Method and device for compensation of self-potential

Abstract

The invention relates to a computer-implemented method for compensating a non-linear self-potential in a time-series representative of a potential measured from a geological structure, said method comprising: receiving (41) as input (21) said time-series comprising a first component being said self-potential and a second component being an induced-potential, iteratively compensating (43) said self-potential on said time-series so as to obtain a compensated time-series representative of the induced-potential corrected from the non-linear variation of the self-potential and providing (44) as output (31) said compensated time-series (31).

Description

METHOD AND DEVICE FOR COMPENSATION OF SELF-POTENTIALFIELD OF INVENTION

[0001] The present invention relates to the domain of method for measurements and evaluation of properties of a geological structure, notably through potential measurements. More precisely, the present invention relates to a method which may be used in the electrical resistivity measurement or in induced polarization measurement domains.BACKGROUND OF INVENTION

[0002] Direct-current resistivity and induced polarization have become widely used methods in the past 40 years. They have been proven notably in the domain of water exploration, mineral exploration, geological and geotechnical investigations.

[0003] Electrical Resistivity Tomography (ERT) and Time-Domain Induced Polarization (TDIP) are based on the injection, in the soil, of a low current in the form of bimodal rectangular pulses wherein the injection is performed during 50% to 100% of the duty cycle. The injected current is diffused in the different layers in the soil and generates an electric potential which can be measured by electrodes inserted in the soil.

[0004] However, firstly, the soil generates naturally a self-potential. Secondly, the potential equilibrium between the electrodes newly inserted in the soil may take several tens of minutes to be reached. Thirdly, when a current is injected with an electrode, the potential of this electrode is modified and the return to the potential equilibrium may also take some tens of minutes.

[0005] All these sources of noise are superimposed to the potential produced by the injected current. The potential produced by the injected current is generally measured infew mV, especially for Deep Electrical Resistivity Tomography (DERT) and is thus hidden under the noise level.

[0006] Several known methods have been developed to retrieve the generated potential. However, these methods are not satisfactory.

[0007] Indeed, a first method is to increase the current so that to increase the generated potential. However, the current must be increased so much that this leads to the use of very big, heavy and unsuitable instruments.

[0008] A second method is to increase the duration of the measured time-series so that to average noise by a gaussian distribution that can be mathematically removed. However, the use of such a long survey leads to a brake in the investigations.

[0009] A third method is to mathematically correct the linear component of the noise. However, this method does not allow to accurately suppress the phenomenon of electrode polarization which leads to a non-linear noise that can be some orders of magnitude larger than the generated potential.

[0010] A fourth method is based on frequency filtering. However, this method is not easily applicable to the frequency ranges used in the ERT and TDIP domains since the self-potential lies in the same frequency range that the generated potential.

[0011] A Cole-Cole model and an Empirical Mode Decomposition (EMD) model have been developed to remove the non-linear noise generated by the electrode polarization. However, the noise suppression in two steps (suppression of the linear component and then of the non-linear component) is not accurate for low TDIP signal. Moreover, the EMD model is very time-consuming.

[0012] There is thus a need for a method for removing the non-linear noise from shortterm time-series generated from the injection of a low amplitude current that is accurate and low time-consuming.

[0013] To this end, the invention related to a method for compensating a non-linear selfpotential in a time-series representative of a potential measured from a geological structure.SUMMARY

[0014] To this end, this invention relates to a computer-implemented method for compensating a non-linear self-potential in a time-series representative of a potential measured from a geological structure, said method comprising: a. receiving as input said time-series comprising previously acquired values representative of said potential, measured between at least one pair of electrodes disposed at least partially in contact with the geological structure; wherein said potential comprises a first component being said self-potential generated by said geological structure, variating non-linearly in time, and a second component being an induced-potential, said induced potential being generated in said geological structure in response to an electrical current injected in said geological structure via one of said at least one pair of electrodes, the injected electrical current being in the form of a periodic signal between a maximum current amplitude and a minimum current amplitude; b. iteratively compensating said self-potential on said time- series so as to obtain a compensated time-series representative of the induced-potential corrected from the non-linear variation of the self-potential; and c. providing as output said compensated time-series.

[0015] Indeed, the inventors surprisingly found that the application of the compensation in an iterative manner allows to correct from the non-linear variation due to self-potential. This correction is very rapid (only several iterations are needed to converge).

[0016] According to an advantageous aspect of the invention, compensating said selfpotential on said time-series is iteratively applied until a predetermined end criterion is satisfied.

[0017] According to an advantageous aspect of the invention, said time-series comprises at least one data, each data being associated to a potential value and an acquisition time, iterative compensating said self-potential on said time-series comprising compensating the self-potential on the time- series by: o for each data of the received time-series, computing a corrected potential value, and o assigning the computed corrected potential value to the data for which it has been computed.

[0018] According to an advantageous aspect of the invention, said time-series comprises at least three sequences, each sequence comprising at least one of the data, computing a corrected potential value corresponding to determining, for each data of one of the sequences, a mean value based on at least one of the data of at least two other sequences.

[0019] According to an advantageous aspect of the invention, the periodic signal is such that a product between the maximum current amplitude and the minimum current amplitude is negative and that the maximum current amplitude and the minimum current amplitude are equal.

[0020] Indeed, the measured potential generally takes the same form as the injected current. Therefore, the measured potential will also present a positive maximum amplitude and a negative minimum amplitude. This allows to ease the compensation by using the symmetry property of the measured potential.

[0021] According to an advantageous aspect of the invention, the injected electrical current is in the form of successive square waves or in the form of a sinusoid.

[0022] Indeed, injecting current in the form of square waves allows to measure a potential whose form is also square waves. The determination of the at least one electrical property of a geological structure is thus based on the variation during the decay phase of the potential.

[0023] According to an advantageous aspect of the invention, the received time-series is periodic and comprises at least two periods, each period being defined by a half-periodcorresponding to a half of the duration of said period, compensating the self-potential on the time-series comprising: o for each data of the received time-series, computing a corrected potential value based on the potential value associated with an acquisition time corresponding to the acquisition time of said data subtracted from said half-period and on the potential value associated with an acquisition time corresponding to the acquisition time of said data added with said half-period; o assigning the computed corrected potential value to the data for which it has been computed.

[0024] Indeed, this allows to use only data over one period to compute the compensation for each data. Therefore, the correction using the method of the invention remains efficient even for very short time-series containing a low number of periods.

[0025] Moreover, the use of a predetermined end criterion avoids too many iterations and therefore limits the computation time when studying several thousands of measurements.

[0026] According to an advantageous aspect of the invention, each period of the received time- series comprises the same number of N data, each data being identified by a timeseries index t positioning said data in the received time-series, and wherein, for each timeseries index t, the corrected potential value is computed as—it[t — N / 2] + 2it[t] — u[t + N / 2]4 u being the potential value associated to the times-series indexes t, t — N / 2 and t + N / 2.

[0027] According to an advantageous aspect of the invention, before iteratively compensating the self-potential, the time-series is completed by prefixing the time-series with a first side-set of data corresponding to the last period of the received time-series and by having the time-series succeeded with a second side-set of data corresponding to the first period of the received time-series, the acquisition time of the first side-set of data and the second side- set of data being adequately shifted by a total duration of the received time- series.

[0028] This allows to correct the side-effects and to keep the same amount of data in the compensated time-series whatever the number of iterations performed.

[0029] According to an advantageous aspect of the invention, the time-series comprises less than 10 periods.

[0030] According to an advantageous aspect of the invention, the predetermined end criterion is configured to stop the iterative compensation after a predefined number of iterations.

[0031] According to an advantageous aspect of the invention, the predetermined end criterion is configured to stop the iterations when, for each data of the time-series, a difference between the acquired uncorrected potential value and the corrected potential computed for said data is inferior to a predefined threshold.

[0032] According to an advantageous aspect of the invention, for each data, a deviation is computed as an absolute value of a difference between the potential value associated to said data and the corrected value computed for said data, and wherein the predetermined end criterion is configured to stop the iterations when said deviation is inferior of a predefined threshold.

[0033] According to an advantageous aspect of the invention, the predefined threshold is less than 10'6mV.

[0034] The invention also relates to a device for compensating a non-linear self-potential in a time- series representative of a potential measured from a geological structure, the device comprising: at least one input configured to receive time-series, each time-series comprising previously acquired values representative of a potential between at least one pair of electrodes disposed at least partially in contact with the geological structure, said potential comprising an induced component generated in said geological structure in response to an electrical current injected in said geological structure via one of the at least one pair of electrodes and a self-potential variating non-linearly, theinjected electrical current being in the form of a periodic signal between a maximum current amplitude and a minimum current amplitude; at least one processor configured to implement an iterative compensation of said non-linear self-potential on said time-series so as to obtain a compensated time-series corrected from the non-linear self-potential; at least one output configured to provide said compensated time-series corrected from the non-linear self-potential.

[0035] In addition, the disclosure relates to a computer program comprising software code adapted to perform a method for compensating a non-linear self-potential in a timeseries representative of a potential measured from a geological structure, compliant with any of the above execution modes when the program is executed by a processor.

[0036] The present disclosure further pertains to a computer-readable medium comprising instructions which, when executed by a computer, cause the computer to carry out the method for compensating a non-linear self-potential in a time-series representative of a potential measured from a geological structure, compliant with any of the above execution modes.

[0037] The present disclosure further relates to a non-transitory program storage device (i.e. computer-readable storage medium), readable by a computer, tangibly embodying a program of instructions executable by the computer to perform a method for compensating a non-linear self-potential in a time-series representative of a potential measured from a geological structure, compliant with the present disclosure.

[0038] Such a non-transitory program storage device can be, without limitation, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor device, or any suitable combination of the foregoing. It is to be appreciated that the following, while providing more specific examples, is merely an illustrative and not exhaustive listing as readily appreciated by one of ordinary skill in the art: a portable computer diskette, a hard disk, a ROM, an EPROM (Erasable Programmable ROM) or a Flash memory, a portable CD-ROM (Compact-Disc ROM).DEFINITIONS

[0039] In the present invention, the following terms have the following meanings:

[0040] The terms “adapted” and “configured” are used in the present disclosure as broadly encompassing initial configuration, later adaptation or complementation of the present device, or any combination thereof alike, whether effected through material or software means (including firmware).

[0041] The term “processor” should not be construed to be restricted to hardware capable of executing software, and refers in a general way to a processing device, which can for example include a computer, a microprocessor, an integrated circuit, or a programmable logic device (PLD). The processor may also encompass one or more Graphics Processing Units (GPU), whether exploited for computer graphics and image processing or other functions. Additionally, the instructions and / or data enabling to perform associated and / or resulting functionalities may be stored on any processor- readable medium such as, e.g., an integrated circuit, a hard disk, a CD (Compact Disc), an optical disc such as a DVD (Digital Versatile Disc), a RAM (Random- Access Memory) or a ROM (Read-Only Memory). Instructions may be notably stored in hardware, software, firmware or in any combination thereof.BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The present disclosure will be better understood, and other specific features and advantages will emerge upon reading the following description of particular and non- restrictive illustrative embodiments, the description making reference to the annexed drawings wherein:

[0043] Figure 1 is a block diagram representing schematically a particular mode of a device for compensating a non-linear self-potential in a time-series representative of a potential measured from a geological structure, compliant with the present disclosure;

[0044] Figure 2 is a flow chart showing successive steps executed with the device for compensating a non-linear self-potential of Figure 1;

[0045] Figure 3 diagrammatically shows a computer integrating the functions of the device for compensating a non-linear self-potential of Figure 1 ;

[0046] Figure 4 represents schematically a particular mode of a system for electrical resistivity tomography or time-domain induced polarization;

[0047] Figures 5A-5B are a combination of graphs. Fig. 5A shows a linear compensation of a time-series representative of the induced-potential. Fig. 5B shows a correction of non-linear self-potential using a particular mode of the method of the invention;

[0048] Figure 6 represents a compensated time-series representative of the induced- potential corrected from the non-linear variation of the self-potential using the method of the invention and a time- series representative of the induced-potential only corrected from the linear variations.DETAILED DESCRIPTION

[0049] The present description illustrates the principles of the present disclosure. It will thus be appreciated that those skilled in the art will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the disclosure and are included within its scope.

[0050] All examples and conditional language recited herein are intended for educational purposes to aid the reader in understanding the principles of the disclosure and the concepts contributed by the inventor to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions.

[0051] Moreover, all statements herein reciting principles, aspects, and embodiments of the disclosure, as well as specific examples thereof, are intended to encompass bothstructural and functional equivalents thereof. Additionally, it is intended that such equivalents include both currently known equivalents as well as equivalents developed in the future, i.e., any elements developed that perform the same function, regardless of structure.

[0052] Thus, for example, it will be appreciated by those skilled in the art that the block diagrams presented herein may represent conceptual views of illustrative circuitry embodying the principles of the disclosure. Similarly, it will be appreciated that any flow charts, flow diagrams, and the like represent various processes which may be substantially represented in computer readable media and so executed by a computer or processor, whether or not such computer or processor is explicitly shown.

[0053] The functions of the various elements shown in the figures may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software. When provided by a processor, the functions may be provided by a single dedicated processor, a single shared processor, or a plurality of individual processors, some of which may be shared.

[0054] It should be understood that the elements shown in the figures may be implemented in various forms of hardware, software or combinations thereof. Preferably, these elements are implemented in a combination of hardware and software on one or more appropriately programmed general-purpose devices, which may include a processor, memory and input / output interfaces.

[0055] The present disclosure will be described in reference to a particular functional embodiment of a device 1 for compensating a non-linear self-potential in a time-series representative of a potential measured from a geological structure 64, as illustrated on Figure 1.

[0056] The potential is measured between at least one pair of electrodes 60 disposed at least partially in contact with the geological structure 64 in response to an electrical current injected in the geological structure 64 via one of said at least one pair of electrodes 60.

[0057] The injected electrical current is in the form of a periodic signal between a maximum current amplitude and a minimum current amplitude. The induced-potential generated in response to the injected electrical current is also preferably in the form of a periodic signal. For example, the injected current is in the form of successive square waves or in the form of a sinusoid. Preferably, the product between the maximum current amplitude and the minimum current amplitude is negative so that the induced-potential also presents positive and negative values. The maximum current amplitude and the minimum current amplitude are preferably equal in absolute value. The physical parameters that could be deduced during geological and geotechnical investigations may be determined from an analysis of said induced-potential. However, the induced-potential is polluted by the self-potential generated by the geological structure.

[0058] The self-potential is naturally present in the soil and is generated by several sources such as storms, electro filtration, leakage of currents in the geological structure, pile effect of a deposit, etc. Moreover, the measuring method itself also generates some self-potential. Indeed, the potential equilibrium between the electrodes newly inserted in the soil may take several tens of minutes to be reached. Moreover, when a current is injected with an electrode, the potential of this electrode is modified and the return to the potential equilibrium may also take some tens of minutes.

[0059] All these sources of noise lead to a non-linear self-potential which is superimposed on the induced-potential (i.e., signal of interest) and which must be corrected in order to improve the reliability of the deduced physical parameters.

[0060] To do so, the device 1 is adapted to produce a compensated time-series corrected from the non-linear variation of the self-potential.

[0061] The time-series is received by the device 1 as an input 21. The time-series is representative of a potential measured from a geological structure 64. Therefore, said time-series comprises data. More precisely, the time-series comprises previously acquired values representative of the potential measured from a geological structure 64 acquired at a predefined acquisition rate. Therefore, each data (i.e., data point of the series) is may be associated to a potential value and an acquisition time. For the received time-series, thepotential value is the measured potential and therefore comprises the induced-potential and self-potential. Each data is identified by a time-series index t positioning said data in the received time- series.

[0062] The received time-series (i.e., measured potential) may comprise at least three sequences, each sequence comprising at least one of the data. The sequences are preferably consecutive, i.e., they do not overlap. Preferably, the sequences are contiguous, such that no data point is non-included in a sequence. Preferably, the received time-series is periodic. In this case, each sequence thus corresponds to one period. The time- series may comprise at least two periods P. Each period P is defined by a half-period HP corresponding to a half of the duration of said period P. The duration of the period P is not limited but is preferably ranging from 2 seconds to 40 seconds. Each period P comprises at least one data, preferably at least three data. Preferably, each period P comprises the same number of N data.

[0063] Though the presently described device 1 is versatile and provided with several functions that can be carried out alternatively or in any cumulative way, other implementations within the scope of the present disclosure include devices having only parts of the present functionalities.

[0064] The device 1 is advantageously an apparatus, or a physical part of an apparatus, designed, configured and / or adapted for performing the mentioned functions and produce the mentioned effects or results. In alternative implementations, the device 1 is embodied as a set of apparatus or physical parts of apparatus, whether grouped in a same machine or in different, possibly remote, machines. The device 1 may e.g. have functions distributed over a cloud infrastructure and be available to users as a cloud-based service, or have remote functions accessible through an API.

[0065] In what follows, the modules are to be understood as functional entities rather than material, physically distinct, components. They can consequently be embodied either as grouped together in a same tangible and concrete component, or distributed into several such components. Also, each of those modules is possibly itself shared between at least two physical components. In addition, the modules are implemented in hardware,software, firmware, or any mixed form thereof as well. They are preferably embodied within at least one processor of the device 1.

[0066] The device 1 comprises a module 11 for receiving the input 21. The input 21 notably includes the time- series . The input 21 may be stored in one or more local or remote database(s) 10. The latter can take the form of storage resources available from any kind of appropriate storage means, which can be notably a RAM or an EEPROM (Electrically-Erasable Programmable Read-Only Memory) such as a Flash memory, possibly within an SSD (Solid-State Disk).

[0067] The device 1 optionally comprises a module 12 for preprocessing the received input 21. The module 12 may notably be adapted to correct the linear compensation using a method known for a person skilled in the art and / or normalize the time-series for sake of efficient and reliable processing. According to various configurations, the module 12 is adapted to execute only part or all of the above functions, in any possible combination, in any manner suited to the following processing stage.

[0068] In advantageous modes, the module 12 is configured for preprocessing the received input 21 so as to have the standardized time-series. This may enhance the efficiency of the downstream processing by the device 1. Such a standardization may be particularly useful when exploited time-series originate from different sources, including possibly different measuring systems.

[0069] Preferably, a batch of received input 21 corresponding to a complete time-series may be fully received and preprocessed before it is submitted to the module 13 since the module 13 performs a method which is applied iteratively on the whole received input 21.

[0070] Indeed, the module 13 is configured to perform an iterative compensation of the self-potential on the time- series so as to obtain a compensated time- series representative of the induced-potential corrected from the non-linear variation of the self-potential. If a preprocessing is performed, the time-series onto which the iterative compensation of the self-potential is performed is the preprocessed time-series.

[0071] The compensation of the self-potential may comprise two successive steps. First, a corrected value is computed for each data of the received time-series. Then, when the corrected values are computed for the overall data, the corrected values are assigned to the data for which it has been computed.

[0072] In the embodiment wherein the received time-series comprises at least three sequences, the corrected value corresponds to a mean value determined based on at least one of the data of at least two sequences other than the sequence into which the corrected value is computed. In the embodiment wherein the received time-series is periodic, the corrected value is based on the potential value associated with an acquisition time corresponding to the acquisition time of said data subtracted from said half-period HP and on the potential value associated with an acquisition time corresponding to the acquisition time of said data added with said half-period HP. In other words, the corrected value of a given data is computed thanks to the value of the data located at the previous half-period HP and at the following half-period HP.

[0073] This allows to use only data over one period P to compute the compensation for each data. Therefore, the correction of the invention remains efficient even for very short time- series containing a low number of periods P for example, for a time- series comprising less than 10 periods P. Moreover, the inventors surprisingly found that this method allows to compensate the polarization of the electrodes and the high-frequency radiations of the self-potential without using a relaxation model such as the Cole-Cole model.

[0074] When each period P of the received time-series comprises the same number of N data, the corrected potential value is computed as—it[t — N / 2] + 2it[t] — u[t + N / 2]4 with u the potential value associated to the times-series indexes t, t — N / 2 and t + N / 2.

[0075] The compensation is iteratively applied to the time-series. In other words, the subsequent iteration computes the new corrected values based on the corrected values computed at the previous iteration.

[0076] The compensation is iteratively applied to the time-series until a predetermined end criterion is satisfied. In one embodiment, the predetermined end criterion is configured to stop the iterative compensation after a predefined number of iterations. For example, the predefined number of iterations is comprised between 6 and 10.

[0077] In an alternative embodiment, the predetermined end criterion is configured to stop the iterations when, for each data of the time-series, a difference between the acquired uncorrected potential value and the corrected potential computed for said data is inferior to a predefined threshold. For example, the predefined threshold is comprised between 0.1 nV and 1 nV. Preferably, the predetermined end criterion is configured to stop the iterations when a computed deviation is inferior of a predefined threshold. The deviation is computed as an absolute value of a difference between the potential value associated to said data and the corrected value computed for said data. For example, the predefined threshold is less than 10'2mV, preferably less than 10'6mV.

[0078] In the embodiment wherein the received time-series is periodic, since the corrected value is computed thanks to the value of the data located at the previous halfperiod HP and at the following half-period HP, some border effects appear. Indeed, the corrected values for the data located in the first half-period HP and the last half-period HP of the time-series cannot be computed precisely. One solution to this problem is to discard these data. However, as long as the iteration is performed, more and more data are discarded thereby reducing the length of the time-series. This is not a problem for very long time-series but can become an issue for a time-series comprising a low number of periods P (i.e., measurement of short time).

[0079] Another solution to this problem is to artificially extend the time- series before the first iteration. The received time-series is completed by prefixing the time-series with a first side- set of data corresponding to the last period P of the received time- series and by having the time- series succeeded with a second side- set of data corresponding to thefirst period P of the received time-series. Of course, the acquisition time of the first sideset of data and the second side- set of data is adequately shifted by a total duration of the received time-series so that the time-series remains time-ordered.

[0080] At each iteration, only the data from the originally received time- series are corrected but, thanks to the artificial extend, the corrected values for the data located in the first half-period HP and the last half-period HP of the time-series are computed precisely thanks to the side- set of data. The potential values of the data of the side- set of data are replaced by the corrected values assigned to the data of the first and last period P before the next iteration.

[0081] The device 1 further comprises a module 14 for extracting the output 31 from the step outputs executed by the module 13 and for outputting those output 31.

[0082] The output 31 may take the visual form of a graph showing the variation of the corrected potential over the time.

[0083] The device 1 is interacting with a user interface 16, via which information can be entered and retrieved by a user. The user interface 16 includes any means appropriate for entering or retrieving data, information or instructions, notably visual, tactile and / or audio capacities that can encompass any or several of the following means as well known by a person skilled in the art: a screen, a keyboard, a trackball, a touchpad, a touchscreen, a loudspeaker, a voice recognition system.

[0084] In its automatic actions, the device 1 may for example execute the following method (Figure 2): receiving, as an input 21, the time-series described above (step 41), optionally preprocessing the time- series in a view to more efficient and / or reliable processing (step 42), iteratively compensating the non-linear self-potential on said time-series so as to obtain a compensated time- series representative of the induced-potential corrected from the non-linear variation of the self -potential (step 43), providing as output the compensated time-series 31 (step 44).

[0085] A computer 9 may be configured to implement the step of iteratively compensating the self-potential. The computer 9, visible on Figure 3, corresponds for example to a workstation, a laptop, a tablet, a smartphone, or a head-mounted display (HMD).

[0086] That computer 9 comprises the following elements, connected to each other by a bus 95 of addresses and data that also transports a clock signal: a microprocessor 91 (or CPU); a graphics card 92 comprising several Graphical Processing Units (or GPUs) 920 and a Graphical Random Access Memory (GRAM) 921; a non-volatile memory of ROM type 96;- a RAM 97; one or several I / O (Input / Output) devices 94 such as for example a keyboard, a mouse, a trackball, a webcam; other modes for introduction of commands such as for example vocal recognition are also possible; a power source 98; and a radiofrequency unit 99.

[0087] According to a variant, the power source 98 is external to the computer 9.

[0088] The computer 9 also comprises a display device 93 of display screen type directly connected to the graphics card 92 to display synthesized images calculated and composed in the graphics card. According to a variant, a display device is external to computer 9 and is connected thereto by a cable or wirelessly for transmitting the display signals. The computer 9, for example through the graphics card 92, comprises an interface for transmission or connection adapted to transmit a display signal to an external display means such as for example an LCD or plasma screen or a video-projector. In this respect, the RF unit 99 can be used for wireless transmissions.

[0089] It is noted that the word "register" used hereinafter in the description of memories 97 and 921 can designate in each of the memories mentioned, a memory zone of low capacity (some binary data) as well as a memory zone of large capacity (enabling a whole program to be stored or all or part of the data representative of data calculated orto be displayed). Also, the registers represented for the RAM 97 and the GRAM 921 can be arranged and constituted in any manner, and each of them does not necessarily correspond to adjacent memory locations and can be distributed otherwise (which covers notably the situation in which one register includes several smaller registers).

[0090] When switched-on, the microprocessor 91 loads and executes the instructions of the program contained in the RAM 97.

[0091] As will be understood by a skilled person, the presence of the graphics card 92 is not mandatory, and can be replaced with entire CPU processing and / or simpler visualization implementations.

[0092] The device 1 may be implemented differently than a standalone software, and an apparatus or set of apparatus comprising only parts of the computer 9 may be exploited through an API call or via a cloud interface.

[0093] The computer 9, may be embodied by the device 1 described above. It may also be embodied in a system 8 for electrical resistivity tomography or time-domain induced polarization. The system 8 represented in figure 4 further comprises:- at least two electrodes 60 configured to be at least partially in contact with a geological structure 64,- a source of current 61 configured to inject current in the form of successive square waves in the geological structure 64 via one of the electrodes 60,- a device 62 for measuring values representative of the potential between at least one pair of the electrodes 60 in response to the injection of the current in the geological structure 64,- a memory 63 for storing the measured values in the form of a time- series.

[0094] Advantageously, the electrodes 60 may be polarizable electrodes.EXAMPLE

[0095] The present invention is further illustrated by the following example.Materials and Methods

[0096] In this example, the system 8 for electrical resistivity tomography or time-domain induced polarization as described above is used.

[0097] Two electrodes 60 are inserted in a geological structure 64.

[0098] A current is injected in the form of successive square waves in the geological structure 64 via one of the electrodes 60. The current is injected during 50% of the duty cycle. The current is injected with an amplitude ranging from hundreds of milli-amperes to few amperes. The period P is 8 seconds. Each period P of the received time-series comprises the same number of data A=100.

[0099] The values of the potential are measured between the two electrodes 60 in response to the injection of the current in the geological structure 64. The time-series 51 comprising the measured values is represented in Figure 5A.

[0100] The time-series 51 is input into the device 1. The module 12 performs a preprocessing of the received input to correct the linear compensation 52. The preprocessed time-series 53 is then iteratively compensated (Figure 5B).

[0101] To do so, the corrected potential value is computed for each time-series index t as

[0102] For example, for the data 55a corresponding to the time-series index t=100 represented by a plus symbol in Figure 5B, the corrected value is based on the data 55b and 55c represented by a star symbol in Figure 5B. When the corrected values are computed for the overall data, the corrected values are assigned to the data for which it has been computed.

[0103] The compensation is iteratively applied to the time-series until the absolute value of a difference between the potential value associated to said data and the corrected value computed for said data is less than 10'6mV.Results

[0104] The compensated time-series 54 is shown in detail during a rise phase and a decay phase of the potential in Figure 6.

[0105] The same measured time-series 51 only corrected with a single linear compensation which results in the time-series 56 is superimposed to the compensated time-series 54 in Figure 6.

[0106] It is clearly visible that the method of the invention allows to recover the decay phase of the induced-potential from which geological parameters could be determined with much less noise.

Claims

CLAIMS1. A computer-implemented method for compensating a non-linear self-potential in a time- series representative of a potential measured from a geological structure (64), said method comprising: a. receiving (41) as input (21) said time-series comprising at least one previously acquired data, each data being representative of a potential value measured at an acquisition time, said potential being measured between at least one pair of electrodes (60) disposed at least partially in contact with the geological structure (64); wherein said potential comprises a first component being said selfpotential generated by said geological structure (64), variating non- linearly in time, and a second component being an induced-potential, said induced potential being generated in said geological structure (64) in response to an electrical current injected in said geological structure (64) via one of said at least one pair of electrodes (60), the injected electrical current being in the form of a periodic signal between a maximum current amplitude and a minimum current amplitude; b. iteratively compensating (43) said self-potential on said time-series so as to obtain a compensated time-series representative of the induced- potential corrected from the non-linear variation of the self-potential; and c. providing (44) as output (31) said compensated time-series.

2. The computer-implemented method according to claim 1, wherein compensating (43) said self-potential on said time-series is iteratively applied until a predetermined end criterion is satisfied.

3. The computer-implemented method according to claim 2, wherein iteratively compensating (43) said self-potential on said time-series comprising compensating the self-potential on the time- series by: o for each data of the received time-series, computing a corrected potential value, ando assigning the computed corrected potential value to the data for which it has been computed.

4. The computer-implemented method according to claim 3, wherein said time-series comprises at least three sequences, each sequence comprising at least one of the data, computing a corrected potential value corresponding to determining, for each data of one of the sequences, a mean value based on at least one of the data of at least two other sequences.

5. The computer-implemented method according to any one of claims 1 to 4, wherein the periodic signal is such that a product between the maximum current amplitude and the minimum current amplitude is negative and that the maximum current amplitude and the minimum current amplitude are equal in absolute value.

6. The computer-implemented method according to claim 1 or 5, wherein the injected electrical current is in the form of successive square waves or in the form of a sinusoid.

7. The computer-implemented method according to any one of claims 4 to 6, wherein the received time-series is periodic and comprises at least two periods (P), each period (P) being defined by a half-period (HP) corresponding to a half of the duration of said period (P), compensating the self-potential on the time-series comprising: o for each data of the received time-series, computing a corrected potential value based on the potential value associated with an acquisition time corresponding to the acquisition time of said data subtracted from said halfperiod (HP) and on the potential value associated with an acquisition time corresponding to the acquisition time of said data added with said halfperiod (HP); o assigning the computed corrected potential value to the data for which it has been computed.

8. The computer-implemented method according to claim 7, wherein each period (P) of the received time-series comprises the same number of N data, each data beingidentified by a time-series index t positioning said data in the received time-series, and wherein, for each time-series index t, the corrected potential value is computed asu being the potential value associated to the times-series indexes t, t — N / 2 and t + N / 2.

9. The computer-implemented method according to claim 7 or 8, wherein, before iteratively compensating (43) the self-potential, the time-series is completed by prefixing the time- series with a first side- set of data corresponding to the last period (P) of the received time-series and by having the time-series succeeded with a second side-set of data corresponding to the first period (P) of the received timeseries, the acquisition time of the first side-set of data and the second side-set of data being adequately shifted by a total duration of the received time- series.

10. The computer-implemented method according to any one of claims 7 to 9, wherein the time-series comprises less than 10 periods (P).

11. The computer-implemented method according to any one of claims 2 to 10, wherein the predetermined end criterion is configured to stop the iterative compensation after a predefined number of iterations.

12. The computer-implemented method according to any one of claims 2 to 10, wherein the predetermined end criterion is configured to stop the iterations when, for each data of the time-series, a difference between the acquired uncorrected potential value and the corrected potential computed for said data is inferior to a predefined threshold.

13. The computer-implemented method according to claim 12 wherein, for each data, a deviation is computed as an absolute value of a difference between the potential value associated to said data and the corrected value computed for said data, andwherein the predetermined end criterion is configured to stop the iterations when said deviation is inferior of a predefined threshold.

14. The computer-implemented method according to claim 13 wherein the predefined threshold is less than 10'6mV.

15. A computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the computer- implemented method according to any one of claims 1 to 14.

16. A computer-readable medium comprising instructions which, when executed by a computer, cause the computer to carry out the computer-implemented method according to any one of claims 1 to 14.

17. A device (1) for compensating a non-linear self-potential in a time-series representative of a potential measured from a geological structure (64), the device (1) comprising: at least one input (21) configured to receive time-series , each time-series comprising previously acquired values representative of a potential between at least one pair of electrodes (60) disposed at least partially in contact with the geological structure (64), said potential comprising an induced component generated in said geological structure (64) in response to an electrical current injected in said geological structure (64) via one of the at least one pair of electrodes (60) and a self-potential variating non- linearly, the injected electrical current being in the form of a periodic signal between a maximum current amplitude and a minimum current amplitude; at least one processor configured to implement an iterative compensation (13) of said non-linear self-potential on said time-series so as to obtain a compensated time-series corrected from the non-linear selfpotential; at least one output (31) configured to provide said compensated timeseries corrected from the non-linear self-potential.

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