial distribution of both the excess charge in the diffuse layer and the water velocity profile. Then the effective excess charge density at the macroscopic scale Qv is estimated using an upscaling procedure based on the integration of the excess charge of all network fractures.

By combining this result and the hydraulic properties derived in [START_REF] Guarracino | A fractal constitutive model for unsaturated flow in fractured hard rocks[END_REF] and [START_REF] Monachesi | A fractal model for predicting water and air permeabilities of unsaturated fractured rocks[END_REF] for the same fracture network, we obtain a closed-form expression for Qv in terms of permeability, porosity, saturation and electrokinetic parameters. This modeling strategy has been successfully used for estimating Qv in classical porous media described by capillary tubes (e.g., Guarracino & Jougnot, 2018;[START_REF] Soldi | An analytical effective excess charge density model to predict the streaming potential generated by unsaturated flow[END_REF][START_REF] Soldi | An effective excess charge model to describe hysteresis effects on streaming potential[END_REF][START_REF] Jougnot | Exploring the effect of the pore size distribution on the streaming potential generation in saturated porous media, insight from pore network simulations[END_REF][START_REF] Rembert | A fractal model for the electrical conductivity of water-saturated porous media during mineral precipitationdissolution processes[END_REF].

Note that this new effective excess charge density model for fractured media is based geometric parameters (i.e., fracture aperture, length, recursion-based construction) that are fundamentally different from capillary tubes (i.e., capillary radius, pore throat). However, the analytical expressions of both models become identical when expressed in terms of macroscopic hydraulic parameters (i.e., permeability, porosity and saturation). This result highlights the intrinsic importance of hydraulic characterization in the analysis of self-potential in any type of porous media. Interpretation of self-potential data in fractured media is often qualitative and based on a visual correlation between signal anomalies and observed fracture orientations. This is the first analytical model that consistently describes both electrokinetic and hydraulic properties in fractured rocks and represents a step forward in the quantitative interpretation of self-potential signals.

2 Conceptual model

Description of the fractured media

To derive the effective excess charge density model we consider the geometrical description of fractured media proposed by [START_REF] Guarracino | A fractal constitutive model for unsaturated flow in fractured hard rocks[END_REF]. The representative elementary volume (REV) is assumed to be a cube of volume a 3 (see Fig. 1b). The voids of the REV are parallel and vertical fractures of length a and aperture b with a horizontal selfsimilar pattern described by a Sierpinski carpet (Fig. 1). The upper and lower cut-offs for the fractal behavior are defined by the largest (b max ) and smallest (b min ) apertures observed in the REV.

A Sierpinski carpet can be geometrically constructed by using recursive algorithms that cut out of the carpet successively smaller pieces in each recursion level [START_REF] Tyler | Fractal processes in soil water retention[END_REF][START_REF] Guarracino | A fractal constitutive model for unsaturated flow in fractured hard rocks[END_REF]. In this study we remove rectangular pieces of length a and aperture b from the carpet in order to obtain fractures with a self-similar pattern. Fig. 2 shows the first 3 levels of recursion for a network of parallel fractures assuming a = 3 cm and

b max = 1 cm.
The geometric pattern of Sierpinski carpet is characterized by the fractal dimension D that can vary between 1 and 2. Assuming that the fracture network is formed by parallel fractures, the fractal dimension can be expressed in terms of the largest fracture aperture b max [START_REF] Guarracino | A fractal constitutive model for unsaturated flow in fractured hard rocks[END_REF]:

D = log a 2 b 2 max -a bmax log a bmax .
(3) manuscript submitted to JGR: Solid Earth

dA = (2 -D)a D b 1-D db. (4)
The velocity distribution inside a single fracture of aperture b and length a under laminar flow conditions can be described by:

v(b, x) = ρ w g 8η b 2 -(b -2x) 2 ∆h a , (5)
where x (m) is the distance from the fracture wall (x = 0) to the center of the fracture (x = b/2), ρ w the water density (kg/m 3 ), g the gravitational acceleration (m/s 2 ), η the dynamic viscosity (Pa s), and ∆h the pressure or tension head drop across the REV (m).

The average velocity v (m/s) in the fracture has the following expression:

v(b) = ρ w g 12η b 2 ∆h a . (6)
The macroscopic hydraulic properties of the fractured media can be described in terms of the geometrical parameters of a fracture network. In [START_REF] Guarracino | A fractal constitutive model for unsaturated flow in fractured hard rocks[END_REF] and [START_REF] Monachesi | A fractal model for predicting water and air permeabilities of unsaturated fractured rocks[END_REF] the following expressions for porosity ϕ, permeability k, saturation S and relative permeability k r are obtained:

ϕ = 1 a 2-D b 2-D max -b 2-D min (7) k = 2 -D 12a 2-D (4 -D) b 4-D max -b 4-D min (8) S(h) = h D-2 -h D-2 max h D-2 min -h D-2 max , h min ≤ h ≤ h max (9) k r (S) = (b 2-D max -b 2-D min )S + b 2-D min 4-D 2-D -b D-4 min b 4-D max -b 4-D min ( 10
)
where h is the tension head (positive), h min = 2σ cos(β)/ρg w b max , h max = 2σ cos(β)/ρ w gb min , σ is the surface tension of water, and β the contact angle.

Electrokinetic properties of a single fracture

The first step to derive the macroscopic effective excess charge density is to estimate the effective excess charge of a single fracture. Let us consider a fracture of aperture b and length a (see Fig. 1a) saturated by a binary symmetric 1:1 electrolyte (e.g., NaCl) in a laminar flow regime.

The excess charge distribution Qv in the diffuse layer at a distance x of wall fracture can be expressed as (Guarracino & Jougnot, 2018):

Qv (x) = N A e 0 C 0 e - e 0 ψ(x) k B T -e e 0 ψ(x) k B T , (11)
where N A is the Avogadro's number (mol -1 ), e 0 the elementary charge (C), C 0 the ionic concentration far from the mineral surface (mol/m 3 ), ψ the local electrical potential in the fracture water (V), k B the Boltzman constant (J/K), and T is the absolute temperature (K).

In this study, the exponential terms of ( 11) are approximated by a four-term Taylor series. Under this approximation, the excess charge distribution can be expressed as:

Qv (x) = -2N A e 0 C 0 e 0 k B T ψ(x) + 1 6 e 0 k B T ψ(x) 3 . (12)
Figure 3a shows the excellent agreement between exact and approximate excess charge distributions described by Eq. ( 11) and ( 12), respectively.

For the thin double layer assumption the local electrical potential can be expressed [START_REF] Hunter | Zeta potential in colloid science[END_REF]: Based on the ideas presented in [START_REF] Guarracino | A physically based analytical model to describe effective excess charge for streaming potential generation in water saturated porous media[END_REF], the effective excess charge density Qb v carried by the water flow in a single fracture of aperture b is defined by:

ψ(x) = ζe -y l D , (13)
l D = ϵk B T 2N A C 0 e 2 0 , (14)
Qb v = 2 v(b)ab b/2 0 Q v (x)v(b, x)a dx. (15)
Then, by substituting (5), ( 6) and ( 12) in ( 15) we obtain:

Qb v = -24N A e0C 0 (b/l D ) 2 e0ζ k B T 1 -2l D b + e -b 2l D 2l D b + b 2l D -12N A e0C 0 (b/l D ) 2 e0ζ 3k B T 3 1 -2l D 3b + e -3b 2l D 2l D 3b -3b 4l D . ( 16
)
Under the thin double layer assumption, the thickness of the electrical diffuse layer is assumed small compared to fracture aperture (l D << b) and Eq. ( 16) can be approximated by:

Qb v = 12N A e 0 C 0 (b/l D ) 2 -2 e 0 ζ k B T - e 0 ζ 3k B T 3 . ( 17
)
Figure 3b shows the very good agreement for b/l D > 3 between exact and approximate excess charge described by Eq. ( 16) and ( 17), respectively. In capillary tube models the thin double layer assumption is valid so long as the capillary radius is greater than 200 l D [START_REF] Jackson | On the validity of the "thin" and "thick" double-layer assumptions when calculating streaming currents in porous media[END_REF]. Assuming that the fracture aperture is 2 times the capillary radius, the validity of the thin double layer assumption for fracture models can be state for apertures b > 400l D . Moreover, if we consider that in monovalent electrolyte concentrations between 1 mol/m 3 and 100 mol/m 3 the Debye length ranges from approximately 1 nm to 10 nm [START_REF] Jackson | On the validity of the "thin" and "thick" double-layer assumptions when calculating streaming currents in porous media[END_REF], the minimum aperture in the REV should be b min > 0.4 10 m -6 for l D = 1 nm and b min > 4 10 m -6 for l D = 10 nm.

It is important to remark that Eq. ( 17) is almost identical to the equation obtained by [START_REF] Guarracino | A physically based analytical model to describe effective excess charge for streaming potential generation in water saturated porous media[END_REF] for the effective excess charge density QR v carried by the water flow in a single capillary tube of radius R, which reads as follows:

QR v = 8N A e 0 C 0 (R/l D ) 2 -2 e 0 ζ k B T - e 0 ζ 3k B T 3 . ( 18
)
Note that the quotient between ( 17) and ( 18) yields to the following relation between the raduis R and the aperture b:

Qb v QR v = 3 2 R b 2 . ( 19
)
The above relation is identical to the one obtained by the quotient between the average velocity in the capillary tube (Poiseuille velocity) and the average velocity in the fracture given by ( 6), indicating that the effective excess charge strongly depends on the flow properties.

Electrokinetic properties of a fractured rock

In order to obtain the effective excess charge density in terms of the macroscopic hydraulic properties of the fractured rock, we consider the REV described in Section 1.

Suppose that the fractured media is initially fully saturated and is drained by a tension head h (m). If we assume that the fractures drain at capillary pressure then the fracture of maximum aperture b h drained by tension head h can be estimated as:

b h = 2σ cos(β) ρg w h . ( 20
QREV v = 1 v BD a 2 b h bmin Qb v v(b) dA(b) (21)
where v BD = ρwg η kk r (S) ∆h a is the Buckingham-Darcy's velocity [START_REF] Buckingham | Studies on the movement of soil moisture[END_REF], a 2 the cross-sectional area of the REV, and dA(b) the area covered by fractures of aperture b defined by Eq. ( 4).

Substituting ( 17), ( 6) and ( 4) in (21) yields:

QREV v = N A e 0 C 0 l 2 D -2 e 0 ζ k B T - e 0 ζ 3k B T 3 a D-2 kk r (S) b 2-D h -b 2-D min . ( 22
)
manuscript submitted to JGR: Solid Earth Table 1. Geometric and hydraulic parameters of fracture networks

b max (m) b min (m) D (-) ϕ (-) k (m 2 ) QREV,sat v (C/m 3 )
Fracture network 1 8.0 10 -3 8.0 10 -6 1.861 0.493 2.76 10 -7 1.010 10 -4 Fracture network 2 5.7 10 -3 5.7 10 -6 1.921 0.361 8.88 10 -8 2.304 10 -4 Fracture network 3 4.4 10 -3 4.4 10 -6 1.946 0.275 3.82 10 -8 4.082 10 -4

Finally, combining (7), ( 9) and ( 22) we obtain the following expression for QREV

v : QREV v = N A e 0 C 0 l 2 D -2 e 0 ζ k B T - e 0 ζ 3k B T 3 ϕS kk r (S) . ( 23
)
The equation ( 23) is the main finding of this study since it predicts the effective excess charge density from both electrokinetic and macroscopic hydraulic parameters such as ionic concentration, ζ-potential, Debye length, porosity, saturation and permeability.

This equation is identical in form to the equation obtained by [START_REF] Soldi | An analytical effective excess charge density model to predict the streaming potential generated by unsaturated flow[END_REF] for a porous medium described by a capillary tubes model with a fractal pore size distribution. Note that although the effective excess charge densities of both models at the pore scale and REV shapes are different, the expressions of effective excess charge density QREV v in terms of macroscopic properties (ϕ, S, k and k r ) are identical. This result shows that Eq. ( 23) is valid for both sedimentary and fractured porous media. The overall dependence of the effective excess charge is also consistent with numerous previous studies (see a data compilation in Fig. 4.2 of [START_REF] Jougnot | Modeling streaming potential in porous and fractured media, description and benefits of the effective excess charge density approach[END_REF] and the empirical relationship proposed by [START_REF] Jardani | Tomography of the darcy velocity from self-potential measurements[END_REF].

To facilitate the analysis of the model we express QREV where

QREV,sat v = N A e 0 C 0 l 2 D -2 e 0 ζ k B T - e 0 ζ 3k B T 3 ϕ k , (25)
QREV,rel

v (S) = S k r (S) . ( 26
)
Note that the relative effective excess charge density defined by Eq. 26 does not depend on electrokinetic parameters but only on hydraulic variables.

A synthetic example of fractured rocks

In this section, we predict the effective excess charge density for different fracture 7) and ( 8). The geometric and hydraulic parameters of fracture networks are listed in Table 1. It can be observed that by reducing the aperture, the fractal dimension increases while both porosity and permeability decrease. To estimate the effective excess charge density we consider a ionic concentration

C 0 = 1 mol/m 3 , ζ-potential ζ = -0.07 V and absolute temperature T = 293.15 K.
The Debye length computed using ( 14) is l D = 9.65 10 -9 m, which is 3 orders of magnitude less than the minimum fracture aperture b min . Saturated effective excess charge density values ( QREV,sat v ) are estimated from (25) and listed in Table 1. The values of QREV,sat v increase the smaller the fracture apertures and the greater the number of fractures (see patterns of Fig. 4). Also note that fractal dimension D goes to 2 for small values of b max . 4 Application of the model to experimental self-potential data

In this section the saturated effective excess charge density model QREV,sat v is confronted to the coupling coefficient C c data obtained by [START_REF] Moore | Self-potential observations during hydraulic fracturing[END_REF] for microcracked Sierra granite samples. These authors investigated the self potential response during hydraulic fracturing in the laboratory and determined C c for different injection pressures. They found that C c is approximately constant for pressures smaller than 2

MPa but then increases with pressure drop up to 80% just prior to hydraulic fracturing. This increasing C c is related to the dilatancy of microcracks at high pressures, which causes an increase in permeability. In their study, permeability values are measured as a function of pressure drop (P ) and the following exponential law is fitted to data: k(P ) = 10 -18 e 2.5 10 -4 P (28

)
where k is in m 2 and P in kPa. The change of C c with pressure drop P is described by the following best fit equation to seven samples of Sierra granite:

∆C c (P ) = 1.83 e 3.73 10 -4 P (29)

where ∆C c is expressed as the percentage of the value of C c at zero pressure drop. Prior to hydraulic fracturing the rock resistivity decreases by up to 2%, which is near to the practical limits of detection.

In order to apply our model to the data of [START_REF] Moore | Self-potential observations during hydraulic fracturing[END_REF], C c is estimated from QREV,sat v by substituting ( 25) in ( 2):

C c = N A e 0 C 0 l 2 D -2 e 0 ζ k B T - e 0 ζ 3k B T 3 ϕ ση . (30)
The coupling coefficient defined by Eq. ( 30) does not depend explicity on permeability, but on porosity. Unfortunately, the variation of porosity with pressure drop was not measured during the laboratory test. However, porosity can be estimated from permeability by combining Eq. ( 7) and ( 8). If we assume that b min << b max , the following relation is obtained:

ϕ = 12(4 -D) a 2 (2 -D) k 2-D 4-D . (31)
Finally, combining (31), ( 28) and ( 30), and assuming that both the electrical conductivity and dynamic permeability do not depend on pressure, the following expression for the variation of C c is obtained:

∆C c (P ) = 100 e 2.5 10

-4 P 2-D 4-D -1 . (32)
Note that the above equation is expressed as a percentage of the initial value and only depends on the fractal dimension D.

Figure 6 shows the fit of Eq. ( 32) to the experimental data obtained by [START_REF] Moore | Self-potential observations during hydraulic fracturing[END_REF]. If we assume a constant fractal dimension, the best fit of our model is obtained for D = 1.67 (solid line in Fig. 6). However, the fractal dimension is expected to vary with pressure P . The increase in permeability with P prior to hydraulic fracturing can be explained by dilatancy of microcracks [START_REF] Moore | Self-potential observations during hydraulic fracturing[END_REF]. According to our model, fractal dimension decreases with increasing aperture (see Table 1) and therefore with increasing pressure. Let us assume the following linear relationship between fractal dimension and pressure: D(P ) = 2 -αP , where α is a fitting parameter. This relationship for D provides a better fit of Eq. ( 32) to the experimental data, as is shown in Fig. 6 with a dashed line (α = 4.8 10 -5 ).

Discussion and conclusions

In this study, we developped a fractal model to estimate the effective excess charge density in fully and partially saturated fractured rocks. The porous medium is described using the Sierpinski carpet, a classical fractal object that contains a self-similar geometric pattern of fractures. The mathematical procedures to estimate the effective parameters are based on the ideas presented in [START_REF] Guarracino | A physically based analytical model to describe effective excess charge for streaming potential generation in water saturated porous media[END_REF] for a classical capillary tubes model. The accuracy of the posed model has been tested to be correct for fracture apertures greater than 3 times the thickness of the electrical diffuse layer, i.e. b > 3l D . This condition is fully satisfied under the thin double layer assumption which is valid for apertures b > 400l D [START_REF] Jackson | On the validity of the "thin" and "thick" double-layer assumptions when calculating streaming currents in porous media[END_REF].

The effective excess charge density model has a closed-form analytical expressions that depends on chemical parameters of the fracture water (ionic concentration, ζ-potential and Debye length) and hydraulic parameters (porosity, saturation and permeability). When expressed as these parameters, the model becomes identical to the ones derived by [START_REF] Guarracino | A physically based analytical model to describe effective excess charge for streaming potential generation in water saturated porous media[END_REF] and [START_REF] Soldi | An analytical effective excess charge density model to predict the streaming potential generated by unsaturated flow[END_REF] for sedimentary porous media using capillary tubes. This result allows the extension of the validity of the models for classic porous media to fractured media. In addition, the model highlights the dependence of the effective excess charge density to the hydraulic properties. In this sense, Eq. ( 23) combined with the water flow models derived by [START_REF] Guarracino | A fractal constitutive model for unsaturated flow in fractured hard rocks[END_REF] and [START_REF] Monachesi | A fractal model for predicting water and air permeabilities of unsaturated fractured rocks[END_REF] constitute a very good alternative to estimate the effective excess charge density since all the model expressions are obtained for the same fractal pattern of fractures.

However, the proposed model can be combined with any constitutive model for water flow in fractured rocks (e.g., [START_REF] Guarracino | A constitutive model for water flow in unsaturated fractured rocks[END_REF].

It is worth mentioning that due to the configuration of the geometry that we considered to develop the model, there is no exchange of water or ions between the fracture network and the matrix. This makes our model different from the numerical schemes proposed in [START_REF] Roubinet | Streaming potential modeling in fractured rock: Insights into the identification of hydraulically active fractures[END_REF] or [START_REF] Desroches | Surface selfpotential patterns related to transmissive fracture trends during a water injection test[END_REF]. We redirect the reader to these references for fractured media in which this exchange occurs and cannot be neglected.

The synthetic tests show that the effective excess charge density increases with the decrease of both the fracture apertures and the degree of saturation. Finally, we show that the model is able to describe experimental data under fully saturated conditions for a published data set of coupling coefficient values measured in laboratory during hydraulic fracturing. Unfortunately, no experimental data are available to test model predictions under partially saturated conditions.

To the best of our knowledge, this is the first analytical model that consistently describes both electrokinetic and hydraulic properties in fully and partially saturated fractured rocks. The model provides simple explicit relations between effective excess charge density, porosity, permeability and saturation. These relations not only increase our general understanding of the electrokinetic phenomenon in fractured rocks, but also provide theoretical basis for quantitatively study of water flow using self-potential data.

Figure 1 .Figure 2 .

 12 Figure 1. (a) Fracture of aperture b and length a; (b) Representative elementary volume (REV) of the fractured medium.

Figure 3 .

 3 Figure 3. (a) Exact and approximate expressions of the excess charge distribution Qv(x); (b) exact and approximate expressions of the effective excess charge Qb v for a single fracture of aperture b. The assumed values of ionic concentration, absolute temperature and ζ-potential are C 0 = 1.0 mol/m 3 , T = 293.15 K and ζ = -0.07 V. The distance x and aperture b are scaled by the Debye length lD.

  where ζ (V) is the ζ-potential on the shear plane, l D the Debye length (m) which represents a characteristic thickness of the diffuse layer, and ϵ the water dielectric permittivity (F/m).

)

  Note that only the fractures of the REV which are fully saturated (b min ≤ b ≤ b h ) contribute to water flow. Then the effective excess charge density of the fractured rock QREV v can be computed as:

  networks generated by Sierpinski carpets. Consider a cubic REV of side a = 4 cm and the patterns of fractures shown in Fig. 4, where the maximum apertures are successively reduced: a) b max= a/5, b) b max = a/7 and c) b max = a/9. Fractal dimensions of Sierpinski carpet are estimated from (3). The minimum aperture b min of each fracture network is considered to be 3 orders of magnitude less than the maximum aperture (i.e. b min = 10 -3 b max ). Porosity (ϕ) and permeability (k) values are computed using (

Figure 4 .Figure 5 .

 45 Figure 4. Parallel fracture networks generated by 2 recursion levels of Sierpinski carpets: (a) D = 1.861; (b) D = 1.921; (c) D = 1.946.

Fig. 5

 5 Fig. 5 shows the influence of saturation degree on effective excess charge density QREV v

Figure 6 .

 6 Figure6. Variation of coupling coefficient with pressure ∆Cc(P ). The empty circles are the experimental data obtained by[START_REF] Moore | Self-potential observations during hydraulic fracturing[END_REF]. The best fit of the proposed models to experimental data are displayed with solid (constant D) and dashed (D linearly dependent on P ) lines.

manuscript submitted to JGR: Solid Earth

Acknowledgments

The authors strongly thank the Editor, Lee Slater, and an anonymous reviewer for their very constructive comments on the original version of the manuscript. This research is partially supported by Universidad Nacional de La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas (Argentina) and ANR EXCITING (grant ANR-17-CE06-0012).

Data Availability Statement

This theoretical paper only uses previously published data [START_REF] Moore | Self-potential observations during hydraulic fracturing[END_REF].

The Fortran source code to estimate the effective excess charge density in fractured rocks and coupling coefficient data extracted from [START_REF] Moore | Self-potential observations during hydraulic fracturing[END_REF] have been archived in the Hydrogeophysics community of Zenodo and can be found at: https://doi.org/ 10.5281/zenodo.5732504.


Franco Eusébio

Thomas Westin
email: thomasw@dsv.su.se

Jérôme Dupire
email: dupire@cnam.fr

Workshop: Towards Inclusive Co-Creation of Inclusive Games

Keywords: Game Development, Game Design, Game Accessibility, Serious Games, End-User Development

Game creation precedes game play. In this workshop, we describe our efforts towards enabling people with different (dis)abilities to co-create and play digital games. We focus on abilities, skills and knowledge to enable collaborative and inclusive co-creation of inclusive games.

Introduction

Digital games extend beyond entertainment. Besides professional game development, multiple domains have been benefiting from games. Education (gamebased learning, gaming literacy), training (serious games), and therapy and rehabilitation (games for health, therapeutic games), game making and modding, and even game playing as a profession (e-sports) are successful examples of games supporting real world activities.

However, despite applications and importance of games, millions of people are still unable to play (reasons include physical, cognitive, and emotional (dis)abilities; social, cultural, and economic issues; and even access to technology itself). Moreover, intended audiences for game creation are currently limited to young people without physical, cognitive, and emotional disabilities, often living in favorable socioeconomic conditions.

A possible way to enable more people to play is enabling more people to design and implement digital games. If we bring diversity to creation, we can potentially achieve greater diversity to resulting games. In this strategy, creation predates play. In this workshop, we explore the framework defined in [START_REF] Garcia | An Inclusive End-User Development Framework for Tailorable Games[END_REF] to present our ongoing efforts towards enabling inclusive co-creation of inclusive games. The goal of the framework is enabling communities of people with heterogeneous interaction needs to co-create games for themselves and for people with different interaction needs (currently traditional audiences, hearing disabilities, and low literacy).

The framework has three main pillars to support its goal: (1) a flexible architecture that enabled use-time modification of human-computer interaction;

(2) a collaborative work model to transform inclusion into a community problem, which the community could collaborate to address; (3) tools to enable the workflow. It aims for maximum inclusion, towards approaching game accessibility modding. The main idea is to transform game accessibility into a community problem, on which people contribute based on their abilities, skills, and knowledge to enable more people to play and create games. In this strategy, whenever someone provides a new alternative, she/he might enable more people to cocreate and play. Once able to co-create, the newly-included may also become able to contribute, transforming accessibility into an iterative process towards maximum inclusion.

To enable the workflow, we provide communities with game creation and modding tools. For instance, a storytelling tool (Lepi) was developed as proof of concept for game creation, considering accessibility to a subset of interaction needs (traditional audiences, hearing disabilities, and low literacy) and a single genre (storytelling) [START_REF] Garcia | An Inclusive End-User Development Framework for Tailorable Games[END_REF][START_REF] Garcia | Able to Create, Able to (Self-)Improve: How an Inclusive Game Framework Fostered Self-Improvement Through Creation and Play in Alcohol and Drugs Rehabilitation[END_REF]. A second example is a support system to aid players with cognitive disabilities to play, exploring community-created content to remove accessibility barriers and enable play [START_REF] Yildiz | Design of a Game Community Based Support System for Cognitive Game Accessibility[END_REF]. Our intention is defining and expanding solutions to include new audiences, aiming for broader inclusion.

Current evaluation has found that each pillar of the framework enabled the proposed workflow for the initial audience [START_REF] Garcia | Able to Create, Able to (Self-)Improve: How an Inclusive Game Framework Fostered Self-Improvement Through Creation and Play in Alcohol and Drugs Rehabilitation[END_REF]. With the tool, people could cocreate story-based games with their abilities; with the collaborative work model, contributors inserted media and content to address other interaction needs of the community; due to architecture, people could insert this new content to the game. This way, people could co-create inclusion as a community -from each according to their abilities, to each according to their needs.

Call for Participation

Game creation precedes game play. In this half-day workshop, mixing tutorials with participatory activities, we describe our efforts towards enabling people with different interaction needs to co-create and play inclusive digital games. We focus on abilities, skills and knowledge to enable collaborative and inclusive co-creation of inclusive games.

Besides game accessibility professionals and researchers, this workshop can benefit professionals exploring games for serious activities, designers aiming for broader inclusion in interactive systems, digital accessibility researches, metadesigners exploring end-user development for inclusion, researchers designing collaborative systems, or professionals exploring Information and Communications Technologies with people with heterogeneous interaction needs.

The workshop provides resources to accommodate people with different computing backgrounds, as the framework encompasses design and programming for professional developers; meta-design and end-user programming for end-users; and individual and community workflows for collaboration.

Outcomes for Participants and for the Workshop

Game design is a discipline on which every area of human knowledge can contribute towards a better project. With suitable approaches, everyone could cocreate according to their own abilities. In this workshop, co-creation is focused on accessibility, abilities, and skills towards maximum inclusion.

In inclusive environments, there might be people with heterogeneous abilities -including people with and without disabilities. With the framework, they can co-create storytelling games accessible for them all. People can create content based on their own abilities. Then members of the community can enrich the game project based on their own abilities: they can convert existing content into alternatives to enable use. Once they provide a new alternative, more people can play -and potentially create new alternatives for inclusion. Thus, people who could not use the original game may become able to further improve it.

At the end of the workshop, participants should be familiar with design and implementation principles described in [START_REF] Garcia | Able to Create, Able to (Self-)Improve: How an Inclusive Game Framework Fostered Self-Improvement Through Creation and Play in Alcohol and Drugs Rehabilitation[END_REF] to achieve co-creation of inclusion4 . A desired outcome towards inclusive co-creation and play could be a curated list of game accessibility related efforts based on participants suggestions. Thus, this workshop may be a starting point to gather these existing efforts in one placefor instance, at the International Game Developers Association Game Accessibility Special Interest Group's Open Educational Resources5 . This could serve as reference for professional developers (for instance, designers, programmers, and artists), and for end-users acting as non-professional developers.

Program

1. Welcome and Overview of the Framework. Participants will learn how each pillar of the framework are combined to promote inclusive co-creation of inclusive games. 2. The Architecture: Game Interaction as Add-Ons. Participants will be introduced a different way to think about digital games. We can design and implement games for semantics of use and define commands to represent players' intents. In particular, this enables us to provide different interaction alternatives for game play. These strategies allow development of games with multiple interaction schemes: we can define multiple ways to enable play by defining how a player should perceive the game content and provide commands to it. 3. The Collaborative Co-Creation of Inclusive Digital Games: End-User Collaboration Towards Inclusion. Participants will learn how communities of people with heterogeneous abilities can promote inclusion. The collaborative work model describes a process to promote the workflow for inclusive co-creation, on which individuals provide inclusion to a community according to their abilities, and a community provides support to individuals according to their interaction needs. 4. The Game Co-Creation Platform: Enabling People with Heterogeneous Interaction Needs to Create and Play Digital Games. We will discuss and present tools and strategies to enable inclusive co-creation of inclusive games. Lepi and the support system are explored as case studies, acting as proof of concept for the strategies defined by the first two pillars. Besides game play, inclusive creation tools allow domain experts to explore game creation and play as a support for their professional activities. Thus, this activity showcases how end-users can co-create accessibility features for inclusion according to their own abilities. 5. Fostering Inclusive Co-Creation and Play by People with Disabilities: Approaches for Content Creation and Play. Aiming to achieve the outcomes for the workshop from Section 3, participants could share game accessibility resources that they know, and suggest improvements and directions to enable broader audiences to create and play. What are possible strategies to enable more people to create and play? Which existing content creation tools are designed for people with disabilities? What game genres and mechanics could become more accessible -or even universally accessible??

(i) Design for Semantics of Use, (ii) Implement for Modification, (iii) Provide Different Ways to Create and Play, (iv) Compose Interaction, (v) Focus on Abilities and Skills, (vi) Foster Community Inclusion, (vii) Consider Inclusion as a Dynamic Process, (viii) Foster Community Collaboration.

5 https://igda-gasig.org/oer/


Christophe Bortolaso
email: christophe.bortolaso@gmail.comjeremy.bourdiol@laposte.net

Jérémy Bourdiol

T C Nicholas Graham

Enhancing Communication and Awareness in Asymmetric Games

Keywords: Game design, asymmetric games, virtual reality

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Modern computer hardware affords a wealth of new styles of gaming. An emerging style is asymmetric games, where cooperating players take on different roles, sometimes using different forms of interaction, different hardware, and different views of the game world. For example, in Maze Commander, two players collaborate to traverse a dangerous maze [START_REF] Sajjadi | Maze Commander: a collaborative asynchronous game using the Oculus Rift & the Sifteo cubes[END_REF]. One player can see the entire maze, using a virtual reality headset, but cannot navigate. The other sees only a small part of the maze, represented by connected Sifteo Cubes, and can manipulate the cubes to move the avatar. The key behind this game is that each player's views and interaction affordances support part of the gameplay task, and the players must cooperate closely to win the game.

Asymmetric games frequently require players to engage in tightly-coupled collaboration [START_REF] Harris | To Asymmetry and Beyond!: Improving Social Connectedness by Increasing Designed Interdependence in Cooperative Play[END_REF], despite having often radically different ways of interacting with the game. Such collaboration can be difficult if players have different views of the game world. Players may lack consistent frames of reference, and may have difficulty understanding what the other player can see. In this paper, we explore the problems of group awareness and communication in asymmetric games. Through Our Virtual Home, a novel house decoration mini-game (Figure 1), we show examples of potential breakdown in collaboration. Our Virtual Home combines a large 2D touch tablet and a VR headset, enabling tablet players to view and position furniture in a house while a VR player explores how the furniture will appear to people. This mini-game is inspired by the house decoration features found in games as varied as Bethesda's The Elder Scrolls V: Skyrim and Microsoft's Minecraft.

This choice of hardware is based on the strengths of the tablet and VR headset devices used. Tablets naturally support planning around 2D representations of physical space such as maps and architectural plans. Example applications support design of interior spaces [START_REF] Kirkpatrick | AutoCAD 2015 for Interior Design and Space Planning[END_REF], exploration for oil and gas [START_REF] Seyed | SkyHunter: a multi-surface environment for supporting oil and gas exploration[END_REF], emergency response planning [START_REF] Chokshi | ePlan multi-surface: A multi-surface environment for emergency response planning exercises[END_REF], and determining routes for military vehicles through hostile terrain [START_REF] Bortolaso | OrMiS: A tabletop interface for simulation-based training[END_REF]. However, some situations require a full understanding of the space represented in the map or plan, and in such cases, a top-down 2D view may not be sufficient. For example, when arranging furniture in a room, it is necessary to have a realistic perception of depth and distance to create an aesthetic and enjoyable space [START_REF] Laseau | Graphic Thinking for Architects and Designers[END_REF]. Adding the use of a VR headset, however, seriously compromises group awareness. The player using the headset cannot see where tablet player is looking or pointing, and may not see when the tablet player is moving furniture. To address this problem, Our Virtual Home provides a novel set of collaborative widgets supporting communication between tablet and VR players.

3D views can help with such tasks by presenting the space directly to the player. For this reason, many commercial games combine immersive first-person views with an additional top-down view for establishing context. For example, Activision's Call of Duty game provides a first-person 3D view of the scene, augmented by an inset 2D "minimap" providing a top-down view. However, switching between views can be cognitively demanding, leading players not to take full advantage of all available perspectives [START_REF] Tory | Visualization task performance with 2D, 3D, and combination displays[END_REF].

Recent advances in virtual reality (VR) technology have made immersive views of 3D spaces widely available. Immersive VR goes beyond the desktop by providing stereoscopic 3D views that can be explored using natural movements. Compared to desktop computers, VR headsets have been found to provide a more accurate sense of distance [START_REF] Ruddle | Navigating large-scale virtual environments: What differences occur between helmet-mounted and desk-top displays? Presence[END_REF], support spatial cognition through the use of natural head movements [START_REF] Pausch | Quantifying immersion in virtual reality[END_REF] and provide a more satisfactory experience [START_REF] Santos | Head-mounted display versus desktop for 3D navigation in virtual reality: a user study[END_REF].

This paper makes two contributions. First, we illustrate a novel combination of a large tablet device with a VR headset in an asymmetric game. Second, we show how communication and group awareness can be supported despite the different perspectives of tablet and VR players.

Related Work

Asymmetric games provide players with different roles, possibly providing different perspectives on the game world, and possibly using different hardware. For example, in Frozen Treasure Hunter, two players attempt to capture trophies while being attacked by snowball-wielding enemies [START_REF] Yim | Using games to increase exercise motivation[END_REF]. The players cooperatively control a single avatar, where one moves the avatar by pedaling a bicycle, and the other swats away the snowballs by swinging a Wii Remote. Asymmetric games allow players to experience a variety of gameplay, allow people with different interests to play together, and provide a form of game balancing by allowing people to choose a role that plays to their strengths [START_REF] Harris | Leveraging Asymmetries in Multiplayer Games: Investigating Design Elements of Interdependent Play[END_REF].

Figure 2 lists examples of asymmetric games. In the simplest case, games such as Riot Games' League of Legends and Blizzard's World of Warcraft allow players to take on different roles in games (character classes), while sharing the same hardware and same perspective on the game's action. As described earlier, Frozen Treasure Hunter is an example of a game where players share the same third person view of their avatar, while playing different roles using different hardware (Wii Remote vs bicycle.) Several commercial games have explored the provision of different perspectives to different players. Unknown World Entertainment's Natural Selection, S2 Games' Savage: The Battle for Newerth, and Iceberg Interactive's Nuclear Dawn all involve a player in a commander's role, using a real-time strategy interface to direct players on the ground who play as individual units.

A more radical form of asymmetric games offers players different playstyles involving both different perspectives on the gameworld and different hardware interfaces to the game. For example, Beam Me 'Round Scotty! allows one player to use a game controller and PC to guide an avatar through a level, while the other player uses a touch tablet to enable special effects that aid the player [START_REF] Harris | To Asymmetry and Beyond!: Improving Social Connectedness by Increasing Designed Interdependence in Cooperative Play[END_REF]. Similarly, in Tabula Rasa, one player uses a standard PC and game controller to navigate platformer levels, while the other player uses a digital tabletop to create and modify these levels on the fly [START_REF] Graham | Villains, architects and micro-managers: what Tabula Rasa teaches us about game orchestration[END_REF]. This form of asymmetric gameplay allows interesting forms of collaboration, where players are responsible for different parts of the gameplay task (e.g., building a level vs playing it). The differing visual perspectives allow players to see the gameworld in ways that are appropriate to their tasks, and the different input modalities are customized to the tasks the players perform (e.g., touch to build a level, controller to navigate it).

Research outside the realm of gaming has shown how collaborative tasks require people to perceive and manipulate physical spaces, and how these tasks can benefit from a system in which some users manipulate the space using a top-down view while others are immersed in the space using a VR headset. This form of work has been termed mixed-space collaboration [START_REF] Grasset | Evaluation of mixed-space collaboration[END_REF][START_REF] Nakanishi | Transcendent communication: location-based guidance for large-scale public spaces[END_REF][START_REF] Stafford | Comparison of techniques for mixedspace collaborative navigation[END_REF]. For example, when designing the layout of an apartment, architects draw the floor plan from a top-down perspective and also draw sketches of the space from a first person perspective [START_REF] Kirkpatrick | AutoCAD 2015 for Interior Design and Space Planning[END_REF]. The floor plan is useful for exploring spatial constraints and helps the architect to share design decisions with other stakeholders. The first-person sketches help with perception of volumes and of the space's look and feel. In military route planning, officers collaboratively plan how their troops will travel through hostile terrain via discussion over a large map [START_REF] Bortolaso | OrMiS: A tabletop interface for simulation-based training[END_REF]. To plan safe routes, commanders determine the visibility of units along the road, from multiple strategic points. A first-person view can help assess the potential of ambush of units following a proposed route. The common element between these collaborative tasks is that planning and design is discussed using a top-down overview of the space, while specific features are verified at a human scale. Top-down views are used to arrange elements, to resolve spatial constraints and to obtain an overview of the space. Conversely, a first-person view helps in understanding distances, volumes and sightlines. Work benefiting from these two perspectives is referred to as mixed-space collaboration.

The benefit of 2D and 3D perspectives on design tasks was identified as early as 1997 in a modeling interface combining both perspectives [START_REF] Coninx | A hybrid 2D / 3D user interface for immersive object modeling[END_REF]. More recently, systems have explored the combined use of a virtual reality headset with a traditional desktop PC display. One user is immersed in the space with the headset while the other controls an overview of the space on a screen. Systems have been created for search and rescue [START_REF] Bacim | Collaborative navigation in virtual search and rescue[END_REF][START_REF] Stafford | Implementation of god-like interaction techniques for supporting collaboration between outdoor AR and indoor tabletop users[END_REF], authoring of virtual environments [START_REF] Holm | A combined immersive and desktop authoring tool for virtual environments[END_REF],

Tabletop to VR VR to Tabletop Deixis

Glowing green column Blue laser pointer Shared Reference Cardinal direction display Compass bar

Awareness

Avatar and vision cone See-through effect; side-icon; dragging sound guided navigation [START_REF] Thuong Huyen Nguyen | Guiding techniques for collaborative exploration in multi-scale shared virtual environments[END_REF], and exploring museum exhibits [START_REF] Sundén | Hybrid virtual reality touch table: An immersive collaborative platform for public explanatory use of cultural objects and sites[END_REF]. This decomposition has been shown to improve efficiency in searching and traveling tasks [START_REF] Grasset | Evaluation of mixed-space collaboration[END_REF][START_REF] Zhang | The effectiveness of multiscale collaboration in virtual environments[END_REF].

A central problem in systems mixing touch tablets and virtual reality is that the hardware can block communication between the two types of players. The virtual reality headset covers the player's eyes, blocking their view of the physical world around them. Consequently, a VR player cannot see the tablet player or where they are looking or pointing, and cannot see the shared artifact displayed on the table. Similarly, the tablet player cannot see where the VR player is looking. Interaction techniques have been proposed to help players overcome this barrier, some of which are summarized by Stafford et al. [START_REF] Stafford | Comparison of techniques for mixedspace collaborative navigation[END_REF]. For example, in the context of disaster relief, Bacim et al. allow a "commander" (PC user) to place waypoints to guide a "responder" (VR player), and allow the responder to place virtual markers to alert the commander to places of interest [START_REF] Bacim | Collaborative navigation in virtual search and rescue[END_REF]. Holm et al. [START_REF] Holm | A combined immersive and desktop authoring tool for virtual environments[END_REF] and Stafford et al. [START_REF] Stafford | Implementation of god-like interaction techniques for supporting collaboration between outdoor AR and indoor tabletop users[END_REF] provide similar "god-like" techniques. These allow the PC user to guide the VR player, where the actions of the PC user are illustrated through movements of a giant hand in the VR view. Nguyen et al. demonstrate a range of cues that a "helping user" can provide for an "exploring user", including directional arrows, a light source to flag paths, and an over-theshoulder camera to allow the helper to see the world from the exploring user's point of view. In the ShareVR game, non-VR players maintain awareness of the virtual world through projection of the world onto the floor [START_REF] Gugenheimer | Sharevr: Enabling colocated experiences for virtual reality between HMD and non-HMD users[END_REF].

Enhancing Communication in Asymmetric Gameplay

To better understand communication in asymmetric games involving different perspectives and input modalities, we introduce the Our Virtual Home house decorating mini-game (Figure 1). The system is composed of a large interactive touch tablet and a VR headset. The tablet shows a top-down view, allowing players to position furniture by dragging and rotating. The headset provides an immersive view where players can change their perspective by moving their head, and can walk through the house using a game controller. This supports a natural division of duties. The tablet player maintains a large-scale view of the house design, allowing them to conceptualize the global layout, and to easily reposition furniture through touch gestures. The VR player can see the furniture layout in place, getting a clearer idea of scale, sightlines and movement through the space. The tablet player may try a decoration idea, and ask the VR player to evaluate it. Equally, the VR player may request modifications to the design based on their first-person view. This means that it must be possible for either player to initiate and guide communication. As discussed earlier, however, the fact that the VR players' eyes are covered by the headset forms a barrier to collaboration. As suggested by Dix' framework [START_REF] Dix | Computer supported cooperative work: A framework[END_REF], users require three forms of communication, all of which are hindered by their different perspectives on the gameworld, and particularly through the reduced visibility of the VR hardware:

-Deixis to establish explicit referents in conversation (e.g., "try putting that chair over there"). -Shared reference (e.g., "what do you see to your left?").

-Awareness (e.g., realizing that a table is being moved).

Our Virtual Home shows how it is possible to support all three forms of communication, originating either from the touch or the VR player. As summarized in Figure 3, Our Virtual Home's collaboration techniques support bi-directional deixis, shared reference and awareness. The techniques are designed to match the capabilities and conventions of the devices. Some techniques have been proposed by others (e.g., Stafford et al.'s "god-like" pointing [START_REF] Stafford | Implementation of god-like interaction techniques for supporting collaboration between outdoor AR and indoor tabletop users[END_REF]); others are new. The key novelty of Our Virtual Home is to demonstrate that this combination of interaction techniques allows all three forms of communication to originate from either player. This affords an equitable collaboration where both the tablet and VR and VR player have the same communication opportunities.

Deixis

Deixis is almost as important as words for face-to-face communication [START_REF] Bekker | Analysis of gestures in face-to-face design teams provides guidance for how to use groupware in design[END_REF]. Traditional finger pointing is hindered when one player wears a VR headset, as that player cannot see the other person's hands or the touch device itself. To help VR players see where tablet players are pointing, we designed and implemented a two-way pointing system.

When the tablet player touches the screen, a glowing, green marker appears below their finger (Figure 4: left). This feedback is immediately reflected in the VR player's view as a column of green light (Figure 4: right), showing the location of the touch. The green feedback follows the tablet player's touch gestures, and its position is updated in real-time in the VR view. This technique, inspired by Stafford's "god-like" pointing technique [START_REF] Stafford | Implementation of god-like interaction techniques for supporting collaboration between outdoor AR and indoor tabletop users[END_REF], enables the tablet player to communicate locations to their VR partner. Deixis is therefore provided via touch. The glowing green marker is important to show the tablet player that the touch is being communicated to the VR player.

In the other direction, the VR player can hold a button on their game controller to trigger a blue laser pointer (Figure 5: right). When the laser pointer appears in the VR view, it also becomes immediately visible on the tablet surface (Figure 5: left). The laser's end point is marked with a lightning ball in order to disambiguate which object is being referenced. Lasers have proven to be users' preferred technique when pointing in collaborative virtual environments [START_REF] Wong | Support for deictic pointing in CVEs: still fragmented after all these years[END_REF]. This enables a VR player to point at objects and locations in the space to communicate with their tablet partner. As with physical deixis, this mechanism can be used to disambiguate references to elements in the space.

Together, these techniques enable deixis in both directions, allowing both tablet and VR players to reference locations or objects for the other to see.

Shared Reference

Another advantage of face-to-face collaboration lies in the establishment of shared references. For example, people working on a map typically have a shared understanding of which direction is north, allowing the use of cardinal references when discussing directions. Similarly, when working side-by-side, it is easy to reference elements using phrases such as "to your left" or "the chair behind the table". In an asymmetric game like Our Virtual Home, these referencing mechanisms are broken because players do not see the space from the same point of view. Müller et al. recognized the importance of shared reference through the inclusion of shared virtual landmarks [START_REF] Mueller | Remote collaboration with mixed reality displays: How shared virtual landmarks facilitate spatial referencing[END_REF].

To afford absolute reference, we designed and implemented a compass widget that is visible using the VR headset. As shown in Figure 6 (right), the compass is a bar at the top of the VR view showing the four cardinal directions. (In the figure, the player is oriented in roughly the southerly direction.) The compass rotates with the player's direction of view. Cardinal directions are also displayed on the tablet, with north pointing toward the top.

To aid with relative references, the position and orientation of the VR player is shown on the tablet. As shown in Figure 6 (left), the VR player is represented as a small avatar (a blue circle) whose current field of view is shown as an open cone (delineated by two white lines). This shows the tablet player the direction in which the VR player is looking, allowing references such as "look to your left".

Awareness

Shared spaces such as our table-sized tablet afford awareness by allowing people to see the actions of others through direct and peripheral vision. VR players cannot see others' work if that work is out of their field of view. For example, if a tablet player moves a piece of furniture behind the VR player or behind a wall, the VR player may not be aware that the movement has taken place. In Our Virtual Home, we addressed this problem via (1) a see-through effect that extends the VR player's sight through obstructions, (2) a "side-icon" indicating activity out of the field of view, and (3) an audio "furniture dragging" sound that is activated when a tablet player moves furniture.

As shown in Figure 6 (right), when a tablet player touches a piece of furniture, it takes on a glowing, green appearance in the VR view, and becomes visible through obstructions such as walls or other furniture. This draws the VR player's attention to furniture that is being moved, even if it is not directly visible. This allows the VR player to see the movement of occluded objects. This see-through effect requires the object to be within the VR player's field of view. To help with this, as an object is moved, a green marker appears on the compass aligned to the horizontal position of the moved object (Figure 6 (right)). If the object is outside the VR player's field of view, this green marker appears on the left or right hand side of the display ("side-icon"), indicating that activity is taking place, and showing the direction in which the VR player should turn their head.

Finally, a "furniture dragging" sound is played when furniture is being moved, providing a second cue to the presence of activity that the VR player may not be able to see.

Thus, the VR player's awareness of group activity is enhanced by the ability to see through walls, the highlighting of furniture selected by tablet players, the side-icon visual cue indicating activity out of the field of view, and the use of an audio cue representing furniture being moved. Meanwhile, the tablet player is provided with cues to help show the location and orientation of the VR player. As seen in figure 4 (left), the position of the VR player is shown on the tablet as a blue circle. White lines delimit the VR player's field of view. This blue-circle avatar and vision cone help the tablet player to understand what the VR player can currently see.

In sum, this section has presented interaction techniques used to support bi-directional communication between tabletop and VR players in an asymmetric house decorating mini-game. As summarized in Figure 3, these techniques support deixis, shared reference, and awareness. The implementation of these techniques in Our Virtual Home shows that it is possible to support all three forms of communication in a bi-directional form. This is key to allowing equitable collaboration, where both players have the ability to lead and respond to the group's activity.

Early Evaluation

To gain feedback about the usability of our combination of techniques, we carried out a qualitative pilot study. We recruited four pairs of participants (7 males, 1 female, 18-31 years old). The participants were asked to arrange furniture in a two-story house to create a functional and aesthetic layout. The participants were provided with the techniques described above, supporting deixis, shared reference and awareness. Participants were assigned to use either the tablet or the VR headset and were directed to rearrange the first floor of the house. They then switched roles, and were directed to rearrange the second floor. On average, each participant spent 10 minutes using each device (M=10:26, SD=1:32). The sessions were video-recorded and participants were interviewed at the end of the task. We performed a video analysis to identify interesting behaviours and communication issues between players.

Results

All groups completed the task without problems and reported in the interviews that they had no difficulty in playing the game and in collaborating. The combination of our interaction techniques with verbal communication supported effective communication. Exchanges between the two players were mostly verbal, supported by our collaboration widgets. For example, the VR player could call the attention of the tablet player to a furniture item and then disambiguate the object referenced by using the laser pointer: "Hey look! Let's put that 〈points at furniture item〉 over here 〈points at location〉". Participants reported that the cardinal references were useful at the beginning of the session when exploring the house.

Not surprisingly, the tablet provided better awareness than the VR view. As stated by group 1, "When you are on the tablet you have full awareness of what the other person is doing", but when using the VR headset, "I was aware that something was going on but not exactly what". The dragging sound was successful in alerting VR players to activity, but players easily overlooked the side-icon indicating the direction of the activity.

All participants reported that the two views were complementary. Tablet players repeatedly asked the VR player how the space felt. Interestingly, not only were the use of space and distance important, but lighting was also frequently discussed. For instance, a tablet player asked a VR player: "Are there enough lamps in the eating area?" When changing from the tablet to the VR headset, participants expressed surprise at how the space looked from the inside. This highlights the complementarity of the two views.

The study showed the importance of bi-directional support for communication. Both tablet and VR players made use of pointing gestures (through the laser pointer and the column of light). The position and orientation of the avatar was used to determine what the VR player was seeing, helping to disambiguate conversation. The see-through movement of furniture objects helped the VR player quickly locate the tablet player's activity.

The video analysis also highlighted interesting behaviours and situations where the techniques were successful, and areas where future work could improve the approach.

Path finding. Although not designed for this purpose, the sky-laser was used to direct the VR player's movement. We observed multiple instances where the tablet player dragged the laser from one location to another to guide the VR player to a specific area. This usage is similar to Bacim et al.'s more explicitlyprovided waypoint feature [START_REF] Bacim | Collaborative navigation in virtual search and rescue[END_REF].

Missed eye contacts. While talking, some tablet players sporadically looked at the VR player even though the VR player couldn't see them. This is a good indicator that the tablet player felt the presence of the VR player and felt the need for non-verbal communication. This hints that while deixis is useful, communication of the tablet player's gaze could helpful to indicate specific instances where the tablet player is attending to the VR player.

Missed gestures above the table. Several participants performed gestures above the table even though the VR player could not see them. For example, one tabletop participant asked the VR player: "is this whole thing roofed?" while gesturing in a circle with his hand above the table. Marquardt et al. have stressed the importance of providing awareness of activities above the table [START_REF] Marquardt | The continuous interaction space: interaction techniques unifying touch and gesture on and above a digital surface[END_REF]; such awareness could be provided to the VR player for example through finger tracking.

In sum, both tablet and VR players made use of interaction techniques for deixis, shared reference, and awareness. Participants played the game as expected, with the tablet player taking advantage of the spatial presentation afforded by the top-down view, while the VR player focused on the immersive 3D presentation of the furniture layout. Participant response was positive, with all dyads successfully completing the task. While this study was based around the specific hardware of a tabletop-sized tablet and a VR headset, these approaches could be applied to other hardware. For example, the touch device could be replaced by a smaller tablet such as an iPad. This would extend awareness difficulties, as the tablet would be harder for two people to view. A VR headset could be replaced by an augmented-reality (AR) headset, such as Microsoft's Hololens product. This could allow the VR player to be more aware of the tablet player's actions; however, current AR headsets obscure the eyes of the wearer, and so awareness cues would still be required.

Conclusion

In this paper, we have explored an asymmetric implementation of a house decorating mini-game, using a touch tablet and a VR headset. We described a set of interaction techniques to support non-verbal communication between the two players. These interaction techniques support equitable collaboration in which both players can take the lead. An informal study revealed that players were able to carry out an interior design task using this asymmetric collaboration, and that they understood and used the widgets supporting communication and group awareness. Opportunities for improvement were identified, such as the use of gaze detection and tracking of the finger above the table, but the lack of these features did not inhibit the players from completing the task.

Fig. 1 .

 1 Fig. 1. The Our Virtual Home game: One player decorates a house on a large tablet device and the other uses immersive VR to assess the result.

Fig. 3 .

 3 Fig. 3. Interaction techniques used in Our Virtual Home to support bi-directional collaboration between tablet and VR players.

Fig. 4 .

 4 Fig. 4. The sky-laser technique supports deixis from tablet to VR. A tablet player's pointing action is shown in the virtual world as a glowing column of light.

Fig. 5 .

 5 Fig. 5. The laser pointer supports deixis from VR to tablet. Here, the VR player is pointing at a sofa.

Fig. 6 .

 6 Fig.6. Left: The tablet player is moving a bench. The blue avatar shows the position and orientation of the VR player. Right: The bench is highlighted with the see-through effect in the VR view. The compass on the top shows that the player is facing south and shows the direction of the selected bench.

  Examples of how asymmetric games can provide players with differing perspectives on the gameworld and different input modalities supported by different hardware.

		Same Perspective	Different Perspective
	Same Input	League of Legends,	Natural Selection, Savage,
	Modalities	World of Warcraft	Nuclear Dawn
	Different Input	Frozen Treasure Hunter	Beam Me 'Round Scotty!, Maze
	Modalities		Commander, Tabula Rasa
	Fig. 2.

Acknowledgements We gratefully acknowledge the support of the SURFNET Strategic Network and the GRAND Network of Centres of Excellence for this research.