Method of calculating temperature and porosity of geological structure

Abstract

A method of calculating the temperature and/or porosity of a geological structure, wherein there is provided at least two geophysical parameters of the geological structure, the method including inverting the at least two geophysical parameters to estimate the temperature and/or porosity of the geological structure.

Claims

1. A method of drilling a geothermal well, the method comprising calculating a temperature and/or porosity of a geological structure, wherein there is provided at least two geophysical parameters of the geological structure, the at least two geophysical parameters comprising magnetic susceptibility or magnetic remanence, the method of calculating the temperature and/or porosity of a geological structure comprising: gathering at least two types of geophysical data of the geological structure, the at least two types of geophysical data comprising electromagnetic data or magnetic data; inverting the at least two types of geophysical data to calculate the at least two geophysical parameters; inverting the at least two geophysical parameters to estimate the temperature and/or porosity of the geological structure; and using the calculated temperature and/or porosity in a decision-making process for the drilling of the geothermal well, wherein the decision-making process comprises deciding where to drill, in which direction to drill, to which depth to drill, and/or whether to stop drilling based on the calculated temperature and/or porosity; wherein the inverting step comprises using one or more models in which there is statistical independence between the at least two geophysical parameters and statistical dependence between each respective geophysical parameter and the temperature and/or porosity of the geological structure, the one or more models comprising a Bayesian network describing a relationship between the at least two geophysical parameters and the temperature and/or porosity of the geological structure; the method further comprising drilling or stopping drilling the geothermal well based on a result of the decision-making process.

2. A method as claimed in claim 1 comprising using both the calculated temperature and the calculated porosity in the decision-making process for the drilling of the geothermal well.

3. A method as claimed in claim 1, wherein the at least two geophysical parameters are any geophysical parameters which are dependent on temperature and/or porosity, such as density, seismic velocity, magnetic susceptibility, electrical conductivity, electrical resistivity or magnetic remanence.

4. A method as claimed in claim 3, wherein the at least two geophysical parameters comprise electrical conductivity.

5. A method as claimed in claim 1, wherein the inverting step comprises using respective forward models for each respective geophysical parameter, the forward models each defining a relationship between the respective geophysical parameter and the temperature and/or porosity of the geological structure.

6. A method as claimed in claim 5, wherein the only variable(s) in each of the respective forward models is the temperature and/or porosity of the geological structure.

7. A method as claimed in claim 5, wherein there is provided calibration data comprising at least one measurement of each of the at least two geophysical parameters and the temperature and/or porosity of the geological structure, and wherein the method comprises optimising the respective forward models based on the calibration data.

8. A method as claimed in claim 1, wherein there is provided at least two types of geophysical data of the geological structure, the method comprising inverting the at least two types of geophysical data respectively to calculate the at least two respective geophysical parameter.

9. A method as claimed in claim 8, comprising obtaining the geophysical data.

10. A method as claimed in claim 1, wherein the method is for calculating the temperature of the geological structure, and wherein porosity data is included as a parameter in the inversion.

11. A method as claimed in claim 1, wherein the method is for calculating the porosity of the geological structure, and wherein temperature data is included as a parameter in the inversion.

12. A method of calculating a spatially-dependent function of temperature and/or porosity of a geological structure, comprising performing the method of claim 1 point-wise for a plurality of points over the geological structure to calculate the temperature and/or porosity at each of the plurality of points, and constructing the spatially dependent function of temperature and/or porosity.

13. A method as claimed in claim 1, wherein the temperature and/or porosity is found in three dimensions.

14. A method as claimed in claim 1, comprising: acquiring new geophysical data during or after drilling; inverting said new geophysical data to find corresponding new geophysical parameters; inverting said new geophysical parameters to provide updated estimates of the temperature and/or porosity.

15. A method of harnessing geothermal energy comprising the method as claimed in claim 1, and producing geothermal energy from the geothermal well.

16. A non-transitory computer program product comprising computer readable instructions that, when run on a computer, is configured to cause a processer to perform the method of claim 1.

17. The method as claimed in claim 14, further comprising using the updated estimates of the temperature and/or porosity in the decision-making process for the drilling of the geothermal well.

18. The method of claim 1, wherein the geophysical data comprise pre-drilling geophysical data.

19. The method of claim 18, wherein the pre-drilling geophysical data are used to provide a pre-drilling estimate of the temperature and/or porosity of the geological structure.

20. The method of claim 18, further comprising acquiring the pre-drilling geophysical data prior to drilling.

21. The method of claim 14, further comprising acquiring the geophysical data during drilling through one or more well logs in a partially-drilled well.

22. The method of claim 14, further comprising acquiring the geophysical data after the drilling of a well through one or more well logs in the well.

23. The method of claim 14, wherein the data acquired during or after the drilling comprises temperature data.

24. The method of claim 23, comprising using the temperature data to update previous temperature estimates by offering a further constraint to the inverting.

25. The method of claim 1, further comprising at least one of: calculating the temperature and/or porosity prior to a drilling operation; calculating the temperature and/or porosity during a drilling operation; and calculating the temperature and/or porosity after a well has been drilled.

Description

BRIEF DESCRIPTION OF THE DRAWING

(1) FIG. 1 shows a Bayesian network (a DAG) representing the model relationship between temperature A and geophysical parameters {σ, χ, ρ, v.sub.p, v.sub.s}. As shown in FIG. 1, the geophysical parameters in turn depend on geophysical data (like magnetotelluric data (MT), magnetic data (mag), gravity data (grav), and seismic data (Seismic)) which can be included in an extended Bayesian network.

DETAILED DESCRIPTION

(2) As is shown in the exemplary method below, the estimation of subsurface temperature is addressed, using inversion of at least two geophysical parameters. As a general workflow of this method, firstly geophysical parameters are obtained by single-domain inversion of respective geophysical data types. This may be 2D or 3D inversion. For instance, the geophysical data types may be two or more of magnetotelluric data (MT), magnetic data (mag), gravity data (grav), and seismic data (Seismic). When these data are inverted, they may find the following respective parameters: electric resistivity (or conductivity) (σ) from magnetotelluric data (MT); magnetic resonance (χ) from magnetic data (mag); density (ρ) from gravity data (grav); p-wave velocity (v.sub.p) from seismic data (Seismic); and s-wave velocity (v.sub.s) from seismic data (Seismic).

(3) Secondly, two or more of the geophysical parameters are inverted to obtain temperature using rock physics forward models. Forward models are illustrated schematically in FIG. 1 with the arrows connecting the temperature (A) with the geophysical parameters, and the respective geophysical parameters with the respective geophysical data types. For the seismic case the term inversion should be understood as either tomography or full-waveform inversion. For the magnetic and gravity data, the inversion is a Gravmag inversion, constrained on geometry.

(4) In the exemplary method below, temperature is computed from geophysical inversion of three geophysical parameters: magnetic resonance (χ), density (φ) and p-wave velocity (v.sub.p). Of course, other parameters or combinations could also be used, as discussed above. A porosity vs. depth trend could also be used to constrain the inversion.

(5) In the present method, it is assumed that the relationship between geophysical data and temperature or porosity can be modelled in terms of the Bayesian network, or directed acyclic graph (DAG), shown in FIG. 1.

(6) The joint probability distribution for a Bayesian network is defined by the marginal distributions of the parent nodes and the conditional distributions for the children. The joint distribution for variables (x.sub.i, . . . , x.sub.n) is then given by

(7) $\begin{array}{cc}p\left(x_i,\mathrm{.Math.},x_n\right)=\underset{i}{.Math.}p\left(x_i|x_i^{\mathrm{Pa}}\right),& \left(1\right)\end{array}$

(8) where x.sub.i.sup.Pa denote parent nodes. The top nodes of the network have no parents, Applying the general Bayesian factorization rule, Equation 1, to the DAG in FIG. 1, the joint probability of temperature and geophysical parameters can be written as

(9) $\begin{array}{cc}p\left(A,m_1,\mathrm{.Math.},m_n\right)=\underset{i=1}{\overset{n}{.Math.}}p\left(m_i|A\right)p\left(A;\lambda \right)& \left(2\right)\end{array}$

(10) where the model parameters m={χ, ρ, v.sub.p, v.sub.s, σ}, χ is magnetic susceptibility, ρ is mass density, v.sub.p is P-wave velocity, v.sub.s is S-wave velocity, σ is electroconductivity (inverse of resistivity) and A is temperature. The prior distribution p(A; λ) depends on the hyperparameter λ, to be discussed later. Using conditional independence of parameters m.sub.i, the joint distribution in Equation 2 can also be written as

(11) $\begin{array}{cc}p\left(A,m_1,\mathrm{.Math.},m_n\right)=p\left(A|m_1,\mathrm{.Math.},m_n\right)\underset{i=1}{\overset{n}{.Math.}}p\left(m_i\right),& \left(3\right)\end{array}$

(12) from equations 2 and 3 the posterior distribution for the temperature can be obtained,

(13) $\begin{array}{cc}p\left(A|m_1,\mathrm{.Math.},m_n\right)=\underset{i=1}{\overset{n}{.Math.}}\frac{p\left(m_i|A\right)}{p\left(m_i\right)}p\left(A;\lambda \right),& \left(4\right)\end{array}$

(14) and substituting the actual parameters for m.sub.i gives the following equation,

(15) $\begin{array}{cc}p\left(A|\chi ,\rho ,{\upsilon }_p\right)=\frac{p\left(\chi |A\right)p\left(\rho |A\right)p\left({\upsilon }_P|A\right)p\left(A;\lambda \right)}{p\left(\chi \right)p\left(\rho \right)p\left({\upsilon }_p\right)}.& \left(5\right)\end{array}$

(16) When the posterior distribution of A is known, the posterior expectation and posterior variance is given by
μ.sub.A|χ,ρ,vp=∫Ap(A|A|χ,ρ,v.sub.p)dA,  (6)
σ.sub.A|χ,ρ,vp.sup.2=∫[A−μ.sub.A|χ,ρ,vp].sup.2p(A|A|χ,ρ,v.sub.p)dA.  (7)

(17) It is equations 4-7 that are most useful for calculate the likely temperature for given geophysical parameters. However, as is clear from equation 4 and 5, in order to do so, it is necessary to know the likelihood functions p(m.sub.i|A) for each of the geophysical parameters m.sub.i. Further it is necessary to know the prior distribution p(A;λ). Methods of calculating these are given below.

(18) Regarding the prior distribution p(A;λ), in the present method it is assumed to be Gaussian,
A˜(μ.sub.A(λ),σ.sub.A.sup.2(λ)),  (8)

(19) where μ.sub.A, and σ.sub.A.sup.2 are the prior expectation and variance, respectively. The prior distribution incorporates the user's prior knowledge regarding the temperature, for instance that the temperature is usually within a relatively narrow range. The hyperparameter λ reflects the user's prior knowledge about the geological setting. If the user's prior knowledge is sparse, the prior variance σ.sub.A.sup.2 should be correspondingly large.

(20) Thus, the prior distribution may preferably be a statistical distribution, preferably a Gaussian distribution. Preferably, the mean and variance of the prior distribution is selected by the user based on the user's prior knowledge of the geological structure in question (e.g. knowledge of typical variances of temperature).

(21) For the likelihood functions p(m.sub.i|A) on the right-hand side of Equations 4 and 5, these are calculated using forward models F.sub.i(A). The forward models are mathematical relationships that compute the relevant geophysical parameter m.sub.i for a given temperature A. Regarding the present method, it is assumed that each of the forward models F.sub.i(A) have respective Gaussian error distributions with zero mean, when compared with the respective measured/observed geophysical parameters, i.e.
m.sub.i−F.sub.i(A)=e.sub.i˜(0,σ.sub.ei.sup.2)  (9)

(22) In the present method, these forward models may be optimised using calibration data.

(23) Once the optimal forward models have been found (by selecting the appropriate forward models and calibrating them), the maximum likelihood functions (i.e. the maximum likelihood of a geophysical parameter given a value of temperature, p(m.sub.i|A) in equations 4 and 5) are given explicitly by

(24) $\begin{array}{cc}p\left(m_i|A\right)=\frac{1}{{\sigma }_e\sqrt{2\pi }}{e}^{-\frac{{\left[m_i-F_i\left(A\right)\right]}^2}{2{\sigma }_{\mathrm{ei}}^2}}& \left(10\right)\end{array}$

(25) These maximum likelihood functions, together with the prior distribution discussed above are used in equations 4-7 to calculate the posterior distribution for the temperature given the measured/obtained geophysical parameters, p(A.sub.|χ,ρ,v.sub.p), the posterior expectation and the posterior variance. It is in this way that the temperature is calculated, i.e. these quantities give the useful values of temperature. If porosity data is available, it may also be used to constrain the inversion calculation.

(26) It should be appreciated that with a Bayesian formulation of the inversion problem, the present method honours the fact that the rock physics models (the forward models) do not perfectly describe the observations (calibration data). This imperfectness is accounted for by the error variance σ.sub.ei in the likelihood distributions given in Equation 10. This in turn provides a quantitative estimate of the posterior variance σ.sub.A|χ,ρ,v.sub.p.sup.2 of the temperature obtained by the inversion. Thus, Equation 3 is effectively a univariate distribution for A, with posterior mean and posterior variance given by Equations 6 and 7.

(27) It should also be appreciated that the above-described steps may merely have calculated temperature, A, for a specific point in the geophysical structure. This point is the location corresponding to the location of the value of the respective geophysical parameters that are used to calculate the temperature. Thus, preferably, all the geophysical parameters that are used in the above steps are taken from the same, or at least similar, locations in the geological structure.

(28) In order to construct a view of temperature over a region, or the entirety, of the geological structure, the above steps for calculating are be carried out for different locations in the geological structure. However, the calibration of the forward models may only be carried out once, i.e. it need not be carried out for each different location. In some circumstance, the calibration may be carried out for each location.

(29) Thus, the above-discussed rock physics inversion is thus applied point-wise to obtain the spatially varying temperature A(x, y, z).

(30) Once the temperature has been calculated, it can be used in the decision-making process for drilling geothermal wells. Temperature may be calculated prior to drilling and used to determine where and how deep to drill the well. Updated temperature may also be calculated during drilling using new geophysical data measured in the partially-drilled well (such as well logs). The updated temperature can be used to decide what direction and depth to drill to, or whether continuing to drill is worthwhile, or whether a different well should be drilled.

(31) The above method illustrated in FIG. 1 has been discussed in terms of calculating the temperature only. However, the porosity could also be found using a similar method, but by using different forward models.

(32) A practical example of the use of the above method will now be presented.

(33) The target of the “IDDP-2” (“Iceland Deep Drilling Project 2”) well at Reykjanes is geothermal resources at supercritical temperatures. The drill site has been mapped by electromagnetic and gravimetric surveys and subsurface temperatures on the IDDP-2 drill site have been predicted by multigeophysical inversion, as described below.

(34) For geothermal exploration in general, it is useful to predict the depth and temperatures of potential reservoir targets. For the IDDP-2 well in particular, it is of great interest to obtain an estimate of the drilling depth needed to fulfill the main objective of the project; reaching supercritical conditions. There is no reflection-seismic data available in the area to build a structural framework. Also, limited amount of core material was recovered. Hence, subsurface information must be assessed from other types of geophysical and geological data, including well and drilling data to characterize rock units in the well.

(35) In summary, the multigeophysical inversion method was used to predict subsurface temperature. Electric resistivity from MT (magnetotelluric) inversion and density from gravity inversion were used to compute a predrill estimate of formation temperature for the IDDP-2 drilling target. Resistivity and core samples acquired while drilling were used to update the temperature estimate and to build a geological model. This information was subsequently passed on to the reservoir engineers for simulation of the hydrothermal system.

(36) A statistical model was constructed for the dependence of geophysical model parameters on temperature, and in turn, the dependence of geophysical data on geophysical model parameters. This can be represented by the Bayesian network shown in FIG. 1, where A is temperature. The first set of dependencies was given by various rock physics relations. The second set of dependencies was given by differential equations, such as the Maxwell equations of electromagnetics, Newton's law of gravity, and the elastic wave equation.

(37) As described above, going from the top to the bottom of the Bayesian network constitutes forward modeling, i.e., computing synthetic geophysical models and data, given a subsurface temperature distribution. Going from the bottom to the top constitutes performing Bayesian inversion. By inversion, geophysical model parameters and subsurface temperature can be computed from observed geophysical data. A pragmatic approach was taken utilising geophysical models obtained with various geophysical inversion methods, and computed by different groups of geophysicists and service providers. Hence, the Bayesian inversion was focused on the second stage of the inversion, computing subsurface temperature from 3D geophysical models. This was effectively a rock-physics inversion.

(38) Given the Bayesian network (FIG. 1), and assuming conditional independence between the nodes not connected by arrows, the posterior probability distribution for the temperature could be written as

(39) $\begin{array}{cc}p\left(T|m_i,\mathrm{.Math.},m_n;\phi \right)=C\underset{i=1}{\overset{n}{.Math.}}p\left(m_i|T;\phi \right)p\left(T\right)& \left(11\right)\end{array}$
where T is temperature, m.sub.i are the geophysical model parameters of interest, C is the normalization constant, and φ is porosity. As described above, the porosity can be treated as a stochastic variable (in the same way as temperature T). However, in the present case, the porosity was assumed to be a hyperparameter, with a given deterministic value. The prior distribution for temperature is denoted p(T).

(40) One or more geophysical parameters can be used to compute the posterior distribution. For instance, electric conductivity (or resistivity) may be used alone. However, as is evident from Equation 11, the product of two (or more) likelihood functions makes the posterior distribution narrower. This implies better posterior mean and smaller variance. Thus, in accordance with the invention two or more physical parameters were used to compute the posterior distribution.

(41) Assuming Gaussian errors, the likelihood distribution for each geophysical parameter, can be written as

(42) $\begin{array}{cc}p\left(m_i|T;\phi \right)=\frac{1}{{.Math.2\pi {.Math.}_{\mathrm{ei}}.Math.}^{\frac{1}{2}}}{e}^{-{\left[m_i-F_i\left(T;\phi \right)\right]}^T{.Math.}_{\mathrm{ei}}^{-1}\left[m_i-F_i\left(T;\phi \right)\right]}& \left(12\right)\end{array}$
where F.sub.i(T; φ) is the rock-physics relation for the dependence of model parameter m.sub.i on temperature, and Σ.sub.ei is the corresponding error covariance. In this way, the fact that the rock physics models are not perfect representations of the subsurface properties may be accounted for. Equation 12 is a Gaussian distribution for model parameter m.sub.i only if the forward model F.sub.i(T; φ) is a linear function of T. This is not the case in general. In principle, both electromagnetic data, potential-field data and seismic data may be utilised. However, in this case, only electric conductivity m.sub.1=σ (or its inverse; resistivity) and density m.sub.2=ρ were utilized. The corresponding rock physics relations are denoted F.sub.1(T;φ)=α(T;φ) and F.sub.2(T;φ)=ρ(T;φ).

(43) Electric conductivity (or resistivity) is the geophysical parameter that has the most direct response to temperature variations. The rock physics model for conductivity σ(T;φ) was designed as a fraction-weighted parallel coupling of (1) non-porous (dry) basaltic rock, (2) clay minerals from hydrothermal alterations and (3) fractures filled with water (brine). The temperature dependence of basaltic rocks was obtained by log-linear regression of conductivity vs. inverse temperature 1/T, using experimental data. The core measurements suggested that the temperature dependence of conductivity of dry basalt σ.sub.a (T) is given approximately by the sum of two Boltzmann distributions (Arrhenius equations)
.sub.Gg(T)=σ.sub.1e.sup.−E.sup.1.sup./k.sup.B.sup.T+σ.sub.2e.sup.−E.sup.2.sup./k.sup.B.sup.T  (13)
where k.sub.B is the Boltzmann constant, and σ.sub.j and E.sub.j (for j=1,2) are calibration parameters. E.sub.j play the role of activation energies for two temperature-dependent conduction mechanisms.

(44) The conductivity of the clay was modeled using the familiar Waxman-Smits equation. Particularly important was to account for the cation-exchange effect in smectite, at relatively shallow depth and low temperatures, below 220° C. The porosity of the basalt was assumed to be dominated by fractures. The fracture conductivity was approximated by the relation published by Brace et al. (Brace, W. F., Orange, A. S., and Madden, T. R., 1965. The effect of pressure on the electrical resistivity of water-saturated crystalline rocks: J. Geophys. Res., 70, 5669-5678), with temperature-dependent water conductivity.

(45) The rock-physics model for density ρ(T;φ) was constructed in a similar way, using the relations presented by Hacker et al (Hacker, B. R, Abers, G. A., and Peacock, S. M., 2003. Subduction factory 1. Theoretical mineralogy, densities, seismic wave speeds and H2O contents: J. Geophys. Res., 108 (B1), 2029), and temperature-dependent water density in the fractures.

(46) The drill-site selected for the IDDP-2 well was mapped by a 3D MT survey, with receivers distributed on an approximately 5×5 km.sup.2 grid. 3D MT inversion was performed using the minimum-norm (data-space Hessian) 3D MT inversion of Siripunvaraporn et al. (Siripunvaraporn, W., G. Egbert, Y. Lenbury, and M. Uyeshima, 2005, Three-dimensional magnetotelluric inversion: Data-space method: Physics of the Earth and Planetary Interiors, 150, 3-15). Inversion of transient electromagnetic (TEM) data was used to obtain independent estimates of shallow resistivity, and to correct the MT data for static shifts, caused by near-surface galvanic currents. The details of the MT and TEM inversion were described by Karlsdóttir et al. (Karlsdóttir, R., Árnason, K., and Vilhjálmsson, A. M., 2012. Reykjanes Geothermal Area, Southwest Iceland. 3D Inversion of MT and TEM Data: Iceland Geosurvey íSOR-2012/059).

(47) A shallow low-resistivity zone, at depth less than 1.5 km, was caused by the high cation-exchange capacity of smectite. At temperatures between 220° C. and 260° C., chlorite with higher resistivity, becomes the dominating alteration mineral. At depths larger than 3 km, a high-resistivity zone, assumed to be associated with sheeted dykes and diabase, was observed. The target of the IDDP-2 well was a zone of reduced resistivity within the high resistive zone, between 3 and 5 km depth.

(48) Gravity surveying had been performed on the Reykjanes Peninsula for the purpose of monitoring the subsidence of the spreading ridge by time-lapse gravimetry. The most recent gravity survey, from 2014, was utilized for temperature prediction at the IDDP-2 drill site. The local gravity data was processed by complete Bouguer corrections, including terrain correction. The local data was then merged with a regional Bouguer anomaly map, to obtain sufficient aperture (15×15 km.sup.2) for 3D inversion.

(49) Gravity inversion is generally ill-posed, and needs to be regularized. Therefore, a density model for the upper zone, down to approximately 2500 m, was built using borehole data from the wells in the Reykjanes geothermal area. The gravity response of the upper zone was modeled and subtracted, to isolate the gravity anomaly associated with the deeper zone of interest. The residual was then inverted for density in the deeper zone, from 2500 m to 7000 m. A Marquardt-Levenberg type 3D inversion scheme, implemented in Matlab, was used to perform the gravity inversion (Hokstad, K., Alasonati Tašárová, Z., Clark, S. A., Kyrkjebø, R., Duffaut, K., and Pichler, C., 2017, Heat production and heat flow from geophysical data: Submitted to Norwegian Journal of Geology).

(50) Also, a porosity vs depth trend is needed for the rock-physics inversion. Little hard information about porosity in the Reykjanes geothermal area had been published. Data for the porosity was only known for the upper ca 2000 m. Assuming an exponential trend, neutron capture logs from vintage wells were used to estimate a porosity trend. The porosity trend was calibrated such that the rock-physics model reproduced approximately the temperature-corrected (Arp's formula) resistivity log from the RN-15 well, given measured formation temperature from the 2010 maintenance stop. The temperature-corrected resistivity log was in good agreement with the resistivity trend from 3D MT inversion. Also, a synthetic density log was computed and used to calibrate the absolute level of the density cube from 3D gravity inversion. In this way, a set of subsurface parameters a, p and F consistent with the rock physics models down to 2.5 km depth were obtained.

(51) The resistivity model from MT inversion, the density model from gravity inversion, and the porosity vs. depth trend, were input to the Bayesian inversion scheme. The prior model for temperature vs. depth was chosen close to the boiling curve down to 2.5 km depth, and then increasing with 80° C./km. The inversion proved to be quite robust, and the value of the prior temperature was not important. Hence, a relatively vague prior, with variance of 400° C. could be used.

(52) From the multigeophysical inversion, the well was predicted to reach supercritical conditions (T>400° C.) at approximately 4 km depth. The predrill estimate for the planned total depth of the well was 513±62° C. at 5 km vertical depth. Reykjanes is in an active sea-floor spreading zone, and earthquakes of magnitude 2 and less occur regularly. The earthquakes are expected to diminish in the ductile zone, starting at about 600° C. This was in fair agreement with the predrill temperature predictions. The estimated source locations of all earthquakes (prior to drilling) were above the 500° C. isotherm from the inversion.

(53) The drilling of the IDDP-2 well started in August 2016. During the drilling period, the temperature in the well was measured regularly. Also, wireline logging of resistivity, neutron capture and gamma ray was performed acquired tripping at 2900 m and 3450 m measured depth (MD). Cold water was used as drilling fluid. Because of the cooling effect of the injected water, the resistivity logs do not record true formation resistivity, Using measured temperatures, neutron logs, and tie to the RN-15 logs in overlapping intervals, the resistivity logs were adjusted to approximately represent the formation resistivity trend, Different correction methods were used, including empirical re-scaling, and corrections based on analytical solutions to the heat equation in cylindrical coordinates. The temperature-corrected resistivity log was used to rerun the inversion for temperature along the planned well path. The results were uncertain due to the uncertainty involved in the log corrections. However, the while-drilling updates indicated that the formation temperature was 50-100° C. higher than the predrill prediction.

(54) A number of core runs were performed to collect samples of the drilled rocks. The cores were used to identify alteration minerals, and to obtain rough constraints on maximum temperatures. The core runs, however, covered only a very small part of the drilled well section.

(55) The described well section and core descriptions, together with the temperature estimates from the multigeophysical inversion, were used to construct, and continuously update a geological model for the IDDP-2 borehole.

(56) Combined data in the geological model supported the temperature predictions suggested by multigeophysical inversion. Several changes in rock parameters had been described to occur during the major temperature changes, most notably reaching of 400° C. and 500° C. further supporting temperature predictions made for the Reykjanes geothermal area.

(57) The drilling of the well was completed late December 2016. In early January 2017, the water injection was reduced for two days, and a new temperature log was run, measuring 427° C. at 4626 m MD. The kinks in the measured temperature curves were associated with high-permeability loss zones.

(58) In summary, the temperatures estimated from the inversion method were in good agreement with the most recent temperature log (acquired 3 Jan. 2017), and with geochemical indications from alteration minerals, and with changes in rock parameters. The method is based on inversion of geophysical data, followed by Bayesian rock physics inversion for direct temperature estimation. The geophysical parameter that responds most directly to changes in formation temperature is electric conductivity (or resistivity). MT data are well suited due to the wide range of frequencies in the source field (i.e. the interaction between the sun and earth magnetic field). The low-frequency part of the source field is needed to image targets down to 5-6 km depth. However, due to the electromagnetic skin effect, only a low-resolution image can be obtained.

(59) Density from gravity inversion is useful to reduce the posterior uncertainty of the method. Also a porosity vs depth trends is important input to the rock physics inversion, A relative reduction of electric resistivity and density can be caused by either increased porosity or increased temperature. Hence, there is an inherent ambiguity in the inversion. Magnetic susceptibility and seismic P-wave and S-wave velocities can also be utilized, but this was not done in this case. The method has been calibrated for and demonstrated on mid-oceanic ridge basalts (MORE). The method may be applied to other tectonic and geological settings following recalibration of the rock physics models used in the Bayesian inversion.

(60) It should be apparent that the foregoing relates only to the preferred embodiments of the present application and the resultant patent. Numerous changes and modification may be made herein by one of ordinary skill in the art without departing from the general spirit and scope of the invention as defined by the following claims and the equivalents thereof.