Determining the influence of pressure and temperature on the elastic constants of anisotropic rock samples using ultrasonic wave techniques

Journal of Applied Geophysics 159 (2018) 715–730

Contents lists available at ScienceDirect

Journal of Applied Geophysics journal homepage: www.elsevier.com/locate/jappgeo

Determining the influence of pressure and temperature on the elastic constants of anisotropic rock samples using ultrasonic wave techniques H.B. Motra a,⁎, J. Mager a, A. Ismail b,c, F. Wuttke a, W. Rabbel d, D. Köhn d, M. Thorwart d, C. Simonetta e, N. Costantino e a

Marine and Land Geomechanics and Geotechnics, Christian-Albrechts-Universität zu Kiel, Ludewig-Meynstr. 10, 24118 Kiel, Germany Boone Pickens School of Geology, Oklahoma State University, 105 Noble Research Center Stillwater, USA National Research Institute of Astronomy and Geophysics, Helwan, Cairo, Egypt d Institute of Geosciences, Applied Geophysics, Christian-Albrechts-Universität zu Kiel, Otto-Hahn-Platz 1, 24118 Kiel, Germany e Enel Green Power (EGP), 120, 56122 Pisa, Italy b c

a r t i c l e

i n f o

Article history: Received 29 December 2017 Received in revised form 14 October 2018 Accepted 18 October 2018 Available online 27 October 2018 Keyword: Anisotropy Elastic stiffness constants Metamorphic rocks Orthorhombic media VTI media Ultrasonic waves

a b s t r a c t Measuring rock elastic constants and anisotropy parameters and understanding their changes in response to changes in pressure and temperature is crucial for modeling and interpreting seismic measurements. The rapid advance in seismic exploration and characterization of conventional and unconventional reservoirs requires a thorough understanding of variations in seismic velocities in response to variations of the rock elastic constants and anisotropy parameters. In attempt to develop this understanding, we measured variations in the elastic constants of three rock samples in the lab as a function of temperature (up to 600 ∘C) and pressure (up to 150 MPa) to simulate the in-situ conditions using a triaxial ultrasonic pulse transmission method. The rock samples used in this study came from a metamorphic rock core sample collected from a geothermal reservoir at the Larderello Geothermal Field in Italy. The rock samples have different chemical and structural composition and inherently contain both vertical transverse isotropy (VTI) and orthorhombic isotropy. We used two different methods to calculate the elastic stiffness constants and corresponding anisotropic parameters including VTI and orthorhombic isotropy. Our results showed that increasing the pressure leads to an increase in the orthorhombic constants while increasing the temperature leads to a decrease in these constants. The lagging decrease of the elastic constants with respect to the decrease in the pressure is explained by the hysteresis phenomenon. These observations and results will promote a better understanding and interpretation of reservoirs within the seismic domain. © 2018 Elsevier B.V. All rights reserved.

1. Introduction The increase in global demand for both renewable and fossil fuel energy sources is accompanied by rapid advances in geophysical exploration and characterization methods. The seismic wave velocities (compressional Vp, shear Vs, seismic anisotropy and shear-wave splitting), are essential attributes used in the exploration and characterization processes (Rabbel and Mooney, 1996, Anderson et al., 2007; Oeberseder et al., 2011; Ismail et al., 2014a;, Ismail et al., 2014b; Zhu and Harris, 2015; Grana, 2016; Motra and Wuttke, 2016, Rabbel et al., 2017, Motra and Zertani, 2018). These attributes depend on the physical properties of the earth’s materials especially elastic constants (Cholach, 2005). Seismic anisotropy, for example, provides useful information about the structural, textural and elastic properties of the subsurface medium (Cholach, 2005; Gurevich, 2003; Spikes,

⁎ Corresponding author. E-mail addresses: [email protected], [email protected] (H.B. Motra).

https://doi.org/10.1016/j.jappgeo.2018.10.016 0926-9851/© 2018 Elsevier B.V. All rights reserved.

2014). Unfortunately the anisotropic nature of the geologic formations of interest poses a significant challenge as it complicates the processing and interpretation of the seismic data (Babuska and Cara, 1991; Lin and Tang, 2007). Seismic anisotropy millimeters in size are manifested in rock samples and can be detected by high frequency ultrasonic laboratory measurements (Migliori, 1993; Rabbel et al., 2017) Alternatively, rock formations hundreds of meters in thickness is studied using 2D and 3D subregional seismic surveys (Jolly, 1956; Winterstein, 1990; Miller et al., 1994; Kebaili and Schmitt, 1997; Cholach, 2005) Determination of elastic constants of different rock types (Aleksandrov and Ryzhova, 1961; Babuška, 1981; Bass, 1961) using various use have been developed significantly during the recent years (Schreiber et al., 1973). Elastic constants derived from the ultrasonic pulse transmission method help in characterizing the wave propagation in rock samples and corresponding anisotropy (Schmitt, 2015; Motra and Wuttke, 2016). Since determining and understanding the elastic constants of the geologic formation aids in evaluating the formation’s seismic anisotropy that describes variation in seismic waves velocity

716

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

with propagation and polarization directions, it will ultimately leads to a better seismic characterization of the formation (Leslie and Lawton, 1999, Martínez and Schmitt, 2013, Motra and Stutz, 2018). Vertical transverse isotropy (VTI) is the most popular symmetry for detailed description of layered and foliated rocks while also having modest requirements for data acquisition. Recent literatures described the application of VTI-symmetry in detail (Abell et al., 2014; Chain and Schmitt, 2015; Lo et al., 1986; Martínez and Schmitt, 2013; Wang, 2002a; and Wang, 2002b), whereas other literatures have fully characterized the anisotropy of VTI-media using the Thomsen anisotropic parameters (Thomsen, 1986). Orthorhombic symmetry, though often discarded in favor of a simpler VTI-assumption, is being successfully used to analyze models featuring more complex anisotropy (Cheadle et al., 1991; Elapavuluri and Bancroft, 2006; Song, 2000). To fully describe the anisotropy and thereby the propagation of elastic waves in orthorhombic media, Tsvankin (1997) extended the original Thomsen Parameters for VTI-Media for the application in the more complex orthorhombic model. Given that elastic constants control wave velocity and anisotropic parameters, measuring elastic stiffness constants (given by Eqs.2 and 9) of the geologic medium was deemed to be necessary. This paper presents the results of the seismic wave velocities measurement in three orientations, the elastic constants, and the anisotropy parameters of the selected samples based on VTI and orthorhombic anisotropic media. The goal of this research is to determine the elastic stiffness constants, quantify the degree of seismic anisotropy in the rock sample under in situ pressure and temperature conditions, and demonstrate their impact on characterizing crystalline rocks. We also assessed the influence of pressure and thermal stresses (loading and heating) on the elastic stiffness constants. To determine these relationships, mechanical and temperature stress tests were conducted on rock samples that were exposed to various loading and thermal stresses. We collected three metamorphic rock samples for this study from the Larderello field, which is a highly active geothermal field in Italy. The geology of the site was well described by Bellani et al. (2004) and Minissale (1991). The Department of Geomechanics and Geotechnics at the Christian-Albrechts-University Kiel conducted the measurement of elastic wave velocity using a multi-anvil pressure apparatus while a comprehensive geological analysis of the samples was investigated by Willems (Willems, 2016). To the best of our knowledge, such measurements have not been conducted on rock samples from active geothermal field before. In the experimental procedure the sample cubes were exposed to a program of varying confining pressure and temperature changes up to 600 MPa and 600 °C. Transducers operated both at 2 MHz and 1 MHz induced elastic waves using the ultrasonic pulse transmission technique. Acoustic emissions were recorded to calculate elastic constants. Measured wave velocities consisted of three mutual orthogonal VPwave speeds (VP(X), VP(Y), VP(Z)) and two corresponding VS-wave speeds respectively as well as three more measurement of Vp-waves at 45° to the X-, Y- and Z- axis of the reference system (Fig. 1). The dimension of the cube sample was approximately 71.1 mm x 71.1 mm x 71.1mm.

2. Theoretical Background The designation of elastic waves is being conducted according to the wave mode, direction of propagation and polarization. The Vi(jk) wave therefore describes the velocity of a wave mode i (VS = transversal, VP = longitudinal) with a propagation in j-direction and a polarization in k-direction. Identical induces occurring with Vpwaves are merged to a single index. The 45° inclining waves are designated according to the plane spanning axes. Hence VP45(YZ) describes the wave velocity of a VP-wave polarized in the YZ-plane with a 45° angle of incidence to the XY-plane (foliation plane), (Fig. 1).

Fig. 1. Designation of elastic wave velocity in a generic medium (modified Yin, 1992). The sample size is 71.1 mm cube.

2.1. Elasticity Hooke’s Law defines the relation of the second-rank stress and strain tensors as follows: σ ij ¼ C i; j;k;l ϵkl

ð1Þ

where σ is the second-rank stress tensor, C represents a fouth-rank tensor of elastic stiffness with 3 4 = 81 elements and ϵ is a second-rank strain tensor and ijkl = 1, 2, 3 indicates one of the three orthogonal axes. The fourth rank stiffness tensor Ci, j, k, l is a factor to the strain tensor ϵkl and in this regard, describes the resistance against the deformation of a medium due to acting stress. With the Voigt notation, four subscripts of the stiffness and compliance tensors are reduced Ci, j, k, l to two rank stiffness matrix Ci, j. Due to the symmetry of stress and strain, the existence of a unique strain potential demanding that Ci, j, k, l = Ck, l, i, j and special relations regarding the chosen crystalsymmetry the stiffness matrix can be further simplified (Kaselow, 2004). Using a VTI-Symmetry the stiffness matrix can be described by Equation 2 below: 0

C 11 B C 12 B B C 13 C ij ¼ B B0 B @0 0

C 12 C 11 C 13 0 0 0

C 13 C 13 C 33 0 0 0

0 0 0 C 55 0 0

0 0 0 0 C 55 0

1 0 0 C C 0 C C 0 C C 0 A C 66

ð2Þ

where C12 = C11 − 2C66. In a VTI-symmetry only five elastic stiffness constants are mutually independent. Expressing the elastic constants as a function of wave velocity based on calculations are described in Eqs. 3-8 and illustrated by figure (2) (Chan and Schmitt, 2015). C 11 ¼ ρV 2P ðX Þ

ð3Þ

C 33 ¼ ρV 2P ðZ Þ

ð4Þ

C 55 ¼

! ρV 2S ðZX Þ þ ρV 2S ðZY Þ 2

ð5Þ

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

C 66 ¼

! ρV 2S ðXY Þ þ ρV 2S ðYX Þ 2

C 12 ¼ C 11 −2C 66 ¼ ρV 2P ðX Þ  2

C 13

ð6Þ ! ρV 2S ðXY Þ þ ρV 2S ðYX Þ 2

0 1  2 2 2 2 2 4ρ V ð XZ Þ−V ð XZ Þ − ð C −C Þ 11 33 P45 SV45 B C ¼@ A−C 55 4

ð7Þ

ð8Þ

where, VP(X, Y,Z) are the P − wave velocities in X, Y, Z directions, VS(ZX) is the S-wave velocity in ZX direction (see Fig. 10 in Appendix) and so on, ρ is the density of sample. Note that the arithmetic mean of the ideally identical shear wave velocity is used for the calculation of C55, C66 and C12 to gain representative elastic constants, while the formula to calculate C13 incorporates Vs-wave velocity as well as the velocity of a wave inclining 45° towards XY-plane. In contrast to a VTI-model an orthorhombic symmetry (Fig. 2) holds a total of nine different elastic stiffness constants and the corresponding stiffness matrix can be described by Equation (9). The elastic constants of this system can also be described by Eqs.(10-15) (Tsvankin, 1997 and Yin, 1992). 0

C 11 B C 12 B B C 13 C ij ¼ B B0 B @0 0

C 12 C 22 C 23 0 0 0

C 13 C 23 C 33 0 0 0

0 0 0 C 44 0 0

0 0 0 0 C 55 0

1 0 0 C C 0 C C 0 C C 0 A C 66

ð9Þ

C 11 ¼ ρV 2P ðX Þ

ð10Þ

C 22 ¼ ρV 2P ðY Þ

ð11Þ

C 33 ¼ ρV 2P ðZ Þ

ð12Þ

C 44 ¼

C 55 ¼

! ρV 2S ðZY Þ þ ρV 2S ðYZ Þ 2 ρV 2S ðZX Þ

þ 2

ð14Þ

Fig. 2. An orthorhombic model featuring three mutually orthogonal planes of symmetry due to vertical cracking of a VTI-medium (Tsvankin, 2001).

! ρV 2S ðXY Þ þ ρV 2S ðXY Þ 2

ð15Þ

Whilst the calculation of C55 and C66 is achieved by using the arithmetic mean of the corresponding shear waves, the calculation of the constants C12, C13 and C23 proves to be more complex. As described by Tsvankin (1997) and Kaselow (2004), those constants are derived by inserting a harmonic plane wave representation into the elastodynamic wave equation which yields the Christoffel Equation, a standard eigenvalue-eigenvector problem. For the final determination of C12, C13 and C23 on the basis of the Christoffel equation, the phase angle (Θ) has to be known. Since this is not the case with the provided data, only the elastic constants along the matrix principal diagonal were calculated. 2.2. Anisotropy For a description of anisotropy in VTI-media, the anisotropic parameters for weak anisotropy introduced by Thomsen (1986) can be calculated by Eqs.(16-18): ϵ≡

C 11 −C 33 2C 33

ð16Þ

γ≡

C 66 −C 55 2C 55

ð17Þ

δ≡

ðC 13 þ C 55 Þ2 −ðC 33 −C 55 Þ2 2C 33 ðC 33 −C 55 Þ

ð18Þ

In this regard ϵ equals VP- wave anisotropy, γ measures SH-wave anisotropy and δ describes the measure of the anellipticity of the VP-wave front. For orthorhombic media the Thomsen parameters have been extended by Tsvankin (1997) for application with three mutually orthogonal planes of isotropy: ϵð1Þ ≡

C 22 −C 33 2C 33

ð19Þ

ϵð2Þ ≡

C 11 −C 33 2C 33

ð20Þ

γð1Þ ≡

C 66 −C 55 2C 55

ð21Þ

γð2Þ ≡

C 66 −C 44 2C 44

ð22Þ

δð1Þ ≡

ðC 23 þ C 44 Þ2 −ðC 33 −C 44 Þ2 2C 33 ðC 33 −C 44 Þ

ð23Þ

δð2Þ ≡

ðC 13 þ C 55 Þ2 −ðC 33 −C 55 Þ2 2C 33 ðC 33 −C 55 Þ

ð24Þ

δð3Þ ≡

ðC 12 þ C 66 Þ2 −ðC 11 −C 66 Þ2 2C 11 ðC 11 −C 66 Þ

ð25Þ

ð13Þ

!

ρV 2S ðXZ Þ

C 66 ¼

717

In this regard ϵ equals VP-wave anisotropy, γ measures SH-wave anisotropy and δ describes the measure of the anellipticity of the VP-wave front. Equivalent to the VTI-parameter ϵ(1) and ϵ(2) describe the anisotropy of VP-waves propagating in the YZ- and XZ-plane while γ(1) and γ(2) describes the anisotropy of the corresponding S-waves. Both ϵ(3) and γ(3) are deemed redundant. δ(1), δ(2) and δ(3) are analogous to

718

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

VTI-media, the measure of the anellipticity of the VP-wave front propagating in the YZ-, XZ- and XY-plane. 3. Rock samples description The Enel Green Power group operating in the Larderello geothermal field in Italy has collected and analyzed three rock samples from a geothermal drilling operation. Willems (2016) provided a thorough description of the mineralogy and structure of the site. Table 1 provides a brief description of the rock samples based on Willems (2016) study. The fine grained quartz mica schist CA-A.11 (Fig. 3b) is part of the local Torrente Mersino Quarzitic Formation and features a distinct foliation, a planar schistosity with spacing sub 1 mm and highly deformational structures. It originates from a depth of 3452.2 m 3455.2 m and possesses a density of 2.722 g/cm 3. While quartz and to a lesser extent muscovite represent the main components, accessory minerals are represented in the form of tourmaline, zircon, chlorite, ilmenite, rutile and rare apatite. Additionally, very large calcitic plaque-crystals and veins are crosscutting the schistosity and grain boundaries often framed by chlorite. The amphibolite PU-B.4 (Fig. 3a) was collected from a depth of 3289.6 m–3296.2 m. It is mainly composed of hornblende, biotite, quartz, minor apatite, titanite and features a density of 2.936 g/cm 3, a planar schistosity and strong foliation, relatively small grain sizes. Both hornblende-dominated and quartz-biotite heterogenously dominated areas of 34 mm thickness were observed whereas elongated hornblende crystals up to 3 mm and smaller crystals in aggregates are present as well. Hydrothermal/metasomatic quartz k-feldspar CG-C.1 (Fig. 3c) comes from 1485.0 m - 1486.0 m depth and is composed of K-feldspar and chlorite, featuring fine grains with no visible preferred orientation and a density of 2.357 g/cm3. Further minor calcite and grains of pyrite as well as rare occurrences of apatite, rutile, titanite and rare earth silicates were observed in this sample. It shows also highly frequent pore space and veins frequently filled with both calcite and chlorite. 4. Experimental procedure Prior to the initial measurements, each rock sample was cut into two rectangular cubes/specimen. The alignment of the first specimen cut is related to the rock-structural features (X-axis parallel to lineation, Y-axis orthogonal to lineation in foliation plane and, Z-axis orthogonal to both lineation and foliation). The alignment of the structural features of the second specimen is rotated by 45° (Fig. 4) with the X-axis being center line to allow for a measurement of elastic wave velocity inclining 45° towards the foliation plain (Fig. 4). Density of each specimen is calculated based on the specimen mass and volume. The measurement of elastic wave velocity was conducted using a multi-anvil pressure apparatus. In order to simulate the in-situ conditions, rock samples were exposed to a gradual isothermal rise of confining pressure up to 150 MPa for the (CA-A.11 and PU-B.4 samples) respectively and up to 101 MPa for the (CG-C.1) sample at 20 ∘C. Subsequently, an isobaric increase in

the same setup, the applied load/pressure was kept constant at the maximum load (may need to make it more clear) while the temperature has increased gradually up to 600 ∘C for (CA-A.11 and PU-B.4) and up to 500 ∘ C for the CG-C.1. After reaching the maximum temperatures, the system was cooled down gradually to the initial temperature of 20 ∘C and elastic wave velocity was measured with the temperature decreasing at fixed intervals. When the samples temperature reached the initial temperature of 20 ∘C, a gradual unloading was applied down to the initial pressure level and the elastic wave velocity was recorded at fixed pressure intervals. We positioned sets of transducers and receivers operating at 2 MHz and 1 MHz at the opposite sides of the ultrasonics pulse transmission piston to induce and receive elastic waves respectively. For the shear-waves measurements, both shear wave transducers and receivers were used. Measuring the total wave run-time and subtracting from it the calibrated piston run-time yields the total run time of elastic waves in the sample. The corresponding wave velocity is calculated as the quotient of path and in-sample travel time. A full set of measured velocities including the measurement of three mutual orthogonal VP-wave velocities (VP(X), VP(Y), VP(Z)) and two corresponding s-wave velocities respectively as well as the measurement of three p-waves inclining 45° to the X-, Y- and Z- axis of the reference system. The latter set of measurement was achieved by measuring the sample cubes prepared 45° to foliation (Fig. 4). A volumetric and thereby density alteration as result of varying pressure and temperature conditions was measured by piston displacement. A schematic diagram of the transducer/piston/sample assembly for the velocity measurements at pressure and temperature is shown in Fig. 5. 5. Results We measured the Vp and VS velocities of the tested metamorphic core samples at a constant temperature and a varying confining pressure of up to 150 MPa and then at a constant confining pressure and a varying temperature up to 600 °C. Measurements were taken in three different directions with respect to the visible foliation plane of the rock samples. Fig. 6 shows the seismic velocity and anisotropy variation for the CA-A.11-90 ∘ (see Table 2). Seismic velocity increases with increasing pressure is a well-known behavior of natural rocks. However, the results showed that Vp is highly dependent on the propagation direction which means the samples are seismically anisotropic (Fig. 6 and Table 2). The slowest Vp was obtained perpendicular to the foliation of the rock (Z-direction), i.e. Vp(X) N Vp(Y) N Vp(Z) was true for all the samples. An incremental change in velocity was observed as loading increased. Loading seismic velocities are slightly lower than unloading velocities; this effect is called hysteresis (Gardner and Wyllie, 1965, Ahrenholz et al., 2008, Lotfollahi et al., 2016). Under increasing confining pressure, all three samples generally yielded faster elastic wave velocity as well as a higher density, while the wave velocity itself was decreasing gradually under increased loading. Up to a load level of approximately 50 MPa, a comparatively high nonlinear increase in elastic wave velocity was observed and referred to closing of the microcracks. Beyond 50 MPa, the velocity increase with pressure became less

Table 1 Mineralogical composition of the analyzed samples. Depth

Rock

[m]

Type

CA-A.11

3452.2 3455.2

Quartz-Mica Schist

PU-B.4

3289.6 3296.2

Amphibolite

CG-C.1

1485.0 1486.0

metasomatic-quartz k-feldspar

Minerals

Qtz, Ms, Chl, Tur, Ilm, Zr, Ap Hbl, Bt, Qtz, Pl, Ap Ms, Chl, Qtz, Py, Cc (+ Chl)

Structure And

Density 3

Porosity

Microstructures

[g/cm ]

[%]

Fine grained, foliated with deformational structures; Abundant Cc in crosscutting plagues and veins

2.722

1%

Small grain size, Hbl-prevailling levels 2 -3 mm thick, alternating with Bt + Qtz levels

2.936

2%

Fine grained, massive, no preferred orientation, highly frequent pores and veins partly filled by Cc (+ Chl)

2.357

9%

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

719

Fig. 3. The three measured rock samples (a) CA-A.11, (b) PU-4.B and (c) CG-C.1. Sample cube cut parallel to foliation (left), sample cube cut 45 to foliation (middle) and thin section of sample cut parallel to foliation plane (Willems, 2016). Red arrow indicates the drilling direction and black arrow indicates the x axis of measurement.

significant and was referred at this stage to the intrinsic effect of the mineral components (Kern and Schenk, 1988; Chan and Schmitt, 2015; and Willems, 2016). In the course of a decompression, a typical reverse velocity-pressure behavior was observed. After completing the

Fig. 4. Schematic designation of the frame of reference of the first sample cube 43 mm (a) with X-axis parallel to lineation, Y-axis normal lineation in foliation plane and Zaxis normal to foliation plane and second sample cube 43 mm (b) with A-Axis parallel to lineation in foliation plane, B = Y + 45 ∘ and C = Z+ 45 ∘ (modified from Willems, 2016).

experimental procedure, both elastic wave velocity and density showed higher values compared to their values prior to applying loading and this behavior was described by the hysteresis phenomenon. An isobaric thermal increase evokes a generally inconsistent change in elastic wave velocity due to differences in structure and mineral composition and a resultant varying thermal behavior, while a decreasing density can be explained by thermal expansion (Willems, 2016). Compressional wave velocities, shear wave velocities, shear wave splitting, anisotropy, density, Possion’s ratio of sample CA-A.11 are presented in Table 2. As discussed earlier, elastic constants are derived as the product of both density and squared wave velocity. The change of elastic constants as a function of pressure and temperature is therefore analogous to the observed trends of elastic wave velocity. The first observation is the significant difference of the measured Vp between the three different sides of the cube. Vp was fastest when measured between the two opposite X (Vpmax) directions normal to the foliation, intermediate between the two opposite Y sides, and slowest between the two opposite Z (Vpmin) sides, parallel to the lineation. A Vp difference between the X and Z directions was estimated at 1680 m/s at the room temperature, which indicate a huge seismic anisotropy and variation in elastic stiffness as the Vp changed dramatically with the change in direction. An increase in pressure yields higher elastic stiffness constants (given in Equation 2 and 9), whereas an unloading results in decreasing elastic constants. At low pressure, the elastic stiffness increases nonlinearly with increasing pressure but at high pressure increases linearly (e.g. see Figs. 7a, 7b, 7c and Table 3). At low pressure, the texture-related anisotropy is

720

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

Fig. 5. True triaxial multi anvil pressure apparatus at Kiel University for direct measurements of VP- and VS-wave travel times (left). Schematic arrangement of VP- and VS- wave transducers, sample, piston and cooling system (modified Kern et al., 1997; Willems, 2016).

superposed with microcrack-related anisotropy. Figs. 7a, 7b, 7c and Table 3 show anisotropic patterns of elastic constants associated with the true triaxial, polyaxial loading and VTI symmetry loading, unloading and heating processes for sample CA-A.11. Figs. 8a, 8b, 8c and Table 4 show anisotropic patterns of elastic constants associated with the true triaxial, polyaxial loading and Orthorhombic symmetry loading, unloading and heating processes for sample CA-A.11. Furthermore, Figs. 9a, 9b, 9c, and Tables 5 and 6 show Thomsen and Tsvankin anisotropic parameters associated with loading, unloading and heating processes for sample CA-A.11. Similarly, Tables 7 to 14 show the elastic constants and anisotropy parameter of PU-B.4 and CG-A.1 rock samples associated with loading, unloading and heating processes in VTI and orthorhombic symmetry conditions. In the case of CA-A.11, an isobaric rise of temperature results in a slight rise of elastic constants value, while for both PU-4.B and CG-C.1 a minor increase of constants values can be observed. Higher elastic constants observed after completing the experiment is explained by the hysteresis phenomenon.

6. Discussion The anisotropy in metamorphic rocks is usually due to the preferred orientation of the rock forming minerals, texture, structural features, pores and micro-cracks. In this research, we studied the sources of seismic anisotropy based on the analysis of velocity-pressure-temperature dependence curves to simulate the in-situ conditions of the rock layer. All independent elastic stiffness including C11, C22, C33, C44, C55, C66,

C12, C13 are determined from the directions-dependent seismic velocities (equations are in Section2). Since elastic constants (Tables 3, 4, 7, 8, 11, 12) are directly derived from elastic wave speed (Table 2), a comparative analysis shows an analogous behavior in a varying stress and temperature domain. In all stages of loading, heating and unloading longitudinal wave speed is considerably higher than transversal wave speed. Being aligned to predominant mineral direction, VP(X) is the fastest while VP(Z) is the slowest due to its polarization normal to foliation plane. The three constants C11, C22 and C33 that are calculated using the axial longitudinal waves (VP(X), VP(Y), VP(Z)) hold accordingly values greater than those being calculated using transversal waves (C44, C55, C66). Furthermore, constants calculated using wave velocities polarized parallel to the lineation direction are always higher. In contrast, elastic constants derived using seismic waves polarized normal to the foliation plane tend to be the lowest in their respective group, due to the corresponding slowest wave velocity. When a sample is loaded up to level of 101 MPa, micro-cracks and pores are closing which results in an increased speed of elastic waves as can be seen in Table 2. At higher pressure the increase in speed is dependent on intrinsic elastic properties of rock-forming minerals. A direct comparison of elastic wave speed and elastic constants shows an equivalent development. A disproportional increase of both wave speed and corresponding elastic properties can be attributed to a closing of the pores and microcracks, whereas a further increase approximates a linear function and is therefore solely dependent on the mineral composition. It is striking that the biggest change manifests in VP(Z)) and its

Fig. 6. CA-A.11: VP wave velocities and Vp wave anisotropy an a function of loading, temperature and unloading

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

721

Fig. 7. CA-A.11: Elastic Constants (VTI Symmetry, (a) as a function of pressure at constant room temperature (b) as a function of temperature at constant pressure 150 MPa (c) unloading at constant room temperature) (figure a and c look similar, mention ’loading’ on figure a and ’unloading’ on figure c)

corresponding elastic constants, which can be attributed to a higher compression capability vertical to foliation. In this regard C12 is an anomaly, showing an increase at the first loading stage followed by a constant decrease to a point slightly above the initial level. This behavior is caused by the natural derivation of the initial VTI − assumption, which is the speed of all elastic waves polarized parallel to foliation plane are equal. C12 is derived by the difference of averaged p − wave speed polarized parallel to foliation plane and twice the s − wave speed normal to the foliation polarized both parallel and vertical to

lineation. Since the initial VTI − assumption is not fulfilled and the wave speeds polarized parallel to lineation do not equal the speeds polarized vertical to lineation, the constant C12 exhibits an abnormal behavior and therefore does not hold significant value for interpretation. As discussed previously, an elastic stiffness tensor describes the resistance against a deformation due to an acting stress, hence the individual elastic constants of natural rocks are to be expected to feature well-defined as well as positive values. In the calculation of PU-B.4 both negative and undefined values occur for C13 up to an isothermic

Fig. 8. CA-A.11: Elastic Constants (Orthorhombic Symmetry, (a) as a function of pressure at constant room temperature (b) as a function of temperature at constant pressure 150 MPa (c) Unloading at constant room temperature)(mention ’loaded’ on figure a and ’unloaded’ on the figure c)

722

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

Fig. 9. CA-A.11: Anisotropic Parameters (a) as a function of pressure at constant room temperature (b) as a function of temperature at constant pressure 150 MPa (c) unloading at constant room temperature

load level of 50 MPa. Since C13 is calculated using the longitudinal and transversal wave velocities of both the parallel and the 45° to foliation cut sample, an inconsistency in structure and mineralogy of both samples leads to distorted or numerically implausible results. In the case of PU-B.4, the two cut sample cubes are not mutually representative, hence a joint calculation utilizing wave velocities of both samples results in comparatively small or undefined values for C13. With the partial exception of C13 of PU-B.4, the full set of elastic constants in a VTIsymmetry can be calculated using the provided data. Using an orthorhomic symmetry, all constants along the matrix main-diagonal can be derived using the known wave velocities. The VTI results indicate that C11 N C33 N C55 N C12 N C66 N C13 in all conditions such as loading, temperature stress and unloading. Furthermore, orthorhomic symmetry indicate that C11 N C22 N C33 N C55 N C66 N C44 in all cases. When a sample is loaded, micro-cracks and pores begin closing at a certain rate; however, during unloading and because of the frictional forces, the opening rate of the micro-cracks and pores is lower than the closing rate for a given loading. At constant loading with increasing temperature, the exiting and the new micro-cracks start to open causing a decrease in the velocities. This may also happen due to chemical reactions that start with increasing the temperature at constant loading. The anisotropic parameters are decreasing as a function of pressure but not as a function of temperature vice versa in VTI and orthorhomic system. The propagation error through the uncertainties for C11, C22, C33, C44, C55, C66, are expected to be lower compared to that for C12, C13 due to uncertainties equations in Section2.2. In an environment of varying pressure and temperature all analyzed sets of elastic constants exhibit similar relations (what kind of reaction). The three constants C11, C22 and C33 that are calculated using the axial longitudinal waves (VP(X), VP(Y), VP(Z)) hold values greater than those being calculated using transversal waves (C44, C55, C66). Furthermore constants calculated using wave velocities polarized parallel to the lineation direction are always higher. In contrast, elastic constants derived using seismic waves polarized normal to the foliation plane tend to be the lowest in their respective group, due to the corresponding slowest wave velocity.

Even though the full set of orthorhombic constants can not be derived using the given data, the calculated constants along the matrix main-diagonal can still be used for the validation of the VTI-model. A hypothetical perfect VTI-symmetry is based on the assumption that C11 equals C22, since both parameters are derived from wave velocities polarized in the horizontal isotropic plane. The coefficient of variation, which describes the relative standard deviation, is used as a relative measure of deviation between two corresponding constants. The maximum deviation of constants calculated from wave velocities propagating in the isotropic plane differs slightly between the three samples and gets further reduced with increasing pressure, whereas a rise in temperature yields a higher divergence of C11 and C22. While CA-A.11 and CG-C.1 showed an absolute decrease of 6.3% and 7.1% (from the initial 13.9% and 14.3%) at maximum load level, Puntone-4B did not show a significant change and stayed at a low level of 5.7%. An increase in temperature at maximum load level led to a temporary and reversible increase in all three samples up to 1.9% (CA-A.11), 0.7% (PU-B.4) and 4.0% (CG-C.1). It can be postulated that increasing the pressure lead to an increase of the viability of the VTI-assumption. PU-B.4 is in this regards an exception and features a low degree of divergence at all load levels. In summary it can be stated that the calculated divergence from an ideal horizontal isotropic plane is sufficiently small and allows for a viable application of the VTI-model. A constant loading with increasing temperature causes the existing as well as the new micro-cracks to open and yields a decrease in velocities. This may also happen due to chemical reactions that start with increasing temperature at constant loading. A comparison of Table 2 and Tables 3, 4, 7, 8, 11, 12) shows an equivalent behavior of the corresponding elastic constants. The decrease of pressure leads to a decrease of the elastic wave speed slightly below the initial values due to reducing compaction and reopening of pores and cracks.It is also noted that due to frictional forces, the opening rate of the micro-cracks and pores is lower than the closing rate for a given loading. The persistent higher wave speed and the comparatively higher elastic constants after unloading can be attributed to hysteresis phenomenon.

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

In order to quantify the anisotropy of the rock samples, we had to calculate Thomsen parameters at VTI and Orthorhombic media for all samples (Figs. 9a, 9b, 9c and Tables 5, 6, 9, 10, 13, 14). Uncertainties are included to comparatively show the influence of the calculated C12 and C13 (Motra et al., 2013a, 2013b, 2014a, 2014b, 2014c, 2016a, 2016b, Motra and Wuttke, 2016; Keitel et al., 2014, Motra and Stutz, 2018). Thomsen parameter ϵ of all samples showed high VP wave anisotropy at low stress, 0.338 at 12 MPa to 0.083 at 150 MPa, mainly due to the closure of the micro-cracks. It was also observed that the samples showed higher hysteresis of δ at lower pressures than at higher pressures. The rate of change of Thomsen parameters at different temperatures and pressures was low for both the VTI and orthorhomic system. On the other hand, all samples showed low V-S- wave anisotropy in all ranges of loading, unloading stress and temperature stress (e.g. at unloading, γ = -0.021 at 150 MPa and γ = -0.051 at 12 MPa) for the VTI system. This also was observed for the elastic stiffness C11 and C33 where they have been subjected to significantly different loading stress and temperature stress in all ranges. The anisotropy parameters for sample CA-A.11, ϵ1 (e.g. 0.146 at 12 MPa and 0.059 at 150 MPa) and ϵ2 (e.g. 0.328 at 12 MPa and 0.145 at 150 MPa) in orthorhombic media depends upon the anisotropy of VP- wave. The values of ϵ1 and ϵ2 are relatively high due to high VP wave anisotropy of the sample (Fig. 6). The values of γ1 and γ2 are relatively low due to low VS-wave anisotropy of this sample.

723

Velocity measurements were taken at normal conditions with a temperature increasing up to 600 ∘C while maintaining a constant pressure. The metamorphic rocks exhibited stress and thermal induced anisotropy in both VTI and Orthorhombic media. Our measurements indicate that crack closure along the direction of increasing pressure, and new and existing crack opening along the direction of thermal stress are the primary causes of this anisotropy effect. From our laboratory measurement and calculated elastic constants and anisotropy parameters, intrinsic wave velocity anisotropy resulted mostly from preferred grain orientation and microcracks system. VTI-symmetry allows for an adequate depiction of the analysed metamorphic rock samples stiffness and can be quantified. The calculation of more complex orthorhombic symmetry can be performed partially and allows for a complementary examination of the constants corresponding with the foliation plane. The occurring anisotropy was the result of pores, cracks, differences of preferred alignment of the petrogenetic minerals, structural features, and secondary geological overprints which led to different wave velocity depending on their respective direction of propagation. A significant decrease of anisotropy can be attributed to the closing of pores and cracks up to a load level of 50 MPa while intrinsic features such as mineral orientation do not change substantially with increasing pressure. The incidence of negative and undefined elastic stiffness constants can be attributed to the experimental set-up and differences in sampling and does not describe the intrinsic material properties in this regard.

7. Conclusion Acknowledgements This paper presented an extensive laboratory study of the elastic stiffness constants and anisotropy parameters of metamorphic rock samples collected from a highly active geothermal field using ultrasonic wave techniques. Ultrasonic Vp and VS- wave velocities were measured under dry conditions at loading and unloading ranging from 12 to 150 MPa at room temperature to simulate the in-situ conditions. Appendix

Fig. 10. Sample reference system

This research is supported by European Union's Horizon 2020 project Drilling in supercritical geothermal condition (DESCRAMBLE) and rock samples provided by ENEL Green Power, which is gratefully acknowledged by the authors.

724

Table 2 Compression wave velocities, shear wave velocities, shear wave splitting, anisotropy, density, Possion’s ratio of sample CA-A.11 Temp

Density

Poisson’s

Comp.wavevelocities(Vp)

Mean

Anisotropy

Shear wave velocities (V s) and shear wave splitting

[MPa]

[∘C]

[g/cm3]

Ratio

X

Y

Z

Vp

A-Vp

YX

ZX

Mean

XY

ZY

Mean

YZ

XZ

[-]

[km/s]

[km/s]

[km/s]

[km/s]

[%]

[km/s]

[km/s]

[km/s]

[km/s]

[km/s]

[km/s]

[km/s]

[km/s]

Loading

12 25 35 50 76 101 150 150

20 20 20 20 20 20 20 20

2.722 2.727 2.729 2.736 2.736 2.739 2.743 2.745

0.182 0.196 0.208 0.207 0.202 0.202 0.202 0.203

5.917 6.062 6.142 6.113 6.263 6.339 6.363 6.366

5.142 5.467 5.581 5.661 5.763 5.821 5.895 5.904

4.270 4.696 5.089 5.315 5.451 5.542 5.674 5.696

5.110 5.408 5.604 5.731 5.825 5.901 5.977 5.989

32.22 25.26 18.79 15.68 13.94 13.50 11.53 11.18

3.381 3.482 3.533 3.598 3.694 3.734 3.767 3.770

3.512 3.648 3.725 3.803 3.863 3.881 3.894 3.893

3.447 3.565 3.629 3.701 3.779 3.807 3.830 3.832

3.250 3.386 3.449 3.489 3.508 3.552 3.613 3.619

2.844 3.065 3.158 3.267 3.362 3.414 3.469 3.473

3.047 3.225 3.303 3.378 3.435 3.483 3.541 3.546

3.032 3.123 3.216 3.326 3.430 3.491 3.551 3.554

Temperatureincrease

150 150 150 150 150 150

100 200 300 400 500 600

2.743 2.734 2.724 2.710 2.694 2.670

0.202 0.200 0.193 0.184 0.169 0.139

6.353 6.336 6.285 6.223 6.131 5.943

5.870 5.840 5.793 5.727 5.631 5.407

5.696 5.691 5.647 5.585 5.473 5.261

5.973 5.956 5.908 5.845 5.745 5.537

10.99 10.83 10.80 10.91 11.46 12.31

3.778 3.773 3.773 3.767 3.763 3.722

3.891 3.885 3.878 3.872 3.860 3.825

3.834 3.829 3.826 3.819 3.812 3.773

3.614 3.613 3.612 3.603 3.588 3.544

3.464 3.456 3.449 3.439 3.425 3.403

3.539 3.534 3.531 3.521 3.506 3.474

Unloading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

2.720 2.724 2.726 2.728 2.730 2.731 2.732

0.196 0.195 0.189 0.189 0.192 0.194 0.195

6.196 6.261 6.295 6.327 6.361 6.376 6.405

5.674 5.778 5.821 5.876 5.910 5.929 5.953

5.198 5.434 5.517 5.607 5.701 5.765 5.807

5.689 5.824 5.878 5.937 5.991 6.023 6.055

17.53 14.19 13.23 12.14 11.02 10.15 9.89

3.663 3.750 3.837 3.840 3.829 3.832 3.837

3.814 3.894 3.944 3.959 3.948 3.945 3.947

3.738 3.822 3.891 3.900 3.889 3.889 3.892

3.478 3.512 3.560 3.628 3.653 3.673 3.691

3.297 3.401 3.452 3.486 3.514 3.532 3.545

3.388 3.456 3.506 3.557 3.584 3.602 3.618

Mean

Anisotropy

Mean

Vs

A-Vs

[km/s]

[km/s]

[%]

3.088 3.259 3.328 3.419 3.502 3.555 3.612 3.615

3.060 3.191 3.272 3.372 3.466 3.523 3.581 3.585

3.184 3.327 3.401 3.484 3.560 3.604 3.651 3.654

20.99 17.51 16.66 15.38 14.09 12.94 11.62 11.51

3.547 3.542 3.540 3.534 3.522 3.486

3.607 3.605 3.612 3.611 3.593 3.530

3.577 3.573 3.576 3.573 3.557 3.508

3.650 3.646 3.644 3.638 3.625 3.585

11.70 11.77 11.77 11.90 12.02 11.75

3.324 3.445 3.496 3.548 3.590 3.619 3.636

3.416 3.508 3.555 3.603 3.649 3.675 3.696

3.370 3.477 3.525 3.575 3.620 3.647 3.666

3.499 3.585 3.641 3.677 3.697 3.713 3.725

14.77 13.74 13.53 12.87 11.76 11.13 10.78

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

Pressure

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

725

Table 3 CA-A.11: elastic constants for VTI-symmetry. Pressure

Temp.

C11

C33

C55

C66

C12

C13

[MPa]

[°C]

[GPa]

[GPa]

[GPa]

[GPa]

[GPa]

[GPa]

Loading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

83.232 90.620 93.763 96.383 98.929 101.255 103.049

49.637 60.146 70.685 77.172 81.295 84.137 88.307

27.489 30.722 32.324 34.146 35.707 36.446 37.180

25.493 27.774 29.216 31.071 32.876 33.989 35.188

32.247 35.073 35.330 34.241 33.178 33.276 32.672

10.585 14.945 17.108 18.406 19.383 20.314 21.022

Temperature increase

150 150 150 150 150 150 150

20 100 200 300 400 500 600

103.297 102.449 101.340 99.332 96.750 93.173 86.000

89.050 89.004 88.556 86.841 84.533 80.686 73.909

37.230 37.089 36.836 36.560 36.220 35.745 34.878

35.264 35.094 34.911 34.828 34.591 34.091 32.861

32.770 32.261 31.519 29.675 27.569 24.991 20.278

21.168 20.253 19.386 18.097 16.577 14.248 10.237

Unloading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

95.793 98.687 100.049 101.570 102.791 103.396 104.303

73.489 80.422 82.982 85.761 88.741 90.775 92.109

34.382 36.239 37.281 37.804 38.011 38.173 38.331

30.888 32.920 33.877 34.876 35.773 36.331 36.716

34.017 32.848 32.296 31.818 31.246 30.734 30.871

2.679 6.243 6.386 7.654 9.755 11.285 12.455

Table 4 CA-A.11: elastic constants for orthorhombic symmetry. Pressure

Temp.

C11

C22

C33

C44

C55

C66

[MPa]

[°C]

[GPa]

[GPa]

[GPa]

[GPa]

[GPa]

[GPa]

Loading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

83.232 90.620 93.763 96.383 98.929 101.255 103.049

71.985 81.496 85.002 87.695 90.868 92.821 95.341

49.637 60.146 70.685 77.172 81.295 84.137 88.307

23.497 26.109 27.722 29.691 31.555 32.650 33.802

29.644 32.525 33.936 35.625 37.110 37.861 38.633

29.922 32.159 33.260 34.310 35.478 36.353 37.357

Temperature increase

150 150 150 150 150 150 150

20 100 200 300 400 500 600

103.297 102.449 101.340 99.332 96.750 93.173 86.000

95.669 94.519 93.250 91.408 88.893 85.424 78.076

89.050 89.004 88.556 86.841 84.533 80.686 73.909

33.876 33.702 33.473 33.263 32.950 32.501 31.689

38.685 38.549 38.343 38.200 37.939 37.411 36.107

37.458 37.467 37.285 37.137 36.795 36.385 35.253

Unloading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

95.793 98.687 100.049 101.570 12.791 103.396 104.303

87.562 90.936 92.383 94.189 95.367 96.019 96.802

73.489 80.422 82.982 85.761 88.741 90.775 92.109

29.808 31.912 32.895 33.740 34.451 34.917 35.221

35.541 37.311 38.326 39.006 39.399 39.650 39.890

34.677 35.908 37.293 38.042 38.214 38.468 38.704

Table 5 CA-A.11: Thomsen parameter for VTI-symmetry. Pressure

Temp.

ϵ

γ

δ

VP(0)

VS(0)

[MPa]

[°C]

-

-

-

[m/s]

[m/s]

Loading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

0.338 0.253 0.163 0.124 0.108 0.102 0.083

-0.036 -0.048 -0.048 -0.045 -0.040 -0.034 -0.027

0.436 0.345 0.179 0.137 0.129 0.118 0.086

5110 5408 5604 5731 5825 5901 5977

3184 3327 3401 3484 3560 3604 3651

Temperature increase

150 150 150 150 150 150 150

20 100 200 300 400 500 600

0.080 0.076 0.072 0.072 0.072 0.077 0.082

-0.026 -0.027 -0.026 -0.024 -0.022 -0.023 -0.029

0.079 0.064 0.053 0.053 0.055 0.066 0.089

5989 5973 5956 5908 5845 5745 5337

3646 3650 3646 3644 3638 3625 3585

(continued on next page)

726

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

Table 5 (continued)

Unloading

Pressure

Temp.

ϵ

γ

δ

VP(0)

VS(0)

[MPa]

[°C]

-

-

-

[m/s]

[m/s]

12 25 35 50 76 101 150

20 20 20 20 20 20 20

0.152 0.114 0.103 0.092 0.079 0.070 0.066

-0.051 -0.046 -0.046 -0.039 -0.029 -0.024 -0.021

-0.027 -0.021 -0.024 -0.028 -0.032 -0.034 -0.032

5689 5824 5878 5937 5991 6023 6055

3499 3585 3641 3677 3697 3713 3725

Table 6 CA-A.11: Tsvankin parameters for orthorhombic symmetry. Pressure

Temp.

ϵ1

ϵ2

γ1

γ2

VP(0)

VS(0)

[MPa]

[°C]

-

-

-

-

[m/s]

[m/s]

Loading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

0.225 0.177 0.101 0.068 0.059 0.052 0.040

0.460 0.333 0.228 0.183 0.160 0.154 0.129

0.005 -0.006 -0.010 -0.018 -0.022 -0.020 -0.017

0.131 0.123 0.112 0.100 0.088 0.080 0.071

5110 5408 5604 5731 5825 5901 5977

3184 3327 3401 348 3560 3604 3651

Temperature increase

150 150 150 150 150 150 150

20 100 200 300 400 500 600

0.037 0.031 0.027 0.026 0.026 0.029 0.028

0.124 0.122 0.120 0.119 0.121 0.127 0.138

-0.016 -0.014 -0.014 -0.014 -0.015 -0.014 -0.012

0.071 0.072 0.073 0.074 0.076 0.076 0.070

5989 5973 5956 5908 5845 5745 5537

3654 3650 3646 3644 3638 3625 3585

Unloading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

0.096 0.065 0.057 0.049 0.037 0.029 0.025

0.210 0.164 0.151 0.137 0.123 0.112 0.108

-0.012 -0.019 -0.013 -0.012 -0.015 -0.015 -0.015

0.096 0.085 0.083 0.078 0.072 0.068 0.066

5689 5824 5878 5937 5991 6023 6055

3499 3585 3641 3677 3697 3713 3725

Table 7 PU-B.4: elastic constants for VTI-symmetry. Pressure

Temp.

C11

C33

C55

C66

C12

C13

[MPa]

[°C]

[GPa]

[GPa]

[GPa]

[GPa]

[GPa]

[GPa]

Loading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

66.621 79.207 86.512 95.121 102.768 113.201 124.839

22.488 32.225 38.143 46.636 58.495 68.007 83.007

16.280 18.880 21.214 23.769 27.348 28.781 32.734

14.941 18.503 20.639 22.921 26.644 28.921 32.615

36.739 42.201 45.233 49.278 49.481 55.359 59.609

-7.113 -8.519 -3.306 5.304 10.845 17.445

Temperature increase

150 150 150 150 150 150 150

20 100 200 300 400 500 600

123.919 126.125 130.678 135.009 135.509 137.265 137.095

85.339 87.553 91.707 96.317 97.584 98.060 98.735

33.110 34.586 36.441 37.064 36.891 37.336 38.936

33.034 34.153 35.980 36.671 36.975 36.757 36.484

57.851 57.820 58.718 61.668 61.558 63.751 64.128

19.176 20.302 22.531 23.291 24.721 24.450 23.528

Unloading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

93.061 105.313 123.059 131.534 132.973 131.358 134.725

52.303 63.330 71.604 77.336 86.749 93.624 97.488

27.383 29.729 31.944 35.287 39.734 40.079 40.103

27.008 30.074 31.608 33.098 34.828 35.810 37.114

39.045 45.164 59.842 65.338 63.316 59.737 60.497

3.554 8.314 5.541 7.846 11.274 16.384 21.883

Pressure

Temp.

C11

C22

C33

C44

C55

C66

[MPa]

[°C]

[GPa]

[GPa]

[GPa]

[GPa]

[GPa]

[GPa]

12 25 35 50

20 20 20 20

66.621 79.207 86.512 95.121

62.830 73.550 80.003 88.302

22.488 32.225 38.143 46.636

14.853 18.201 20.317 22.473

16.372 19.187 21.544 24.230

23.547 26.821 28.680 31.381

Table 8 PU-B.4: elastic constants for orthorhombic symmetry.

Loading

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

727

Table 8 (continued) Pressure

Temp.

C11

C22

C33

C44

C55

C66

[MPa]

[°C]

[GPa]

[GPa]

[GPa]

[GPa]

[GPa]

[GPa]

76 101 150

20 20 20

102.768 113.201 124.839

97.417 106.211 117.855

58.495 68.007 83.007

26.894 28.735 32.342

27.096 28.967 33.008

34.182 36.248 39.185

Temperature increase

150 150 150 150 150 150 150

20 100 200 300 400 500 600

123.919 126.125 130.678 135.009 135.509 137.265 137.095

119.296 122.713 125.414 131.621 133.207 131.305 130.946

85.339 87.553 91.707 96.317 97.584 98.060 98.735

32.811 34.049 35.769 36.591 36.813 36.745 37.204

33.334 34.690 36.654 37.144 37.054 37.348 38.199

39.770 42.114 44.611 43.533 43.847 44.380 43.977

Unloading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

93.061 105.313 123.059 131.534 132.973 131.358 134.725

80.803 92.509 114.078 129.921 132.995 129.436 133.908

52.303 63.330 71.604 77.336 86.749 93.624 97.488

27.571 29.668 31.779 35.025 37.032 37.686 38.463

26.823 30.136 31.773 33.352 37.450 38.144 38.725

34.310 36.308 38.852 40.480 42.895 44.128 44.563

Table 9 PU-B.4: Thomsen parameter for VTI-symmetry. Pressure

Temp.

ϵ

γ

δ

VP(0)

VS(0)

[MPa]

[°C]

-

-

-

[m/s]

[m/s]

Loading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

0.981 0.729 0.634 0.520 0.378 0.332 0.252

-0.041 -0.010 -0.014 -0.018 -0.013 0.002 -0.002

-0.046 -0.097 -0.049 0.026 0.006 -0.001

4098 4561 4811 5109 5413 5720 6089

2481 2686 2816 2961 3148 3248 3425

Temperature increase

150 150 150 150 150 150 150

20 100 200 300 400 500 600

0.226 0.220 0.212 0.201 0.194 0.200 0.194

-0.001 -0.006 -0.006 -0.005 0.001 -0.008 -0.031

0.001 0.022 0.042 0.012 0.009 0.011 0.028

6097 6151 6.276 6402 6431 6476 6496

3447 3521 3620 3630 3642 3659 3683

Unloading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

0.390 0.331 0.359 0.350 0.266 0.202 0.191

-0.007 0.006 -0.005 -0.031 -0.062 -0.053 -0.037

0.129 0.075 -0.030 0.014 0.048 0.032 0.049

5160 5553 5985 6212 6352 6407 6526

3168 3307 3419 3534 3679 3726 3767

Table 10 PU-B.4: Tsvankin parameters for orthorhombic symmetry. Pressure

Temp.

ϵ1

ϵ2

γ1

γ2

VP(0)

VS(0)

[MPa]

[°C]

-

-

-

-

[m/s]

[m/s]

Loading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

0.897 0.641 0.549 0.447 0.333 0.281 0.210

1.068 0.820 0.723 0.596 0.425 0.385 0.295

0.219 0.199 0.166 0.148 0.131 0.126 0.094

0.051 0.027 0.030 0.039 0.004 0.004 0.010

4098 4561 4811 5109 5413 5720 6089

2481 2686 2816 2961 3148 3248 3425

Temperature increase

150 150 150 150 150 150 150

20 100 200 300 400 500 600

0.199 0.201 0.184 0.183 0.183 0.170 0.163

0.254 0.240 0.242 0.219 0.206 0.231 0.226

0.097 0.107 0.109 0.086 0.092 0.094 0.076

0.008 0.009 0.012 0.008 0.003 0.008 0.013

6097 6151 6276 6402 6431 6476 6496

3447 3521 3620 3630 3642 3659 3683

Unloading

12 25 35 50 76 101 150

20 20 20 20 20 20 20

0.272 0.230 0.297 0.340 0.267 0.191 0.187

0.515 0.439 0.424 0.361 0.266 0.212 0.195

0.140 0.102 0.111 0.107 0.073 0.078 0.075

-0.014 0.008 0.000 -0.024 0.006 0.006 0.003

5160 5553 5985 6212 6352 6407 6526

3168 3307 3417 3534 3679 3726 3767

728

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

Table 11 CG-C.1: elastic constants for VTI-symmetry. Pressure

Temp.

C11

C33

C55

C66

C12

[MPa]

[°C]

[GPa]

[GPa]

[GPa]

[GPa]

[GPa]

C13 [GPa]

Loading

12 25 35 50 76 101

20 20 20 20 20 20

54.810 58.412 60.652 63.382 66.969 69.067

37.331 44.058 46.718 50.062 54.274 57.432

15.071 16.597 18.261 19.165 19.969 20.284

14.061 15.024 15.731 16.834 17.610 18.633

2.,689 28.365 29.189 29.715 31.748 31.801

8.336 10.030 9.511 9.330 9.547 10.689

Temperature increase

101 101 101 101 101 101

20 100 200 300 400 500

64.763 65.559 67.451 68.366 68.078 68.750

58.147 60.244 62.139 62.777 62.293 61.187

19.881 2.050 20.427 18.969 20.339 18.776

18.662 18.278 19.112 19.864 19.483 19.102

27.439 29.003 29.226 28.638 29.112 30.546

11.376 20.312 21.703 22.120 20.506 21.534

Unloading

12 25 35 50 76 101

20 20 20 20 20 20

56.268 58.944 60.442 61.976 64.038 65.414

46.010 50.596 53.151 56.370 59.730 61.513

16.322 17.690 18.534 19.267 19.894 20.206

16.588 17.853 18.374 19.379 20.019 20.544

23.092 23.237 23.695 23.219 24.001 24.327

19.585 19.975 20.032 20.620 20.848 20.783

Temp.

C11

C22

C33

C44

C55

C66

Table 12 CG-C.1: elastic constants for orthorhombic symmetry. Pressure [MPa]

[°C]

[GPa]

[GPa]

[GPa]

[GPa]

[GPa]

[GPa]

Loading

12 25 35 50 76 101

20 20 20 20 20 20

54.810 58.412 60.652 63.382 66.969 69.067

48.256 54.394 56.735 59.308 62.273 64.190

37.331 44.058 46.718 50.062 54.274 57.432

14.252 15.279 16.172 16.903 17.449 18.444

14.874 16.331 17.792 19.092 20.142 20.482

15.492 16.752 17.345 19.019 19.770 20.341

Temperature increase

101 101 101 101 101 101

20 100 200 300 400 500

64.763 65.559 67.451 68.366 68.078 68.750

64.521 65.194 65.867 66.252 66.203 65.727

58.147 60.244 62.139 62.777 62.293 61.187

18.499 18.120 18.916 19.622 19.249 18.911

20.050 20.216 20.631 19.207 20.579 18.966

20.458 20.739 21.060 19.686 20.982 19.307

Unloading

12 25 35 50 76 101

20 20 20 20 20 20

56.268 58.944 60.442 61.979 64.038 65.414

50.760 56.370 58.809 61.422 63.833 65.379

46.010 50.596 53.151 56.370 59.730 61.513

16.573 17.656 18.167 19.071 19.716 20.215

16.337 17.887 18.743 19.576 20.198 20.534

16.427 17.515 18.522 19.124 19.619 20.798

Table 13 CG-C.1: Thomsen parameter for VTI-symmetry. Pressure

Temp.

ϵ

γ

δ

VP(0)

VS(0)

[MPa]

[°C]

-

-

-

[m/s]

[m/s]

Loading

12 25 35 50 76 101

20 20 20 20 20 20

0.234 0.163 0.149 0.133 0.117 0.101

-0.034 -0.047 -0.069 -0.061 -0.059 -0.041

0.032 -0.019 -0.014 -0.046 -0.082 -0.099

4541 4757 4860 4986 5141 5239

2512 2613 2690 2784 2840 2886

Temperature increase

101 101 101 101 101 101

20 100 200 300 400 500

0.057 0.044 0.043 0.045 0.046 0.062

-0.031 -0.044 -0.032 0.024 -0.021 0.009

-0.109 0.003 0.007 -0.042 -0.018 -0.034

5134 5186 5266 5306 5299 5311

2881 2920 2874 2933 2920 2850

Unloading

12 25 35 50 76 101

20 20 20 20 20 20

0.111 0.082 0.069 0.050 0.036 0.032

0.008 0.005 -0.004 0.003 0.003 0.008

0.149 0.101 0.079 0.051 0.015 -0.005

4730 4874 4953 5041 5143 5206

2641 2737 2797 2854 2896 2945

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

729

Table 14 CG-C.1: Tsvankin parameters for orthorhombic symmetry.Thomsen parameter for VTI-symmetry. Pressure

Temp.

ϵ1

ϵ2

γ1

γ2

VP(0)

VS(0)

[MPa]

[°C]

-

-

-

-

[m/s]

[m/s]

Loading

12 25 35 50 76 101

20 20 20 20 20 20

0.146 0.117 0.107 0.092 0.074 0.059

0.328 0.210 0.192 0.175 0.162 0.145

0.021 0.013 -0.013 -0.002 -0.009 -0.003

0.022 0.034 0.050 0.065 0.077 0.055

4541 4757 4860 4989 5141 5239

2512 2613 2690 2784 2840 2886

Temperature increase

101 101 101 101 101 101

20 100 200 300 400 500

0.055 0.041 0.030 0.028 0.031 0.037

0.059 0.047 0.056 0.062 0.062 0.087

0.010 0.013 0.010 0.012 0.010 0.009

0.042 0.058 0.045 -0.011 0.035 0.001

5134 5186 5266 5306 5299 5311

2879 2881 2920 2874 2933 2850

Unloading

12 25 35 50 76 101

20 20 20 20 20 20

0.052 0.057 0.053 0.045 0.034 0.031

0.174 0.108 0.084 0.055 0.038 0.032

0.003 -0.010 -0.006 -0.012 -0.014 0.006

-0.007 0.007 0.016 0.013 0.012 0.008

4730 4874 4953 5041 5143 5206

2641 2737 2797 2854 2896 2945

References Abell, B.C., Shao, S., Pyrak-Nolte, L.J., 2014. Measurements of elastic constants in anisotropic media. Geophysics 79 (5), D349–D362. https://doi.org/10.1190/GEO20140023.1. Ahrenholz, B., Toelke, J., Lehmann, P., Peters, A., Kaestner, A., Krafczyk, M., Durner, W., 2008. Prediction of capillary hysteresis in a porous material using lattice-boltzmann methods and comparison to experimental data and a morphological pore network model. Adv. Water Resour. 31, 1151–1173. https://doi.org/10.1016/j. advwatres.2008.03.009. Aleksandrov, K.S., Ryzhova, T.V., 1961. The elastic properties of crystals. Sov. Phys. -Cryst. 6, 228–252. Anderson, N.L., Thitimakorn, T., Ismail, A., Hoffman, D., 2007. A comparison of four geophysical methods for determining the shear wave velocity of soils. Environ. Eng. Geosci. 13, 11–23. https://doi.org/10.2113/gseegeosci.13.1.11. Babuška, V., 1981. Anisotropy of vp and vs in rock-forming minerals. Geophysics 50, 1–6. Babuska, V., Cara, M.: Seismic Anisotropy in the Earth, Modern Approach. Geophys., vol. 10. Springer, Dordrecht (1991). https://doi.org/10.1007/978-94-011-3600-6 Bass, J.D., 1961. Elasticity of minerals, glasses, and melts, in mineral physics and crystallography: A handbook of physical constants. AGU Ref. Shelf 2, 45–63. Bellani, S., Brogi, A., Lazzarotto, A., Liotta, D., Ranalli, G., 2004. Heat flow, deep temperatures and extensional structures in the larderello geothermal field (italy): Constraints on geothermal fluid flow. J. Volcanol. Geotherm. Res. 132 (1), 15–29. https://doi.org/ 10.1016/S0377-0273(03)00418-9. Chan, J., Schmitt, D.R., 2015. Elastic anisotropy of a metamorphic rock sample of the canadian shield in northeastern alberta. Rock Mech. Rock. Eng. 48 (4), 1369–1385. https:// doi.org/10.1007/s00603-014-0664-z. Cheadle, S.P., Brown, R.J., Lawton, D.C., 1991. Orthorhombic anisotropy: A physical seismic modeling study. Geophysics 56 (10), 1603–1613. https://doi.org/10.1190/1.1442971. Cholach, P.Y., 2005. The elasticity of intrinsically anisotropic rocks. University of Alberta, Edmonton, Dissertation. Elapavuluri, P., Bancroft, J.C., 2006. Estimation of anisotropy parameters in orthorhombic media. SEG Technical Program Expanded Abstracts. Society of Exploration Geophysicists (2006), pp. 164–168 https://doi.org/10.1190/1.2369837. Gardner, G., Wyllie, M., 1965. Droschak: Hysteresis in the velocity-pressure characteristics of rocks. Geophysics 30, 111–116. Grana, D., 2016. Pressurevelocity relations in reservoir rocks: Modified macbeth’s equation. J. Alloed Geophys. 132, 234–241. https://doi.org/10.1016/j.jappgeo.2016.07.020. Gurevich, B., 2003. Elastic properties of saturated porous rocks with aligned fractures. J. Appl. Geophys. 57, 203–218. https://doi.org/10.1016/j.jappgeo.2002.11.002. Ismail, A., Benny, F.B., Metwaly, M., 2014a. Comparing continuous profiles from masw and shear-wave reflection seismic methods. J. Appl. Geophys. 105, 67–77. https://doi.org/ 10.1016/j.jappgeo.2014.03.007. Ismail, A., Stumpf, A., Bauer, R., 2014b. Seismic characterization of glacial sediments in central illinois. J. Appl. Geophys. 101, 1–10. https://doi.org/10.1016/j. jappgeo.2013.11.009. Jolly, R.N., 1956. Investigation of shear waves. Geophysics 21, 905–938. Kaselow, A., 2004. The stress sensitivity approach: Theory and application. Dissertation. Freie Universität Berlin, Berlin http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000001276. Kebaili, A., Schmitt, D.R., 1997. Velocity anisotropy observed in wellbore seismic arrivals: combined effect of intrinsic properties and layering. Geophysics 61, 12–20. Keitel, K., Jung, B., Motra, H., Stutz, H., 2014. Quality assessment of coupled partial models considering soil-structure coupling. Eng. Struct. 59, 565–573. https://doi.org/10.1016/ j.engstruct.2013.11.003.

Kern, H., Schenk, V., 1988. A model of velocity structure beneath calabria, southern italy, based on laboratory data. Earth Planet. Sci. Lett. 87 (3), 325–337. https://doi.org/ 10.1016/0012-821X(88)90020-9. Kern, H., Liu, B., Popp, T., 1997. Relationship between anisotropy of p and s wave velocities and anisotropy of attenuation in serpentinite and amphibolite. J. Geophys. Res. Solid Earth 102 (B2), 3051–3065. https://doi.org/10.1029/96JB03392. Leslie, J.M., Lawton, D.C., 1999. A refraction-seismic field study to determine the anisotropic parameters of shales. Geophysics 64, 1247–1252. Lin, C.P., Tang, S.H., 2007. Comprehensive wave propagation model to improve tdr interpretations for geotechnical applications. Geotech. Test. J. 30, 90–97. https://doi.org/ 10.1520/GTJ100012. Lo, T.w., Coyner, K.B., Toksöz, M.N., 1986. Experimental determination of elastic anisotropy of berea sandstone, chicopee shale, and chelmsford granite. Geophysics 51 (1), 164–171. https://doi.org/10.1190/1.1442029. Lotfollahi, M., K., I., B., M., W., A., H., C., J., K., W., M., D., D., 2016. Foam generation hysteresis in porous media: Experiments and new insights. Transp. Porous Media 116, 687–703. https://doi.org/10.1007/s11242-016-0796-6. Martínez, J.M., Schmitt, D.R., 2013. Anisotropic elastic moduli of carbonates and evaporites from the weyburn-midale reservoir and seal rocks. Geophys. Prospect. 61 (2), 363–379. https://doi.org/10.1111/1365-2478.12032. Migliori, A.F., 1993. Crystals and ultrasound. Los Alamos Sci. 21, 182–194. Miller D. E.L.S., B.W.H.: An in situ estimation of anisotropic elastic moduli for a submarine shale. J. Geophys. Res. 99(B11), 21,659–21,665 (1994) Minissale, A., 1991. The larderello geothermal field: A review. Earth Sci. Rev. 31 (2), 133–151. https://doi.org/10.1016/0012-8252(91)90018-B. Motra, H.B., Stutz, H., 2018. Geomechanical rock properties using pressure and temperature dependence of elastic p- and s-wave velocities, Geotech. Geotech. Geol. Eng. https://doi.org/10.1007/s10706-018-0569-9 (in press). Motra, H.B., Wuttke, F., 2016. Temperature dependence of elastic p- and s-wave properties of rocks: Applications to geothermal reservoir evaluation. Energy Geotechnics Proceedings of the 1st International Conference on Energy Geotechnics, ICEGT 2016, pp. 311–316. Motra, H.B., Zertani, S., 2018. Influence of loading and heating processes on elastic and geomechanical properties of eclogites and granulites. J. Rock Mech. Geotech. Eng. 10, 127–137. https://doi.org/10.1016/j.jrmge.2017.11.001. Motra, H.B., Dimmig-Osburg, A., Hildebrand, J., 2013a. Influence of measurement uncertainties on results of creep prediction of concrete under cyclic loading. Proceedings of the 8th International Conference on Fracture Mechanics of Concrete and Concrete Structures. Framcosl, pp. 805–814 isbn 978-84-941004-1-3. Motra, H.B., Dimmig-Osburg, A., Hildebrand, J., 2013b. Uncertainty quantification on creep deflection of concrete beam subjected to cyclic loading. Safety, Reliability, Risk and Lifecycle Performance of Structures and Infrastructures, Proceedings of the 11th International Conference on Structural Safety and Reliability. ICOSSAR. Motra, H.B., Dimmig-Osburg, A., Hildebrand, J., 2014a. Influenceof specimen dimensions and orientations on the tensile properties of structural steel. Materialpruefung/ Mater. Test 56 (11-12), 929–936. https://doi.org/10.3139/120.110659. Motra, H.B., Dimmig-Osburg, A., Hildebrand, J., 2014b. Quality assessment of models with an application to cyclic creep prediction of concrete. Int. J. Reliab. Saf. 8 (2), 262–283. doi.org/10.1504/IJRS.2014.069513. Motra, H.B., Dimmig-Osburg, A., Hildebrand, J., 2014c. Assessment of strain measurement techniques to characterize mechanical properties of structural steele. Eng. Sci. Technol. Int. J. 17 (4), 260–269. https://doi.org/10.1016/j.jestch.2014.07.006. Motra, H.B., Stutz, H., Wuttke, F., 2016a. Quality assessment of soil bearing capacity factor models of shallow foundations. Soils Found. 56 (2), 265–276. https://doi.org/ 10.1016/j.sandf.2016.02.009.

730

H.B. Motra et al. / Journal of Applied Geophysics 159 (2018) 715–730

Motra, H.B., Hildebrand, J., Wuttke, F., 2016b. Monte carlo method for the evaluation of measurement uncertainty: application to determine material properties. Probabil. Eng. Mech. 45, 220–228. https://doi.org/10.1016/j.probengmech.2016.04.005. Oeberseder, T., Behm, M., Kovacs, I., 2011. Falus: A seismic discontinuity in the upper mantle between the eastern alps and the western carpathians: Constraints from wide angle reflections and geological implications. Tectonophysics 504, 122–134. https://doi.org/10.1016/j.tecto.2011.03.009. Rabbel, W., Mooney, W.D., 1996. Seismic anisotropy of the crystalline crust: what does it tell us? Terra Nova 8 (1), 16–21. Rabbel, W., Koehn, D., Motra, H.B., Niederau, J., Schreiter, L., Thorwart, M., Wuttke, F., 2017. Seismic velocity uncertainties and their effect on geothermal predictions: A case study. Energy Procedia 125, 283–290. https://doi.org/10.1016/j. egypro.2017.08.178. Schmitt, J.C.R.: Elastic anisotropy of a metamorphic rock sample of the canadian shield in northeastern alberta. Rock Mech. Rock. Eng. 48, 1369–1385 (2015). DOI DOI 10.1007/ s00603-014-0664-z Schreiber, E.O., Anderson, L., Soga, N., 1973. Elastic constants and their measurement. 10. McGraw-Hill, New York. Song, L.P., 2000. Approximate formulae for acoustic wave group slownesses in weakly orthorhombic media. J. Phys. D. Appl. Phys. 33 (17), 81–86. Spikes, K.T., 2014. Error estimates of elastic components in stress-dependent vti media. J. Appl. Geophys. 108, 110–123. https://doi.org/10.1016/j.jappgeo.2011.06.004. Thomsen, L., 1986. Weak elastic anisotropy. Geophysics 51 (10), 1954–1966. https://doi. org/10.1190/1.1442051.

Tsvankin, I., 1997. Anisotropic parameters and p –wave velocity for orthorhombic media. Geophysics 62 (4), 1292–1309. https://doi.org/10.1190/1.1444231. Tsvankin, I., 2001. Seismic signatures and analysis of reflection data in anisotropic media. Handbook of Geophysical Exploration : SEISMIC Exploration, 1. ed. 29. Pergamon, Amsterdam U.A. Wang, Z., 2002a. Seismic anisotropy in sedimentary rocks, part 1: A single–plug laboratory method. Geophysics 67 (5), 1415–1422. https://doi.org/10.1190/1.1512787. Wang, Z., 2002b. Seismic anisotropy in sedimentary rocks, part 2: Laboratory data. Geophysics 67 (5), 1423–1440. https://doi.org/10.1190/1.1512743. Willems, T., 2016. Pressure and temperature Dependence of Elastic p- and s- Waves in Geothermal Core Samples at Reservoir Characterization. Christian-AlbrechtsUniversität zu Kiel, Kiel, Masterarbeit. Winterstein, D.F., 1990. P.B.N.P.: elocity anisotropy in shale determined from crosshole seismic and vertical seismic profile data. Geophysics 55, 470–479. Yin, H., 1992. Acoustic Velocity and Attenuation of Rocks: Isotrophy, Intrinsic Anisotropy, and Stress-induced Anisotrophy. Dissertation. Stanford University, Stanford https:// pangea.stanford.edu/departments/geophysics/dropbox/SRB/public/docs/theses/SRB_ 052_DEC92_YIN.pdf. Zhu, T., Harris, J.M., 2015. Improved estimation of p-wave velocity, s-wave velocity, and attenuation factor by iterative structural joint inversion of crosswell seismic data. J. Appl. Geophys. 123, 71–80. https://doi.org/10.1016/j.jappgeo.2015.09.005.