WO2010000967A2  Method for the probabilistic processing of geophysical data  Google Patents
Method for the probabilistic processing of geophysical data Download PDFInfo
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 WO2010000967A2 WO2010000967A2 PCT/FR2009/000676 FR2009000676W WO2010000967A2 WO 2010000967 A2 WO2010000967 A2 WO 2010000967A2 FR 2009000676 W FR2009000676 W FR 2009000676W WO 2010000967 A2 WO2010000967 A2 WO 2010000967A2
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 238000001914 filtration Methods 0.000 claims abstract description 17
 230000035897 transcription Effects 0.000 claims abstract description 10
 280000398338 Seismic companies 0.000 claims description 21
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Classifications

 G—PHYSICS
 G01—MEASURING; TESTING
 G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS
 G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
 G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
 G01V1/36—Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
 G01V1/364—Seismic filtering
Abstract
Description
METHOD FOR THE PROBABILISTIC TREATMENT OF GEOPHYSICAL DATA
The present invention relates to a method for the probabilistic processing of geophysical data.
It applies more particularly, but not exclusively, to geophysical data, imaging data obtained by physical methods such as medical imaging, sonar, nondestructive testing of materials or any type of sampling of natural phenomena such as mining reconnaissance campaigns, geochemical inventories, pollution sensors, satellite data, oceanographic data, water analysis ...
Indeed, during reconnaissance campaigns of a natural resource (seismic geophysical campaigns for the recognition of oil deposits), the data are obtained by any acquisition system proceeding by a signal emission from sources (vibration or explosion in seismic acquisition), propagated in the environment to be explored and collected by recording receivers (geophones or hydrophones in seismic acquisition).
The receiver records the temporal variations of the signal emitted by the source after its journey in the spatial medium traversed.
The object of any geophysical treatment is the extraction and positioning in the physical space where the analyzed medium is deployed, variations of amplitude of the component of the recording related to the physical characteristics (speed, density, impedance, saturation in fluids) localized from this medium. The result of this treatment is a geophysical image of the medium recognized by the acquisition device (profile, section and cube of seismic amplitudes for example).
The usual geophysical treatments are based on deterministic (causal) theories of wave propagation linking the sensor recordings to the properties of the medium by a set of physical laws. The application of these physical laws to the recorded data is supposed to lead to a measurement of the properties of the medium, notably its impedance in the case of seismic acquisitions. These treatments give firstorder satisfactory results, that is to say to detect and locate the main changes in the physical composition of the medium studied.
Whatever the quality of the acquisition and geophysical treatment (coverage rate and oil seismic resolution), the question always arises of the fine match between the geophysical variations observed and those of the composition of the environment. At this second order of fine observation, the geophysicists agree to recognize the presence of a radical residual indetermination on the geophysical characterization of the medium, linked at the same time to the characteristics of the geophysical measurement (frequency band, presence a noisy component in particular) and the limits of application of the deterministic processing models used.
By its very nature, this radical residual indeterminacy is not quantifiable by the usual processes and results in a certain lack of coherence between the direct observations of the medium (data of drilling or oil production) and their geophysical image. This lack of coherence on a small scale makes the geophysical image unclear or uncertain when it comes to using it to make environmental management decisions. This geophysical uncertainty is spreading to all the modeling of the environment using geophysical data (structural geomodel, reservoir modeling in exploration and oil production).
One of the visible and major consequences of this indeterminacy of the geophysical treatment is therefore the difference between the expected character of the medium recognized by the geophysical device (the impedance, the thickness or the porosity of a reservoir) and the actual character revealed by the direct measurement (well drilling).
In oil exploration, this type of difference can mean the gain or loss of sizeable sums of money in millions of dollars (unproductive drilling or low hydrocarbon recovery rate, for example).
The geophysical treatments implemented are above all deterministic models supported by underlying models of wave propagation in heterogeneous media. To judge their reliability and thus the contribution to operational decisionmaking (drilling, exploitation strategy), it is necessary to have a quantification of the uncertainties associated with these modelizations in the generic form of "confidence intervals" . Deterministic modelizations do not allow the calculation of confidence intervals sensu stricto except by the realization of several alternative scenarios, which is more and more expensive in engineer time and in computing time as the development of modelizations "heavy Like the prestack inversion for example.
The only realistic alternative to this deterministic "trial and error" method is the use of probabilistic models.
The probabilistic approach abandons considering sensor data as indirect measures of the physical properties of the environment. It consists of seeking the best possible estimate of the physical property of the environment from the indirect and fragmentary information constituted by the sensor records. The best possible estimate is defined from the concept of estimation error, specific to the socalled "geostatistical" models, which introduces the notion of the inevitable error committed by replacing the true but unknown value of the unknown property of the medium in one given location, by an estimator calculated from the values measured by the sensors.
This error is of course itself unknown, but it is possible to identify the probabilistic model that minimizes its mean (which must be nil to ensure the unbiasedness of the estimate) and its variance called estimation variance (variance of the unknown error committed by replacing an unknown true value by a modeled value).
The problem lies then in the choice and the specification of the probabilistic model to use. It is certain that in the geophysical field, these models must conform to the physical laws underlying the deterministic models. _ _
There are two types of probabilistic approaches used in petroleum engineering, the "Bayesian" type (a priori known probability) and the "Matheronian" type (probability derived from a correctly chosen and specified probabilistic model), referring respectively to T. BAYES and G. MATHERON.
Geostatistics is the application of probabilities to natural phenomena that develop in space and time, hence the prefix "geo". This theory is particularly exposed in the book "The theory of regional variables" by G. MATHERON (MASSON Publisher).
Regionalised data is data referenced by coordinates in an Ndimensional space, most commonly in a one, two, or threedimensional geographic space. These data can be single or multivariable, that is, one or more variables are measured or calculated at the data points.
Thus this theory of regionalized variables provides the appropriate language and tools for the estimation of any quantity, unknown a priori, locatable in a given space, from necessarily fragmentary sampling of this same quantity.
To estimate this unknown quantity, geostatistics proposes to elaborate the probabilistic model or models appropriate to the situation, then to choose judiciously among the existing models, according to the available data and the quantity to be estimated, the relevant probabilistic model and the parameters. from its specification to the case treated. The geostatistical reference estimator is known as kriging, a term referring to the work of D. G. KRIGE.
More than the estimate, the probabilistic model also gives an indicator of the accuracy of the estimate. This indicator, called the estimation variance, is a valuable tool because it opens the way to a possible management of uncertainties (translated in terms of variance).
In the context of stationary probabilistic models of order 1 or 2, which assume the translation invariance in space of the mean (order 1) and the variance (order 2) of the modeled variable, the covariance tool or variogram is used to quantify the spatial variability of the data. For a nonstationary model, it is the generalized covariance that is used. Geostatistical models also make it possible to anticipate validly on a future state, for example of the exploitation of the natural resource, when the available data will be more numerous and the problems of estimation will arise differently to the operator.
Whatever the business context of the exploitation of the natural resource, the question always arises of the adequacy of the available data to the resolution of the operational problem.
To the intrinsic quality of each data is added the quality of the spatial integration of this data within the entire game. This is why it is interesting to complete the experimental survey by a geostatistical control associated with geographical coordinates, temporal or other.
The usual methods of quality control or coherence of regionalized data sets are either visual, morphological (shape studies) or statistical (without taking into account spatial coordinates). When used, the filtering processes (frequency or spatial) generally work on monovariable data and on regular grids. Consequently, they are poorly suited to the decomposition of multivariate data irregularly located in the anomalous and coherent component space. _ _
Similarly, the definition of the criteria used to define anomalies is often arbitrary and does not lend itself to experimental verification.
As such, the Applicant has proposed a method for quantifying the spatial quality of a regionalised data set through the determination of a geostatistical index called SQI for "
Spatial Quality Index ", this index being used to locate anomalous prior data and thus to judge the quality of the measurements or digital processing that generated the dataset (patent no. 02 02578 issued to EARTH
RESOURCE MANAGEMENT SERVICES Limited Liability Company FR).
Nevertheless, kriging estimation techniques, which means "best linear estimator verifying this or that unbiased condition," do not respond in a completely satisfactory way to the quantification of uncertainties and therefore to the optimization of the treatments. geophysical oriented tank.
In order to eliminate these drawbacks, the invention proposes to reconsider the usual deterministic treatments of the geophysical data in terms of estimating the physical properties of the reservoirs from the records of the sensors, according to the following operating phases:
a first phase of probabilistic transcription of the deterministic filtering of the aforesaid geophysical data, for example of the "Wiener in the time domain" type, comprising a factorial kriging estimation of the signal component, this first phase comprising: _ _
• the taking into account of all the traces to be filtered by the realization of a stationary random function Zam of order 2 (am being the amplitudes of the measured traces),
• the determination of the factorial kriging consisting in estimating the Zas component (as: amplitude signal) by minimizing its estimation variance from experimental values Zam,
a second phase of development of a probabilistic model comprising: the decomposition of said random function Zam into the sum of two random functions Zas (as: amplitude signal) and Zab (ab: amplitude noise), Zas and Zab being two independent random functions (uncorrelated),
The verification by a set of statistical tests of the validity of the noncorrelation of said random functions Zas and Zab,
The modeling of the experimental spatial covariance (autocorrelation function) of the data of said random function Zam, measured using a sum of two authorized covariance models representing one the spatial covariance of Zas and the other the covariance of Zab, and
a third phase of realization of the aforesaid probabilistic treatment of the geophysical data comprising: the choice of a neighborhood of the trace to be filtered (set of neighboring experimental data participating in the filtering of a given measurement point) guided by the study of the associated estimation variance with a stabilization around its minimum value,
The calculation of the weightings to be applied to each of the points of the neighborhood by the resolution of the linear equation system of said factorial kriging of the component Zas, or at the choice of the component Zab, in the vicinity of the trace to be filtered,
The application of all said weighting units by linear combination of the points with said neighborhood considered, and successively with all the measurement points to be filtered by sliding of the neighborhood retained around each of these points, and
The application of all said weightings by linear combination of the points in said neighborhood considered by making an estimation of the component to be filtered (Zab) or retaining the component (Zas) according to the choice of the operator, at each point of measured seismic amplitude.
Of course, the aforesaid first phase of probabilistic transcription of the deterministic filtering of the aforesaid geophysical data, the aforementioned second phase of the development of a probabilistic model, and the aforementioned third phase of realization of the aforesaid probabilistic treatment of the geophysical data, will be carried out by an automaton. computer science.
Thus the process for the probabilistic processing of geophysical data consists in:
 transcribe in a probabilistic framework each of the usual deterministic treatments of geophysical data,
develop the corresponding probabilistic mathematical models according to the criteria of objectivity exposed by G. MATHERON in the book "Estimate and Choose",
 specify the operating mode and the implementation of these probabilistic models in order to proceed: • the optimal estimation of the geophysical signal or any other geophysical feature that is the subject of the treatment, and
Calculating, from the estimation variance associated in the model to the estimator, confidence indices or other type of confidence interval that can be used to quantify the accuracy of the optimal estimate of the geophysical signal or any other other geophysical character object of the treatment.
More precisely, conventional treatments of seismic data for the purpose of characterization of petroleum reservoirs consist of a series of successive elementary treatments mainly comprising several steps:
filtering and deconvoluting the acquisition data to separate the different types of seismic waves,
optimization of the signaltonoise ratio along the seismic traces recorded by the receivers,
 indepth localization of the seismic wave path as a function of the respective positions of the sources and receivers and interference with the geophysical conditions of the medium traversed,
 inversion of the geophysical signal in petrophysical characters of the environments crossed.
Each of these deterministic processing steps can be transcribed in a probabilistic framework. Operational experience has already been gained with probabilistic models of depth conversion (vertical conversion by kriging with external drift or cokriging with or without the use of seismic velocities), an experience that demonstrates the need for compatibility between deterministic and probabilistic approaches.
Expanding the development of "Matheronian" models adapted to more and more varied geophysical treatments (wave separation, inversion, tomography) is a clear and lowrisk technological differentiation pathway.
The description, the hierarchy, the criteria of choice of these global and local probabilistic models are exposed in the book "Estimate and Choose" by G. MATHERON (Edition Ecole des Mines de Paris).
One embodiment of the invention, more specifically concerning the deterministic method of "Wiener filtering in the time domain", used in geophysical signal processing, will be described below, by way of nonlimiting example, with reference in the accompanying drawings in which:
Figure 1 is a schematic representation illustrating the main phases of transcription in a probabilistic framework of a usual deterministic treatment (Wiener filtering) of geophysical data;
FIG. 2 a representation of a set of seismic traces to be filtered by the Wiener method;
Figure 3 is a representation of the modeling of the experimental covariance of the measured amplitudes as the sum of two covariance models associated with the signal and noise components of the measured amplitudes;
FIG. 4a is a representation of the result of the filtering in terms of estimation of the "signal" component, and
FIG. 4b is a representation of the result of the filtering in terms of estimation of the "noise" component.
Given a collection of seismic traces in the time domain, the Wiener geophysical filters are used to filter coherent noises along the traces but not correlated from one trace to another and also not correlated to the signal contained in the trace. .
The geophysical filter of a seismic trace consists in elaborating a linear filter (linear combination of the data of the trace) whose pulse response minimizes in the least squares sense the error made by replacing the "desired" signal contained in the trace by the filter result.
This minimization involves the experimental functions of autocorrelation of the trace and its intercorrelation with a reference trace.
Translated into probabilistic terms, this probabilistic transcription amounts to considering the set of traces to be filtered as the realization of a random function Zam (am: measured amplitudes) and the filter as a factorial kriging of the signal component Zas (as: amplitude signal) contained in Zam. Factorial kriging is a classical geostatic estimator consisting of, knowing the experimental values Zam, best estimating the Zas component of the model in minimizing its estimation variance.
The development of the probabilistic model amounts to decomposing the random function Zam into the sum of two random functions Zas (as: amplitude signal) and Zab (ab: amplitude noise), Zas and Zab being two functions independent (uncorrelated). The classical formalism of factorial kriging is applicable to best estimate Zas as a linear combination of the Zam information present in the vicinity of the trace to be filtered. The result of the factorial kriging is the calculation of the weighters to be applied to the surrounding Zam data (impulse response of the filter) and the calculation of the estimation variance of Zas, minimized by kriging.
The practicalization of the probabilistic model of factorial kriging consists in firstly checking by a set of statistical tests the validity of the hypothesis of noncorrelation of a "signal" component and a "noise" component within experimental data measured.
It is then necessary to model the experimental spatial covariance (autocorrelation function) of the Zam data measured using a sum of two authorized covariance models representing one the spatial covariance of Zas and the other the one from Zab. Once the covariance model has been established, a neighborhood of the trace to be filtered (a set of neighboring experimental data participating in the filtering of a given measurement point) will be chosen in which the weights to be applied to each of the points of the neighborhood will be calculated by resolution. of the linear equation system of the factorial kriging of the Zas component, or at the choice of the Zab component. This choice of neighborhood will be guided by the study of the associated estimation variance that will be sought to stabilize around its minimum value.
This set of weights will be applied by linear combination of the points of the neighborhood considered, and successively to all the measuring points to be filtered by sliding of the neighborhood retained around each of these points.
The application of the set of weightings by linear combination of the points in the neighborhood considered results in an estimate of the component to filter (Zab) or hold (Zas) according to the choice of the operator, at each point of measured seismic amplitude.
In accordance with the methodology illustrated in FIG. 1, the probabilistic transcription of a Wiener filter applied to seismic traces in the time domain is represented in the form of two mapped procedures; the approach described in the left frame concerns the deterministic filter of Wiener; the approach described in the right frame concerns the probabilistic filter, the underlying hypothesis being that the trace of measured amplitudes Am (t) is the sum of a "signal" trace As (t) and a trace " brait »An (t) not correlated with each other.
In the example shown in Figure 2a, the amplitude traces are measured by different sensors positioned along a well, the source being located vertically of the device. Thus the set of seismic traces to be filtered are indicated as a function of time along the ordinate axis and the depth along the abscissa axis.
Figure 2b shows the experimental variogram (equivalent of the autocorrelation function in the context of secondorder stationary probabilistic models used to describe the seismic amplitudes along the tracks) of the seismic section, i.e. evolution of the experimental variance (figured on the time axis in ordinate), according to the distance between the measurements (distance axis in abscissa).
This set of measured amplitudes is horizontalized according to the first arrival of each trace and normalized in terms of energy so as to satisfy the secondorder stationary hypothesis.
It is a question of separating in this set of measured amplitudes located in a space (offset, time), the train of socalled descending waves that is to say in line direct source sensor of the rising wave train (after reflection on the geological interfaces) and residual noise.
It is thus a question of interpreting the amplitudes measured in probabilistic terms, namely: the measured amplitudes are considered as the realization of a stationary random function of order 2, itself sum of two orthogonal random functions representing the components " signal "or" downwaves "and" noise "or" rising waves "plus" residual noise ". Figure 3 shows the modeling of the experimental variogram of the amplitudes measured in the vertical (time) and horizontal (offset) directions. The horizontal direction represents the direction of "descending waves". In the vertical direction, the vertical variogram is the strict equivalent of the autocorrelation function used in Wiener filtering.
Thus, the variogram model of the measured amplitudes is decomposed as a sum of two variogram models of signal (downwave) and noise (risingwave and residual noise) variograms.
Figure 4 represents the result of the factorial kriging (estimation) of the "signal" (downwave) and "noise" components (rising waves and residual noise) of the measured amplitudes.
We can note the good reproduction of the horizontal character of the descending waves and the noncorrelation with the estimate of the rising waves and the residual noise.
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US5051963A (en) *  19900709  19910924  Mobil Oil Corporation  Process for cancelling stationary sinusoidal noise in seismic data 
WO2003058279A1 (en) *  20020114  20030717  Compagnie Generale De Geophysique  Method for filtering seismic data, particularly by kriging 

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US5051963A (en) *  19900709  19910924  Mobil Oil Corporation  Process for cancelling stationary sinusoidal noise in seismic data 
WO2003058279A1 (en) *  20020114  20030717  Compagnie Generale De Geophysique  Method for filtering seismic data, particularly by kriging 
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