METHOD FOR CHARACTERISING THE UNDERLYING GROUND OF A REGION USING PASSIVE SEISMIC SIGNALS, AND CORRESPONDING SYSTEM

Abstract

A method of characterizing a subsurface of a region includes preparing a plurality of spectra illustrating a spectral density of passive seismic signals obtained in a vicinity of a surface of the region at one or more points of the region where recordings are made of the passive seismic signals. Each spectrum is prepared from an associated signal representative of a movement. The method also includes determining at least one spectral attribute for each frequency appearing in each spectrum so as to obtain a set of spectral attributes associated with the recordings and with the frequencies. The method further includes organizing the set of spectral attributes in a matrix in which each row is associated with one of the recordings. In addition, the method includes applying a principal component analysis method to the matrix in order to determine principal components and deduce therefrom one or more characteristics of the subsurface.

Claims

1. A method of characterizing a subsurface of a region, the method comprising: preparing a plurality of spectra illustrating a spectral density of passive seismic signals obtained in a vicinity of a surface of the region at one or more points of the region where recordings are made of the passive seismic signals, each spectrum being prepared from an associated signal representative of a movement; determining at least one spectral attribute for each frequency appearing in each spectrum so as to obtain a set of spectral attributes associated with the recordings and with the frequencies; organizing the set of spectral attributes in a matrix in which each row is associated with one of the recordings; and applying a principal component analysis method to the matrix in order to determine principal components and deduce therefrom one or more characteristics of the subsurface.

2. The method according to claim 1, wherein: each movement comprises at least one of: a vertical movement or a horizontal movement; and the spectral attributes for each frequency comprise at least one of: a ratio between a spectral density for vertical seismic movements and a spectral density for horizontal seismic movements, a derivative of the spectral density as a function of frequency for the horizontal seismic movements, and a derivative of the spectral density as a function of frequency for the vertical seismic movements.

3. The method according to claim 2, wherein at least one of the derivative of the spectral density as the function of frequency for the horizontal seismic movements or the derivative of the spectral density as the function of frequency for the vertical seismic movements are calculated by applying a linear regression around a selected number of spectral points.

4. The method according to claim 1, wherein preparing each spectrum from a signal comprises: dividing the associated signal into a plurality of consecutive sub-signals all having a same duration: preparing a spectral density sub-spectrum for each sub-signal; for each frequency of the sub-spectra, determining a statistical attribute of the spectral density from spectral density values for that frequency in each sub-spectrum; and obtaining the spectrum that is to be prepared from all of the statistical attributes of all of the frequencies.

5. The method according to claim 4, wherein each sub-signal other than a first of the sub-signals overlaps a preceding sub-signal over at least a non-zero duration of the preceding sub-signal.

6. The method according to claim 1, wherein the recordings are made at different points of the region, each attribute of the set of spectral attributes also being associated with one of the points.

7. The method according to claim 1, wherein the recordings are made over a predetermined duration and from a predetermined time.

8. The method according to claim 7, wherein: the recordings are made in groups of recordings that are made simultaneously, each group corresponding to a day during which the recordings of the group are made, and the recordings are made at different points of the region, from different instants, or at different points of the region and from different instants.

9. The method according to claim 1, wherein columns of the matrix associated with a given attribute are all adjacent.

10. The method according to claim 8, wherein: each group of recordings is associated with a group of rows of the matrix, and for each group of rows, values of the attributes are normalized.

11. The method according to claim 1, wherein: the principal components are projectors, and the matrix is projected onto each projector so as to obtain, for each projector, a graphical representation of the region showing a result of the projection of the matrix for each recording.

12. The method according to claim 11, wherein a number K of projectors is determined from among the projectors.

13. The method according to claim 12, further comprising: projecting the matrix onto the K projectors so as to obtain, for each row of the matrix, a vector of length K; obtaining a second matrix from the vectors of length K; applying to the second matrix a classification method that is organized in one or two dimensions in order to obtain N classes of rows; allocating at least one value to each row of the matrix representing a magnitude of an anomaly of the subsurface of the region; preparing a class head for each class of rows; obtaining a third matrix of dimensions N by K from the class heads; and applying a pseudo-inversion method to the third matrix in order to obtain a fourth matrix of dimensions N times a number of frequencies appearing in each row of the matrix of spectral attributes.

14. The method according to claim 12, further comprising: projecting the matrix onto the K projectors so as to obtain, for each row of the matrix, a vector of length K; obtaining a second matrix from the vectors of length K; applying a pseudo-inversion method to the second matrix in order to obtain a third matrix having same dimensions as the matrix of spectral attributes; applying to the third matrix a classification method organized in one or two dimensions in order to obtain N classes of rows; allocating at least one class number to each row of the matrix representing the magnitude of an anomaly of the subsurface of the region; preparing a class head for each class of rows; and obtaining from the class heads a fourth matrix of dimensions N times a number of frequencies appearing in each row of the initial matrix of spectral attributes.

15. A system for characterizing a subsurface of a region, the system comprising: a memory configured to store instructions; and a processor configured, when executing the instructions, to: prepare a plurality of spectra representative of a spectral density of passive seismic signals obtained in a vicinity of a surface of the region at one or more points of the region where recordings are made of the passive seismic signals, each spectrum being prepared from an associated signal representative of a movement; determine at least one spectral attribute for each frequency appearing in each spectrum so as to obtain a set of spectral attributes associated with the recordings and with the frequencies; organize the set of spectral attributes in a matrix in which each row is associated with one of the recordings; and apply a principal component analysis method to the matrix in order to determine principal components and deduce therefrom one or more characteristics of the subsurface.

16. The system according to claim 15, wherein: each movement comprises at least one of: a vertical movement or a horizontal movement; and the spectral attributes for each frequency comprise at least one of: a ratio between a spectral density for vertical seismic movements and a spectral density for horizontal seismic movements, a derivative of the spectral density as a function of frequency for the horizontal seismic movements, and a derivative of the spectral density as a function of frequency for the vertical seismic movements.

17. A non-transitory computer readable data medium storing a computer program including instructions that when executed cause a processor to: prepare a plurality of spectra representative of a spectral density of passive seismic signals obtained in a vicinity of a surface of the region at one or more points of the region where recordings are made of the passive seismic signals, each spectrum being prepared from an associated signal representative of a movement; determine at least one spectral attribute for each frequency appearing in each spectrum so as to obtain a set of spectral attributes associated with the recordings and with the frequencies; organize the set of spectral attributes in a matrix in which each row is associated with one of the recordings; and apply a principal component analysis method to the matrix in order to determine principal components and deduce therefrom one or more characteristics of the subsurface.

18. The non-transitory computer readable data medium according to claim 17, wherein: each movement comprises at least one of: a vertical movement or a horizontal movement; and the spectral attributes for each frequency comprise at least one of: a ratio between a spectral density for vertical seismic movements and a spectral density for horizontal seismic movements, a derivative of the spectral density as a function of frequency for the horizontal seismic movements, and a derivative of the spectral density as a function of frequency for the vertical seismic movements.

19. The non-transitory computer readable data medium according to claim 17, wherein the instructions that when executed cause the processor to prepare each spectrum comprise instructions that when executed cause the processor to: divide the associated signal into a plurality of consecutive sub-signals all having a same duration: prepare a spectral density sub-spectrum for each sub-signal; for each frequency of the sub-spectra, determine a statistical attribute of the spectral density from spectral density values for that frequency in each sub-spectrum; and obtain the spectrum that is to be prepared from all of the statistical attributes of all of the frequencies.

20. The non-transitory computer readable data medium according to claim 19, wherein each sub-signal other than a first of the sub-signals overlaps a preceding sub-signal over at least a non-zero duration of the preceding sub-signal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Other characteristics and advantages of the present invention appear from the following description made with reference to the accompanying drawings, which show an example having no limiting character.

[0091] In the figures:

[0092] FIG. 1 is a diagram showing the steps of a method in an implementation of the invention;

[0093] FIG. 2 is a diagram showing a system in an embodiment of the invention;

[0094] FIG. 3 is a section view of the subsurface of a region;

[0095] FIG. 4 is a diagram showing how a spectrum is obtained from a signal;

[0096] FIG. 5 shows the matrix in which attributes are organized;

[0097] FIG. 6 shows the projection of the matrix onto the projectors;

[0098] FIG. 7 is a graph showing the classification of re-projected vectors; and

[0099] FIG. 8 shows the graphical representation that is obtained after associating a parameter with each re-projected vector.

DETAILED DESCRIPTION OF AN EXAMPLE

[0100] There follows a description of a method and a system for characterizing the subsurface of a region in accordance with a particular example of the invention.

[0101] FIG. 1 is a diagram showing various steps in a method of characterizing the subsurface of a region.

[0102] The method may be performed to determine whether fluids or a plurality of phases of a single fluid are present in the subsurface of a region.

[0103] Typical applications for using this method relate for example to monitoring reservoirs containing hydrocarbons (e.g. natural gas), steam, and various types of gas (e.g. CO.sub.2, H.sub.2), prospecting for hydrocarbons, prospecting in the geothermal field.

[0104] In a first step E01 of the method, a plurality of spectra are prepared that illustrate the spectral density of passive seismic signals obtained in the vicinity of the surface of said region at at least one point of said region where passive seismic signals are recorded, each spectrum being prepared from a signal illustrating a movement.

[0105] In other words, steps of acquiring signals illustrating horizontal movements (possibly two signals in different directions) and/or vertical movements are performed beforehand. These signals may be acquired by using seismometers, such as the apparatus sold by the Canadian supplier Nanometrics under the trade name T-40. Such apparatuses can be arranged regularly in the vicinity of the surface of a region or on the surface of the region, as described below with reference to FIG. 3, and the apparatuses are preferably used at night so as to reduce anthropic noise. All of the signals are associated with a respective instant and/or a respective location or point of the region under study.

[0106] It may be observed that apparatus of the kind mentioned above provides movement speed signals that are representative of the movement.

[0107] Each spectrum may be obtained from the signal corresponding thereto by determining the power spectral density (PSD) of the signal.

[0108] It is also possible to perform processing that seeks to smooth the spectrum that is obtained, as described below with reference to FIG. 4.

[0109] After step E01, spectra are obtained, or indeed spectra that may comprise both a spectrum associated with the horizontal movements and also a spectrum that is associated with the vertical movements, these spectra being associated with the recordings and thus with their properties as constituted by the point of the region and the instant or the day of acquisition.

[0110] It may be observed that obtaining a single spectrum for horizontal movements from two signals representative of movement in two different directions may be done by calculating the geometrical mean of the spectra corresponding to each direction. Specifically:

Fh(f)={square root over (PSD.sub.E.sup.2+PSD.sub.N.sup.2)}

where f is frequency, Fh(f) is the spectrum corresponding to horizontal movements, PSD.sub.E is the spectrum corresponding to horizontal movements in a first direction (specifically east), and PSD.sub.N is the spectrum corresponding to horizontal movements in a second direction (specifically north).

[0111] Thus, the spectra are sampled and relate to a finite number of frequencies contained in a previously selected broad range.

[0112] In a second step E02, spectra attributes are determined. These attributes may be selected from the group formed by the ratio between the spectral density for vertical seismic movements and the spectral density for horizontal seismic movements, the derivative of the spectral density as a function of frequency for the horizontal seismic movements, and the derivative of the spectral density as a function of frequency for the vertical seismic movements.

[0113] These three attributes can be written as follows:

[00001]$\frac{\mathrm{Fv}\left(f\right)}{\mathrm{Fh}\left(f\right)}$$\frac{\mathrm{dFh}\left(f\right)}{\mathrm{df}}$$\mathrm{and}$$\frac{\mathrm{dFv}\left(f\right)}{\mathrm{df}}$

where Fv(f) is the spectrum corresponding to vertical movements.

[0114] It may be observed that the derivative of the spectral density as a function of frequency for the horizontal seismic movements and/or said derivative of the spectral density as a function of the frequency of vertical seismic movements can be calculated by applying a linear regression around a selected number of spectrum points.

[0115] By way of indication, the selected points may be obtained by dividing the frequency axis into spans of 0.5 Hz.

[0116] The step E02 serves to obtain a set of attributes associated with frequencies (which may differ between the different types of attributes), with the recordings, and thus with the points of the region, and also with the instants and/or the days at which the signals were acquired.

[0117] In a step E03, this set of attributes is organized into a matrix in which each row is associated with a recording (i.e. with one point of the region, and with one instant and/or one day when recording was made).

[0118] This organization is described in greater detail with reference to FIG. 5.

[0119] In a step E04, a method of principal component analysis is applied to said components in order to determine the principal components and deduce therefrom the characteristics of said subsurface.

[0120] FIG. 2 is a diagram showing a system 1 suitable for performing the steps E01 to E04 as described with reference to FIG. 1.

[0121] The system 1 may be a computer system and it comprises a processor 2 and a memory 3.

[0122] Instructions of a computer program 4 are stored in the memory 3. The computer program 4 comprises instructions 41 for performing the steps E01, instructions 42 for performing the step E02, instructions 43 for performing the steps E03, and instructions 44 for performing the step E04.

[0123] In combination, the instructions 41 to 44 and the processor together form modules of the system 1 that are adapted respectively to performing the steps E01 to E04.

[0124] FIG. 3 is a section view of the subsurface of a region that it is desired to characterize by performing the method of the invention.

[0125] For this purpose, seismometers 100 were buried in the vicinity of the surface of the region and seismometers 100 forming part of a group 101 can be seen in the plane of the section. By way of example, seismometers 100 were buried at a depth of about fifty centimeters. Such an installation is particularly simple for a technician.

[0126] Alternatively, the seismometers could be placed on the surface, providing that configuration enables good coupling to be obtained with the ground. The person skilled in the art knows how to place seismometers in order to obtain good coupling.

[0127] In this example, the subsurface of the region includes a zone 200 containing gas, and a zone 300 containing water. This region may be a reservoir. The presence of these two fluids with different phases makes it possible to perform the method of the invention.

[0128] In the example shown, in the groups 101, the seismometer 100 that is arranged in the middle of the figure will present spectra that are different from the spectra of the seismometers 100 that are arranged on the right and on the left, since only the middle seismometer is vertically above the reservoir.

[0129] In order to enable recordings to be made within a region with few apparatuses, it is possible to take measurements in groups.

[0130] For example, on a first day from midnight to 4 in the morning, the seismometers 100 are arranged to form the group 101 and acquire data. On a second day from midnight to 4 in the morning, the seismometers 100 are arranged to form the group 102 and acquire data. On a third day from midnight to 4 in the morning, the seismometers 100 are arranged to form the group 103 and acquire data. On a fourth day from midnight to 4 in the morning, the seismometers 100 are arranged to form the group 104 and acquire data.

[0131] FIG. 4 is a diagram showing how a spectrum is obtained from a signal, e.g. a signal obtained by the seismometers 100 described with reference to FIG. 3.

[0132] In this figure, there can be seen a signal SIG that is representative of movements, specifically of movement speed along one direction. The signal was acquired during a four-hour long acquisition starting from midnight: this serves to reduce the appearance of anthropic noise.

[0133] The signal SIG may be divided into a plurality of sub-signals that are all of the same duration, the sub-signals being consecutive, and each sub-signal in this example overlapping the preceding sub-signal over at least half of the duration of the preceding sub-signal (this overlap is not essential). In the figure, the sub-signals are represented by curly braces under the signal SIG.

[0134] It may be observed that some of the sub-signals may be omitted and not processed thereafter if they present excessive noise. By way of indication, it is possible to eliminate sub-signals having an absolute value that exceeds a threshold. For example, it is possible to exclude sub-signals that have an absolute value situated beyond the 99% quantile defined for the entire signal SIG.

[0135] Thereafter, a sub-spectrum is prepared for each sub-signal. In the figure, three spectral density sub-spectra are shown: PSD_1, PSD_2, and PSD_3.

[0136] For each frequency of the sub-spectra, a median value is determined for the spectral density on the basis of the spectral density values for that frequency in each sub-spectrum. The spectrum PSD_m is then obtained from all of the median values. In other words, the spectrum is made up of these median values.

[0137] FIG. 5 shows how attributes are organized within a matrix M for organizing attributes obtained for signals as acquired at different points and on days that may be different.

[0138] In the matrix M, the following notation is used:

[0139] Attr_i: attribute of type i;

[0140] x_j: point j in the region (this point is associated with the day of the measurement);

[0141] f_k: the frequency k of the spectral attribute. In the matrix M, each row is associated with a recording and with a point x_j of the region, and each column is associated with an attribute type Attr_i and with a spectral attribute frequency f_k.

[0142] In the matrix, the columns of the matrix that are associated with a given attribute are all adjacent. Thus, the rows of said matrix corresponding to groups of recordings made simultaneously (e.g. within the groups 101 to 104 described with reference to FIG. 3) are all grouped together in the matrix so as to form groups of rows, and each group is associated with one day in this example.

[0143] Preferably, for each day, or for each group of rows, the values of the attributes are normalized.

[0144] Organizing the attributes in the matrix M makes it possible to perform a method of principal component analysis in which each row is an individual and each column is a variable. The principal component analysis serves to obtain principal components that are referred to as projectors. The projectors are thus vectors written p, which are of length L that is equal to the product of the number of different attribute types multiplied by the number of frequencies present for each attribute type.

[0145] The projection of a row of index i (lying in the range 1 to m, which is the number of rows in the matrix M) of the matrix M onto a projector p is calculated as follows:

[00002]$M|p.Math.\left(i\right)=\underset{j=1}{\overset{j=L}{.Math.}}.Math..Math.M\left(i,j\right).Math.p\left(j\right)$

[0146] Since the result of this projection corresponds to a point of the region, it is possible to obtain a graphical representation of the projection of the matrix M at all points of the region where signal acquisitions were performed.

[0147] Such graphical representations are shown in FIG. 6. This figure shows four graphical representations corresponding to projections: PRJ1, PRJ2, PRJ3, and PRJ4. The outline of a known reservoir RES is highlighted on these graphical representations.

[0148] The graphical representations that present gray scale variations that correspond best to the expected spatial representation are considered as being good projectors. The person skilled in the art knows how to interpret these maps.

[0149] Under each graphical representation of the region, there is also shown the projector itself as a function of frequency.

[0150] In the example shown, the projectors PRJ1 and PRJ2 are considered to be good projectors. A number K of projectors is thus determined as being equal to two of the projectors, these projectors being written p1 and p2.

[0151] Thereafter, the matrix can be projected onto the two projectors p1 and p2 by using the following formula:

M|(p1,p2)(i)=(M|p1),M|p2)

This obtains a number m (the number of rows in the matrix, or the number of recordings) of vectors belonging to a two-dimensional space. These vectors may be organized to form the rows of a second matrix.

[0152] FIG. 7 shows the individuals present in this second matrix in their initial reference frame represented by the axis x1, x2. Each individual corresponds to a cross in the figure.

[0153] Thus, by applying a classification method organized in one dimension for obtaining N classes, it is possible to classify these individuals by determining a curve written that approximates the individuals, and then by determining classes that are represented by circles on a curvilinear abscissa along the curve that corresponds to a class number (that varies in this example from 1 to 1). It may be observed that the radius of the circles corresponds to their covariance radius.

[0154] This figure also shows the axes that correspond to the two projectors that have been retained, which axes are referenced e1 and e2 and do not enable the anomaly to be represented well enough.

[0155] In this example, the class number represents the magnitude of the anomaly in the subsurface of the region.

[0156] Thus, the centers of the circles are considered as class heads.

[0157] It is then possible to obtain a third matrix of dimensions N by K from the class heads. Thereafter, it is possible to perform pseudo-inversion of the matrix in order to obtain a fourth matrix of dimensions N times the number of frequencies appearing in each row of the initial matrix of the spectral attributes.

[0158] FIG. 8 shows the map that is obtained by displaying the value of the magnitude of the anomaly by means of a class number for each point of the region, it being possible to obtain this map after the pseudo-inversion.

[0159] In this figure, for each class head, there are also shown the curves that reveal the variations as a function of frequency in the attributes corresponding to the class heads, with this being done for two attributes, the derivative to the spectrum corresponding to the vertical movements as a function of frequency, and the ratio between the vertical and horizontal movements.

[0160] It should be observed that these curves show behaviors that are very different, including in frequency ranges that are lower than 1 Hz.

[0161] The inventors have observed that the peak specified by the document Phenomenology of tremor-like signals observed over hydrocarbon reservoirs (S. Dangel et al., Journal of Volcanology and Geothermal Research) is in fact preceded by a decrease in the spectrum when the measurement is taken vertically above a reservoir. By using a large frequency range, and by using principal component analysis, the invention enables anomalies to be shown up more clearly than in the solutions of the prior art.

[0162] It may also be observed that the various graphs shown in the present description were obtained from measurements taken over and around a known reservoir.