An interpolation method, device, equipment, medium and program based on prior data

Abstract

The present disclosure relates to the technical field of seismic processing, and particularly relates to an interpolation method and device based on prior data, equipment, a storage medium and a computer program. The method comprises the following steps: acquiring seismic data, performing τ-P positive conversion on the seismic data in a preset data processing domain to obtain converted data; selecting unaliasing and preset numerical aliasing data in the converted data, and collecting the selected unaliasing and preset numerical aliasing data into to-be-processed data; performing five-dimensional interpolation on the to-be-processed data to obtain an interpolation result; and performing five-dimensional regularization processing on the seismic data according to the interpolation result to obtain a processing result. The present application can adapt to interpolation processing based on prior data.

Description

Technical Field

[0001] This disclosure relates to the field of earthquake processing technology, and in particular to an interpolation method, apparatus, device, storage medium, and computer program based on prior data. Background Technology

[0002] In recent years, regularization methods have developed rapidly. They can not only compensate for the irregularities in the observation system caused by budget constraints and construction conditions during the data acquisition process, but also improve the signal-to-noise ratio of the data. Currently commonly used regularization methods include: three-dimensional regularization technology, five-dimensional regularization technology, OVT domain regularization technology, and multi-directional radial five-dimensional regularization technology.

[0003] Conventional methods involve interpolation along five dimensions: main survey line, connecting survey line, offset, azimuth, and time. However, they lack necessary analysis and optimization of the interpolation data, resulting in poor performance in complex, low-signal-noise-ratio regions. Furthermore, the conventional five-dimensional regularization technique involves a cumbersome data preparation process, demanding high signal-to-noise ratios from the prepared data, requiring a data volume many times larger (as it is grouped with azimuth), and incurring significant computational costs. All of these methods place high demands on the interpolation data preparation, leading to unsatisfactory interpolation results in low-signal-noise-ratio regions. Moreover, the problem of poor structural characterization in complex, low-signal-noise-ratio regions remains unresolved. Summary of the Invention

[0004] This disclosure provides an interpolation method, apparatus, device, storage medium, and program based on prior data.

[0005] Firstly, this disclosure provides an interpolation method based on prior data, including:

[0006] Seismic data is acquired, and the seismic data is subjected to a τ-P positive transformation within a preset data processing domain to obtain transformed data.

[0007] Select the non-aliased and preset numerical aliased data from the transformed data, and aggregate the selected non-aliased and preset numerical aliased data into data to be processed;

[0008] Five-dimensional interpolation is performed on the data to be processed to obtain the interpolation result;

[0009] The seismic data is subjected to five-dimensional regularization based on the interpolation results to obtain the processing result.

[0010] In this embodiment of the invention, the step of performing a τ-P positive transformation on the seismic data within a preset data processing domain to obtain transformed data includes:

[0011] Determine the processing domain of the seismic data;

[0012] The seismic data are coplanarly stacked according to the processing domain to obtain the stacking result;

[0013] The superposition result is subjected to a τ-P positive transformation to obtain the transformed data.

[0014] In this embodiment of the invention, selecting non-aliased and preset numerically aliased data from the transformed data, and aggregating the selected non-aliased and preset numerically aliased data into data to be processed, includes:

[0015] Extract the frequency range and tilt range of the converted data;

[0016] The conversion data is selected based on the frequency range and tilt angle range to obtain the selected data;

[0017] The selected data is inversely transformed to obtain inversely transformed data;

[0018] Based on the inverse transformation data, un-aliased and preset numerical aliased data are generated, and the un-aliased and preset numerical aliased data are aggregated into data to be processed.

[0019] In this embodiment of the invention, performing five-dimensional interpolation on the data to be processed to obtain the interpolation result includes:

[0020] The data to be processed is subjected to interference removal to obtain undisturbed data;

[0021] The undisturbed data is spatially interpolated using a spatial interpolation method to obtain the spatial interpolation result;

[0022] Based on the spatial interpolation result, temporal interpolation is performed on the undisturbed data to obtain the temporal interpolation result;

[0023] Extract the attribute values ​​of the undisturbed data;

[0024] Based on the time interpolation result, attribute interpolation is performed on the attribute values ​​of the undisturbed data to obtain the attribute value interpolation result;

[0025] The interpolation result is generated by combining the spatial interpolation result, the temporal interpolation result, and the attribute value interpolation result.

[0026] In this embodiment of the invention, the step of performing five-dimensional regularization processing on the seismic data based on the interpolation result to obtain the processing result includes:

[0027] The seismic data is divided into multiple groups of seismic units;

[0028] The data within each seismic unit is corrected to obtain corrected data.

[0029] The corrected data is then processed according to the interpolation results to obtain regularized data;

[0030] The processing result is generated based on the rule-based data.

[0031] In this embodiment of the invention, the step of performing regularization processing on the corrected data to obtain regularized data includes:

[0032] The corrected data is divided into multiple groups of regional data according to a preset spatial region;

[0033] Spatial regularization is performed on each of the aforementioned regional data to obtain spatial regularization results;

[0034] Based on the spatial regularization result, the corrected data is subjected to temporal regularization to obtain the temporal regularization result;

[0035] The corrected data is then subjected to attribute regularization to obtain the attribute regularization result;

[0036] Regularized data is generated based on the spatial regularization results, temporal regularization results, and attribute regularization results.

[0037] Secondly, this disclosure provides an interpolation apparatus based on prior data, comprising:

[0038] The acquisition module is used to acquire earthquake data;

[0039] The forward transformation module is used to perform a τ-P forward transformation on the seismic data within a preset data processing domain to obtain transformed data;

[0040] The selection module is used to select non-aliased and preset numerical aliased data from the converted data;

[0041] The five-dimensional interpolation module is used to perform five-dimensional interpolation on the data to be processed to obtain the interpolation result;

[0042] The processing module is used to perform five-dimensional regularization processing on the seismic data based on the interpolation results to obtain the processing results.

[0043] Thirdly, this disclosure provides a computer device including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the interpolation method based on prior data described in the above aspects.

[0044] Fourthly, this disclosure provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the interpolation method based on prior data described in the above aspects.

[0045] Fifthly, this disclosure provides a computer program product, including a computer program / instructions, which, when executed by a processor, implements the steps of the prior data-based interpolation method described above.

[0046] This disclosure provides an interpolation method, apparatus, device, storage medium, and computer program based on prior data. Five-dimensional interpolation can better fit and interpolate data in the spatial dimension, thereby improving the spatial resolution of the data and obtaining more accurate spatial information and features. Five-dimensional interpolation can not only interpolate in the spatial dimension but also in the temporal and attribute dimensions, thus supplementing missing time series and attribute data. Frequency tilt analysis is performed on the interpolation preparation data to reduce the influence of aliasing signals during acquisition, obtaining optimal overall structural features. The method proposes extracting un-aliased or slightly aliased mid-to-low frequency data in the OVT domain for τ-P interpolation, and then using the interpolated data as prior data to constrain the five-dimensional interpolation of the entire full-band data, thus highlighting the structural features of low signal-to-noise ratio (SNR) areas in complex structures to a greater extent. Application to actual data shows that the five-dimensional interpolation matches the structural features of high SNR areas, and significantly improves the characterization of structural features in low SNR areas, proving the practicality of the method. Attached Figure Description

[0047] The present disclosure will be described in more detail below based on embodiments and with reference to the accompanying drawings:

[0048] Figure 1 This is a flowchart illustrating an interpolation method based on prior data, provided in an embodiment of this disclosure.

[0049] Figure 2 This is a functional block diagram of an interpolation device based on prior data provided in Embodiment 3 of this disclosure.

[0050] Figure 3 This is a flowchart of the prior data extraction and processing for τ-P low-frequency interpolation in the OVT domain provided in Embodiment 1 of this disclosure.

[0051] Figure 4 This is a schematic diagram of the frequency-wavenumber domain and tilt angle filtering relationship provided in Embodiment 1 of this disclosure.

[0052] Figure 5 The flowchart for five-dimensional rule-based processing based on prior data is provided in Embodiment 1 of this disclosure.

[0053] Figure 6 This is a cross-sectional view before interpolation provided in Embodiment 2 of this disclosure.

[0054] Figure 7 This is a cross-sectional view of the Ladon domain interpolation superposition provided in Embodiment 2 of this disclosure.

[0055] Figure 8 This is a low-frequency five-dimensional interpolation superposition cross-sectional view provided in Embodiment 2 of this disclosure.

[0056] Figure 9 This is a regularized overlay cross-sectional view of the hole-filling method provided in Embodiment 2 of this disclosure.

[0057] Figure 10 This is a conventional five-dimensional fully regularized overlay cross-sectional view provided in Embodiment 2 of this disclosure.

[0058] Figure 11 The above is a five-dimensional fully regularized overlay profile diagram based on low-frequency tau-p domain interpolation as prior data, provided in Embodiment 2 of this disclosure.

[0059] Figure 12 This is a schematic diagram of the composition structure of an electronic device based on an interpolation method using prior data, as provided in Embodiment 1 of this disclosure.

[0060] In the accompanying drawings, the same parts are referred to by the same reference numerals, and the drawings are not drawn to scale. Detailed Implementation

[0061] To enable those skilled in the art to better understand the technical solutions of this disclosure, and to fully understand and implement the process of how this disclosure applies technical means to solve technical problems and achieve corresponding technical effects, the technical solutions in the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, not all embodiments. The embodiments of this disclosure and the various features within them can be combined with each other without conflict, and the resulting technical solutions are all within the protection scope of this disclosure. All other embodiments obtained by those skilled in the art based on the embodiments of this disclosure without creative effort should fall within the protection scope of this disclosure.

[0062] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this disclosure described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0063] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0064] Example 1

[0065] Figure 1 This is a flowchart illustrating an interpolation method based on prior data, provided as an embodiment of this disclosure. Figure 1 As shown, an interpolation method based on prior data includes:

[0066] S1. Acquire earthquake data, and perform a τ-P positive transformation on the earthquake data within a preset data processing domain to obtain transformed data.

[0067] In this embodiment of the invention, the τ-P positive transformation refers to transforming the seismic data in the domain of time offset and travel slope to obtain the seismic data in the domain of common center point offset (CDP) and reflection angle.

[0068] Specifically, the preset data processing domain refers to the OVT domain. OVT (offset vector tile) is a commonly used data processing method that processes data within the TP domain. It can perform multi-channel summation transformation processing. The TP domain refers to the domain formed by expanding the hyperbola composed of time offset T and travel slope P in space. When performing OVT transformation, it is necessary to select non-aliased or slightly aliased data for processing.

[0069] In this embodiment of the invention, the step of performing a τ-P positive transformation on the seismic data within a preset data processing domain to obtain transformed data includes:

[0070] Determine the processing domain of the seismic data;

[0071] The seismic data are coplanarly stacked according to the processing domain to obtain the stacking result;

[0072] The superposition result is subjected to a τ-P positive transformation to obtain the transformed data.

[0073] In this embodiment of the invention, the "determination" refers to determining the seismic data and processing domain that need to be subjected to τ-P positive transformation, the "coplanar stacking" refers to stacking the seismic data according to a common centroid, and the "τ-P positive transformation" refers to transforming the seismic data in the domain of time offset and travel slope to obtain the seismic data in the common centroid offset (CDP) and reflection angle domains.

[0074] Specifically, the τ-P positive transformation refers to a transformation within the domain of time migration and travel slope. First, it's necessary to determine the seismic data and processing domain for which the τ-P positive transformation is required. Typically, the processing domain includes the time and space domains or the dip and migration domains. The choice of processing domain depends on the specific needs and available data. Seismic records are stacked along a common center point to obtain coplanar time-distance (CSP) stacked records. Coplanar stacking improves the signal-to-noise ratio (S / N) of the seismic records and enhances signal quality. Next, the CSP records undergo a TP positive transformation, converting the seismic data from the CSP domain to the dip and migration domains. The TP positive transformation can be implemented using methods such as the fast Fourier transform and the Radon transform. The result of the TP positive transformation is a conversion of the seismic records from the depth domain to the dip and migration domains, making the frequency characteristics and reflection coefficients of the seismic records clearer.

[0075] In detail, for regions with complex structures and low signal-to-noise ratios, given that the τ-P transform can remove linear interference waves and multiple waves, and can also be used for interpolation, P-wave separation, and S-wave conversion, the τ-P spectrum will change accordingly with frequency and dip angle. Therefore, in the τ-P domain, data can be processed separately according to different frequencies and dip angles to obtain prior data that reflects the overall structural characteristics and has fewer high-frequency aliasing phenomena.

[0076] For the OVT data after preprocessing following denoising and static correction, the data is transformed to the τ-P domain and expressed using the formula:

[0077] k=ωр=2πfρ

[0078] Where k is the wave number; ω is the angular frequency; f is the frequency; and ρ is the ray parameter.

[0079] For a given time frequency f, the transformation between the space wavenumber k and ρ can be expressed by the following formula:

[0080] Y(ω,ρ)=∑e iwρχ (e: natural constant, approximately 2.71828, i: imaginary unit, w: frequency variable, ρ: parameter related to signal characteristics, χ: original signal)

[0081] Y(ω,χ)=Y(ω,κ)|κ=ωρ

[0082] Where k is the wave number; ω is the angular frequency; f is the frequency; and ρ is the ray parameter.

[0083] In this embodiment of the invention, coplanar stacking involves superimposing seismic data along a common center point. This allows identical signals to be superimposed, thereby increasing signal energy and canceling out noise, thus improving the signal-to-noise ratio and making the seismic data clearer. Simultaneously, coplanar stacking eliminates noise from non-phase axes, improving the interpretability and accuracy of the seismic data. Raw seismic data obtained from seismic exploration, after coplanar stacking processing, yields clearer seismic records and images, improving image quality, reducing interference, and providing a better foundation for subsequent seismic data processing and geological interpretation.

[0084] In this embodiment of the invention, the τ-P positive transformation can filter out some superimposed noise and make the interpretable seismic signals more apparent. For strata with large variations in reflection coefficients, the τ-P positive transformation can also improve the dynamic range and resolution of seismic data, thereby better reflecting subsurface geological characteristics; the τ-P positive transformation can make the frequency characteristics and reflection coefficients of seismic data clearer, better reflecting subsurface geological structures. This helps seismologists better interpret seismic data and improves the interpretability of the data.

[0085] S2. Select the non-aliased and preset numerical aliased data from the converted data, and aggregate the selected non-aliased and preset numerical aliased data into data to be processed.

[0086] In this embodiment of the invention, the selection refers to selecting non-aliased or slightly aliased data from the transformed data to ensure that the transformed data is more accurate and reliable, while also reducing the time and workload required for calculation.

[0087] Specifically, in the process of seismic data processing, different strata have different velocities and reflection coefficients for the propagation of seismic waves, resulting in different amplitudes and phases in the seismic data, which leads to distortion of the superimposed seismic data. Therefore, it is necessary to perform seismic data removal processing to better reflect the underground geological structure.

[0088] In this embodiment of the invention, selecting non-aliased and preset numerically aliased data from the transformed data, and aggregating the selected non-aliased and preset numerically aliased data into data to be processed, includes:

[0089] Extract the frequency range and tilt range of the converted data;

[0090] The conversion data is selected based on the frequency range and tilt angle range to obtain the selected data;

[0091] The selected data is inversely transformed to obtain inversely transformed data;

[0092] Based on the inverse transformation data, un-aliased and preset numerical aliased data are generated, and the un-aliased and preset numerical aliased data are aggregated into data to be processed.

[0093] In this embodiment of the invention, the extraction refers to extracting two features of the frequency range and tilt range of the transformed data; the selection refers to selecting data within the transformed data of a set frequency range and tilt range according to the required frequency range and tilt range; the inverse transformation refers to inversely transforming the selected data back to the time domain; and the generation refers to replacing the inversely transformed data with unaliased or slightly aliased data.

[0094] Specifically, for seismic data after a positive τ-P transformation, the frequency range is generally determined by analyzing the main frequency bands of the waveform. Assuming the seismic data sampling rate is fs and the frequency range is fmin to fmax, then fmin can be determined by examining the low-frequency waveforms of the seismic data, while fmax can be determined by examining the high-frequency waveforms. Then, using the zero-crossing rate calculation method, a more precise frequency band can be determined. Additionally, the Radon transform or other relevant transforms can typically be used to extract the dip range, and then the seismic data is transformed from the τ-P domain to the xt domain. For dip range extraction, it is generally necessary to select a representative dip window in the τ-P domain and maintain a good balance between temporal and spatial resolution. Choosing different dip windows allows for a trade-off between different resolutions and seismic information loss.

[0095] In detail, by processing the frequency and dip ranges, a subset of data can be selected as the primary data. Next, the selected data is transformed from the τ-P domain back to the original time and location domain using the inverse τ-P transform (a process that converts seismic data in the τ-P domain back to the time-distance domain), yielding the inverse-transformed data. The inverse τ-P transform process is similar to the τ-P transform, only requiring the dip and frequency ranges to be reversed. After obtaining the inverse-transformed data, further processing and optimization can be performed using methods such as filtering and denoising to improve the clarity of the seismic signal. Based on the inverse-transformed data, unaliased or slightly aliased data can be generated. This can be achieved by selecting clear, stable seismic records with a high signal-to-noise ratio, and by using signal processing techniques to remove clutter and noise, thus transforming the inverse-transformed data into clear, unaliased seismic information.

[0096] Furthermore, the data is constructed by generating a taup-px-py dataset from lower-frequency data, which can be defined in the τ-P domain as a linear t = τ + px integral along a straight line in the tx domain, where the record is the projected intercept in the τ-P domain and the slope is p:

[0097] φ(τ,p)=∫1φ(t,x)dl=∫1dxφ(τ+px,x)

[0098] By selecting the dominant frequency band and tilt angle, data with no or slight aliasing is obtained.

[0099] φ(t,x)=∫φ(t-px,p)dp

[0100] The τ-P inverse transform is performed to obtain data that reflects the overall structural characteristics and has fewer high-frequency aliasing phenomena. Then, five-dimensional interpolation is performed on the data to obtain the prior data, i.e., the interpolation result.

[0101] In this embodiment of the invention, after the selected data is inversely transformed from the τ-P domain back to the time-distance domain, a series of traditional seismic data processing methods can be applied for further analysis, such as profile matching, pre-stack depth migration, and seismic imaging. Compared with the τ-P domain, the time-distance domain has stronger interpretability and intuitiveness, and is therefore more suitable for seismic exploration data analysis and interpretation. The τ-P transformation provides a novel method for representing seismic data, making seismic data processing and analysis more flexible and efficient. Through inverse transformation, seismic data in the τ-P domain can be directly compared with other time-distance domain data, providing a clearer understanding of the structure and properties of the subsurface medium.

[0102] In this embodiment of the invention, because different layers of the medium absorb and reflect energy differently, data attenuation occurs, leading to contamination. Selecting un-overlapped or slightly-overlapped data avoids the effects of this attenuation, resulting in more accurate subsurface medium information. Un-overlapped or slightly-overlapped data means that the energy in the seismic record is not completely separated due to mutual interference. This is precisely the kind of predictable location that helps seismologists identify subsurface structures. Therefore, selecting un-overlapped or slightly-overlapped data helps to better identify subsurface structures, such as faults and rock mass boundaries. Un-overlapped or slightly-overlapped data is also clearer, avoiding unnecessary steps and time in the data processing process. This saves time on computer operation and manual processing, improving data processing efficiency.

[0103] S3. Perform five-dimensional interpolation on the data to be processed to obtain the interpolation result.

[0104] In this embodiment of the invention, the five-dimensional interpolation refers to correcting the spatial and temporal discontinuities of non-aliased or slightly aliased data through interpolation methods to obtain data with better continuity and higher accuracy.

[0105] Specifically, five-dimensional interpolation involves multiple steps, including data acquisition, data preprocessing, spatial interpolation, temporal interpolation, and attribute interpolation. Spatial interpolation requires common spatial interpolation methods such as triangulation, TIN interpolation, and inverse distance weighted interpolation. Temporal interpolation often employs methods such as wavelet transform. Attribute interpolation can utilize methods such as inverse distance weighted interpolation and Kriging interpolation.

[0106] In this embodiment of the invention, performing five-dimensional interpolation on the data to be processed to obtain the interpolation result includes:

[0107] The data to be processed is subjected to interference removal to obtain undisturbed data;

[0108] The undisturbed data is spatially interpolated using a spatial interpolation method to obtain the spatial interpolation result;

[0109] Based on the spatial interpolation result, temporal interpolation is performed on the undisturbed data to obtain the temporal interpolation result;

[0110] Extract the attribute values ​​of the undisturbed data;

[0111] Based on the time interpolation result, attribute interpolation is performed on the attribute values ​​of the undisturbed data to obtain the attribute value interpolation result;

[0112] The interpolation result is generated by combining the spatial interpolation result, the temporal interpolation result, and the attribute value interpolation result.

[0113] In this embodiment of the invention, interference removal refers to preprocessing un-aliased or slightly aliased data to remove outliers and noise, etc. Spatial interpolation refers to predicting and estimating attribute values ​​at unknown locations based on the spatial positional relationships and attribute similarities of the un-aliased data. Temporal interpolation refers to interpolating missing or discontinuous data in the time dimension to obtain complete time series data. Attribute interpolation refers to inferring attribute values ​​of unknown points using a mathematical model, given the known spatial coordinates, temporal information, and attribute values ​​of the un-aliased data.

[0114] Specifically, the data is preprocessed to remove outliers and noise, the collected data is gridded, and common spatial interpolation methods are used to interpolate the four-dimensional coordinates (x, y, z, and t) of the target region. Spatial interpolation methods include triangulation, inverse distance weighting, and Kriging interpolation. Based on spatial interpolation, temporal interpolation is performed on un-aliased or slightly aliased data to supplement the missing time dimension. Temporal interpolation methods include wavelet transform and waveform interpolation. Based on temporal interpolation, attribute values ​​are interpolated. Commonly used attribute interpolation methods include inverse distance weighting and Kriging interpolation.

[0115] In detail, for example, in a certain exploration area in Mexico, the geological structure is very complex, with relatively well-developed salt domes and faults, especially the characterization of Mesozoic tectonic traps, which is particularly difficult. The collected data generally exhibits a signal-to-noise ratio that is "higher in the north and lower in the south," and a frequency that is "lower in the west and higher in the east." Due to the relatively well-developed salt domes in this area, in order to more clearly characterize the Mesozoic structures, a five-dimensional interpolation technique based on low- and mid-frequency τ-P domain interpolation as prior data was established, while maintaining amplitude and fidelity. Prior data is obtained by interpolating low-frequency information in the Radon domain. This method can select advantageous information by frequency and dip angle and perform interpolation in the Radon domain. Three-dimensional Radon domain interpolation is performed from the OVT domain. The method of selecting advantageous information such as frequency and dip angle in the τ-P domain to interpolate prior data not only allows for five-dimensional interpolation but also effectively saves project time.

[0116] In this embodiment of the invention, spatial interpolation can be used to predict and estimate attribute values ​​at unknown locations, supplementing missing or discontinuous spatial data to obtain a set of continuous and accurate spatial data, thereby providing more accurate spatial information for subsequent research. Temporal interpolation is performed to interpolate missing or discontinuous time series data, thereby obtaining complete time series data, improving the continuity and accuracy of data in the time dimension, and providing more complete and stable time series data for earthquake research. Finally, attribute interpolation aims to further supplement missing or inaccurate attribute data, obtaining more refined and reliable geophysical characteristics and spatial information, and providing a more comprehensive and accurate foundation for data analysis and modeling in earthquake research.

[0117] In this embodiment of the invention, the data that is not aliased or slightly aliased is already relatively complete in the spatial dimension. Five-dimensional interpolation can better fit and interpolate the data in the spatial dimension, thereby improving the spatial resolution of the data and obtaining more accurate spatial information and features. Five-dimensional interpolation can not only interpolate in the spatial dimension, but also in the time dimension and attribute dimension, thereby supplementing missing time series and attribute data. Due to the uncertainty of the data itself and sampling errors, there are often aliasing or inaccuracies in the original data. Using interpolation methods to process the data can reduce the regional errors of the data, thereby improving the overall consistency and accuracy of the data.

[0118] S4. Perform five-dimensional regularization processing on the seismic data based on the interpolation results to obtain the processing results.

[0119] In this embodiment of the invention, the five-dimensional regularization process refers to regularizing, normalizing, and fitting seismic data in three spatial dimensions, time dimensions, and attribute dimensions to eliminate noise bias.

[0120] Specifically, the τ-P domain is used to separate non-aliased data and select dominant frequency bands and tilt angles to perform structural characterization as interpolation results, i.e., prior data. Then, the prior data is used as a constraint to perform five-dimensional interpolation on the entire frequency band, ultimately laying a data foundation for better structural characterization of complex low signal-to-noise ratio regions.

[0121] In this embodiment of the invention, the seismic data is subjected to five-dimensional regularization processing based on the interpolation result to obtain the processing result, including:

[0122] The seismic data is divided into multiple groups of seismic units;

[0123] The data within each seismic unit is corrected to obtain corrected data.

[0124] The corrected data is then processed according to the interpolation results to obtain regularized data;

[0125] The processing result is generated based on the rule-based data.

[0126] In this embodiment of the invention, the splitting refers to dividing the seismic data into different spatial regions or units based on the spatial distribution characteristics of the seismic data; the correction processing refers to performing smoothing, denoising, normalization, and fitting operations on the data within the seismic unit; and the regularization processing refers to performing spatial, temporal, and attribute regularization processing on the seismic data.

[0127] Specifically, before performing five-dimensional regularization, the interpolated seismic data needs to be preprocessed, including removing outliers and noise, and performing smoothing and correction operations to ensure the accuracy and stability of the data.

[0128] In detail, based on the spatial distribution characteristics of seismic data, it is divided into different spatial regions or units. Data within each region undergoes regularization processing, including smoothing, denoising, normalization, and fitting. After spatial regularization, the temporal dimension of the seismic data needs to be regularized, with data at each time point being normalized, smoothed, and fitted to ensure the continuity and stability of the time series. Besides spatial and temporal dimensions, seismic data may also contain attribute dimensions, such as seismic wave amplitude, velocity, and energy. During five-dimensional regularization, these attribute dimensions need to be regularized to maintain consistency and accuracy among data attributes. Analyzing and modeling the regularized seismic data yields a more accurate and stable seismic data foundation, providing better data support for seismic exploration, monitoring, and research.

[0129] In this embodiment of the invention, the step of performing regularization processing on the corrected data to obtain regularized data includes:

[0130] The corrected data is divided into multiple groups of regional data according to a preset spatial region;

[0131] Spatial regularization is performed on each of the aforementioned regional data to obtain spatial regularization results;

[0132] Based on the spatial regularization result, the corrected data is subjected to temporal regularization to obtain the temporal regularization result;

[0133] The corrected data is then subjected to attribute regularization to obtain the attribute regularization result;

[0134] Regularized data is generated based on the spatial regularization results, temporal regularization results, and attribute regularization results.

[0135] In this embodiment of the invention, the division refers to dividing the corrected data into different spatial regions or units, the spatial regularization refers to processing the spatial distribution characteristics of the corrected data, the temporal regularization refers to processing the temporal dimension of the corrected data, and the attribute regularization refers to processing the continuous attribute dimensions of the corrected data.

[0136] Specifically, five-dimensional regularization is a process of regularizing interpolated data to eliminate noise and bias, and improve the accuracy and stability of the data. Five-dimensional regularization can include operations such as denoising, smoothing, normalization, and fitting. More complex regularization processes can also be performed based on the characteristics of seismic data, such as removing source effects and reconstructing past seismic images.

[0137] In detail, the interpolation results can serve as prior data. The prior data can be used as a function to establish that coherent energy superposition and aliased energy or noise tend to cancel each other out. In the desired target observation system, the data undergoes five-dimensional regularization. At higher frequencies, spatially aliased energy is interpolated, and the prior factor is used as a weight to search for the Fourier dominant coefficients at higher frequencies. Assuming that the spectrum contains both original and aliased energy, this weighted multiplication amplifies the correct energy, thus selecting the correct energy. This achieves a relatively effective improvement in constructing morphology in the low signal-to-noise ratio region, indirectly improving the signal-to-noise ratio.

[0138] Furthermore, based on the prior data obtained by interpolation of low frequencies and dominant tilt angles selected in the τ-P domain, and the preprocessed data, full-band five-dimensional regularization is performed. Prior parameters are calculated by analyzing the spatial bandwidth (a linear function of frequency) of the low-frequency prior data to ensure that the input data is non-aliased (for anti-aliasing). In addition to anti-aliasing, the prior data also needs to be interpolated. By referencing the mid-to-low frequency structure of the prior data, interpolation is performed on the specified mid-to-high frequency band to obtain high-quality anti-aliasing five-dimensional regularized data.

[0139] In this embodiment of the invention, seismic data typically lacks spatial, temporal, and attribute continuity and contains noise and bias, all of which affect data accuracy and results. Spatial regularization, temporal regularization, and attribute regularization can reduce the impact of noise and bias, improving data accuracy and stability. Seismic data acquisition is subject to temporal and spatial limitations, inevitably resulting in gaps in the data. Interpolation and regularization processes can simultaneously fill these gaps, making the seismic data more complete for better subsequent analysis and research. They can also reduce the impact of noise and bias, revealing the spatial, temporal, and attribute patterns of seismic data, better showcasing seismic characteristics and patterns, and providing fundamental data and support for seismological research.

[0140] In this embodiment of the invention, five-dimensional regularization processing makes seismic field images more accurate, stable, and continuous, displaying the spatial, temporal, and attribute structure of earthquakes. This is of great help in earthquake analysis, earthquake prediction, and earthquake disaster prevention. It also better reflects the spatial, temporal, and attribute patterns of seismic data: through five-dimensional regularization processing, the spatial, temporal, and attribute patterns of seismic data become more prominent, revealing hidden patterns and characteristics in the data, thus providing a more accurate and reasonable data foundation for earthquake research and applications. Simultaneously, the low-to-medium frequency five-dimensional interpolation method effectively avoids the false frequency problem caused by high-frequency signal interpolation, while improving structural morphology, internal reflection signals, and signal-to-noise ratio. The cross-sectional waves and micro-scale structural morphology are not affected by interpolation and are even slightly enhanced, resulting in a significant improvement in the overall imaging effect, confirming the effectiveness and practicality of the method presented in this paper.

[0141] Example 2

[0142] To better understand the present invention, a second embodiment is provided below to further explain how the present invention performs five-dimensional interpolation on the un-aliased or slightly aliased data to obtain the interpolation result.

[0143] In this embodiment of the invention, since most of the energy in seismic data is typically "fan-shaped," the energy distribution in the fk domain (where spatial bandwidth is a linear function of frequency) generally maintains a similar shape across different frequency slices. This prior factor-based interpolation method utilizes a Fourier dictionary for matching and tracking, based on an irregularly sampled input wavefield and constrained by regular, non-aliased or slightly aliased lower-frequency prior data, employing an iterative method to reconstruct the wavefield in the Fourier domain. After estimating the wavefield in the Fourier domain, a new seismic trace is reconstructed at any desired spatial location (e.g., on a regular grid) using the standard discrete inverse Fourier transform.

[0144] Assume the data of the regularized observation system of length M is x = [x1, x2, x3, ..., x...]. mThe irregular original data is y = [y1, y2, y3, ..., ym]. The sampling matrix represents the relationship between the regularized and irregular data.

[0145] The linear observation system is established using the following formula:

[0146] y = Ax + n

[0147] Where y is the observation vector; A is the observation matrix; x is the state vector to be estimated; and n is the observation noise vector.

[0148] Seismic data with a bandwidth of Ω can be expressed using the following formula:

[0149]

[0150] Where x: raw seismic data; B: prior operator; M: normalization factor; F: discrete Fourier transform matrix, F * Given its conjugate transpose; and A being an M×M diagonal matrix, the prior information is derived as follows:

[0151]

[0152] Where A is an M×M diagonal matrix; B refers to the prior operator. This refers to seismic data with a bandwidth of Ω, where the prior factor constraint is expressed by the following formula:

[0153]

[0154] in, μ refers to the prior factor, μ refers to the weighting factor, and L refers to the Euclidean norm.

[0155] right Taking the derivative and setting it to zero, we get:

[0156]

[0157] Among them, A T It refers to the transpose of matrix A, and P refers to the slope.

[0158] Therefore, based on prior data obtained from low-frequency data that is either unaliased or slightly aliased, the interpolation process relies on prior information. Under the constraint of anti-aliasing, the energy spectrum distribution (power density spectrum) at high aliasing frequencies can be inferred from the energy distribution at low unaliased frequencies. The prior can be used as a function to establish that coherent energies superimpose while aliased energies or noise tend to cancel each other out. In the desired target observation system, the data undergoes five-dimensional regularization, interpolating spatially aliased energies at higher frequencies. The prior factor will be used as a weight for searching the Fourier dominant coefficients at higher frequencies. Assuming that the spectrum contains both original and aliased energies, this weighted multiplication will amplify the correct energies, thereby selecting the correct energies. This achieves a relatively effective improvement in the structural characterization of morphology in the low signal-to-noise ratio region, indirectly improving the signal-to-noise ratio.

[0159] Furthermore, from Figure 6 and Figure 7 The comparison shows that OVT-domain 3D Radon domain interpolation effectively improves imaging in low signal-to-noise ratio regions, while Figure 7 and Figure 8 The comparison reveals that low-frequency five-dimensional interpolation provides a clearer characterization of the low signal-to-noise ratio region and a more focused phase axis compared to three-dimensional Radon domain interpolation in the OVT domain. This demonstrates that prior data obtained through five-dimensional interpolation using advantageous information such as frequency and tilt angle in the τ-P domain exhibits a more significant advantage.

[0160] Furthermore, Figure 9 To create a regularized overlay profile for filling gaps, this method is based on the principle of high quality and amplitude preservation, and only performs interpolation at data gaps. In areas with low signal-to-noise ratio, high-frequency noise is relatively developed, resulting in a relatively blurry structure. Figure 10 It is a conventional five-dimensional fully regularized superimposed profile, which is relatively... Figure 9 Its structural form has not changed, but for areas with low signal-to-noise ratio, high-frequency noise is suppressed to a certain extent, and the overall structure is relatively clear. Figure 11 To create a five-dimensional fully regularized overlay profile based on low- and mid-frequency τ-P domain interpolation of prior data, compared to Figure 9 and Figure 10 The comparison shows that the overall structural morphology remains unchanged, the overall amplitude energy is more uniform, the structural morphology is clearer, the in-phase axis is more focused, the internal reflection signal is strengthened, and the signal-to-noise ratio (especially in the original low signal-to-noise ratio region of complex structures) is significantly improved. The cross-sectional wave and micro-amplitude structural morphology are not affected by interpolation and are even slightly enhanced to some extent. The above results indicate that the five-dimensional interpolation method based on mid-to-low frequency τ-P domain interpolation as prior data has good effects in terms of fidelity preservation, amplitude preservation, and signal-to-noise ratio improvement, and also has good timeliness and practicality in production operation.

[0161] Example 3

[0162] like Figure 2The diagram shown is a functional block diagram of the interpolation device based on prior data provided in this embodiment.

[0163] The interpolation device 100 based on prior data described in this embodiment can be installed in an electronic device. Depending on the functions implemented, the interpolation device 100 based on prior data may include an acquisition module 101, a forward transformation module 102, a selection module 103, a five-dimensional interpolation module 104, and a processing module 105. The module described in this invention can also be called a unit, which refers to a series of computer program segments that can be executed by the processor of an electronic device and can perform a fixed function, and which are stored in the memory of the electronic device.

[0164] In this embodiment, the functions of each module / unit are as follows:

[0165] The acquisition module is used to acquire earthquake data;

[0166] The positive transformation module is used to perform a τ-P positive transformation on the seismic data within a preset data processing domain to obtain transformed data;

[0167] The selection module is used to select non-aliased and preset numerical aliased data from the converted data;

[0168] The five-dimensional interpolation module is used to perform five-dimensional interpolation on the data to be processed to obtain the interpolation result;

[0169] The processing module is used to perform five-dimensional regularization processing on the seismic data based on the interpolation results to obtain the processing results.

[0170] Example 4

[0171] like Figure 12 As shown, this embodiment also provides a computer device, which may include a processor 10, a memory 11, a communication bus 12 and a communication interface 13, and may also include a computer program stored in the memory 11 and executable on the processor 10, such as a multi-scale stratigraphic division program.

[0172] In some embodiments, the processor 10 may be composed of integrated circuits, such as a single packaged integrated circuit or multiple integrated circuits with the same or different functions, including combinations of one or more central processing units (CPUs), microprocessors, digital processing chips, graphics processors, and various control chips. The processor 10 is the control unit of the electronic device, connecting various components of the entire electronic device through various interfaces and lines. It executes programs or modules stored in the memory 11 (e.g., executing multi-scale stratigraphic division programs) and calls data stored in the memory 11 to perform various functions of the electronic device and process data.

[0173] The memory 11 includes at least one type of readable storage medium, including flash memory, portable hard drive, multimedia card, card-type memory (e.g., SD or DX memory), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the memory 11 can be an internal storage unit of an electronic device, such as a portable hard drive. In other embodiments, the memory 11 can be an external storage device of the electronic device, such as a plug-in portable hard drive, Smart Media Card (SMC), Secure Digital (SD) card, Flash Card, etc. Furthermore, the memory 11 can include both internal and external storage units of the electronic device. The memory 11 can be used not only to store application software and various types of data installed on the electronic device, such as the code of a multi-scale stratigraphic division program, but also to temporarily store data that has been output or will be output.

[0174] The communication bus 12 can be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus, etc. This bus can be divided into an address bus, a data bus, a control bus, etc. The bus is configured to enable communication between the memory 11 and at least one processor 10, etc.

[0175] The communication interface 13 is used for communication between the aforementioned electronic device and other devices, including a network interface and a user interface. Optionally, the network interface may include a wired interface and / or a wireless interface (such as a Wi-Fi interface, Bluetooth interface, etc.), typically used to establish communication connections between the electronic device and other electronic devices. The user interface may be a display, an input unit (such as a keyboard), or, optionally, a standard wired or wireless interface. Optionally, in some embodiments, the display may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen, etc. The display may also be appropriately referred to as a screen or display unit, used to display information processed in the electronic device and to display a visual user interface.

[0176] The figure only shows an electronic device with components. Those skilled in the art will understand that the structure shown in the figure does not constitute a limitation on the electronic device and may include fewer or more components than shown, or combine certain components, or have different component arrangements.

[0177] For example, although not shown, the electronic device may also include a power supply (such as a battery) to power the various components. Preferably, the power supply can be logically connected to the at least one processor 10 through a power management device, thereby enabling functions such as charging management, discharging management, and power consumption management. The power supply may also include one or more DC or AC power supplies, recharging devices, power fault detection circuits, power converters or inverters, power status indicators, and other arbitrary components. The electronic device may also include various sensors, Bluetooth modules, Wi-Fi modules, etc., which will not be described in detail here.

[0178] It should be understood that the embodiments described are for illustrative purposes only and are not limited to this structure in the scope of the patent application.

[0179] The multi-scale stratigraphic division program stored in the memory 11 of the electronic device is a combination of multiple instructions, which, when run in the processor 10, can achieve the following:

[0180] Seismic data is acquired, and the seismic data is subjected to a τ-P positive transformation within a preset data processing domain to obtain transformed data.

[0181] Select the non-aliased and preset numerical aliased data from the transformed data, and aggregate the selected non-aliased and preset numerical aliased data into data to be processed;

[0182] Five-dimensional interpolation is performed on the data to be processed to obtain the interpolation result;

[0183] The seismic data is subjected to five-dimensional regularization based on the interpolation results to obtain the processing result.

[0184] Specifically, the specific implementation method of the processor 10 for the above instructions can be referred to the description of the relevant steps in the corresponding embodiment of the accompanying drawings, and will not be repeated here.

[0185] Furthermore, if the modules / units integrated into the electronic device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. The computer-readable storage medium can be volatile or non-volatile. For example, the computer-readable medium may include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, or a read-only memory (ROM).

[0186] Example 5

[0187] Based on the above embodiments, this embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps of the interpolation method based on prior data described in the above embodiments.

[0188] In some embodiments of this example, a computer-readable storage medium is provided, on which a computer program is stored, characterized in that, when the computer program is executed by a processor, it implements the steps of the interpolation method based on prior data described in the above embodiments.

[0189] In some embodiments of this example, a computer program product is provided, including computer program instructions, characterized in that, when the computer program is executed by a processor, it implements the steps of the interpolation method based on prior data described in the above embodiments.

[0190] The processor may include, but is not limited to, one or more processors or microprocessors. Each processor may be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Digital Signal Processing Device (DSPD), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic component, for executing the methods in the above embodiments.

[0191] Computer-readable storage media can be implemented by any type of volatile or non-volatile storage device or a combination thereof. Computer-readable storage media may include, but are not limited to, random access memory (RAM), read-only memory (ROM), flash memory, EPROM memory, EEPROM memory, registers, and computer storage media (e.g., hard disks, floppy disks, solid-state drives, removable disks, CD-ROMs, DVD-ROMs, Blu-ray discs, etc.).

[0192] Computer-readable storage media may also store at least one computer-executable program / instruction, such as computer-readable instructions. Computer-readable storage media include, but are not limited to, volatile memory and / or non-volatile memory. Volatile memory may include, for example, random access memory (RAM) and / or cache memory. Computer-readable storage media may include, for example, read-only memory (ROM), hard disk, flash memory, etc. For example, a non-transitory computer-readable storage medium may be connected to a computing device such as a computer, and then, when the computing device executes the computer-readable instructions stored on the computer-readable storage medium, the various methods described above can be performed.

[0193] In addition, the computer device may include (but is not limited to) a data bus, an input / output (I / O) bus, a display, and input / output devices (e.g., keyboard, mouse, speakers, etc.).

[0194] The processor can communicate with external devices via the I / O bus through wired or wireless networks.

[0195] In one embodiment, the at least one computer-executable instruction may also be compiled into or comprise a software product / computer program product, wherein one or more computer-executable instructions are executed by a processor to perform the steps of the various functions and / or methods in the embodiments described herein.

[0196] In the embodiments provided in this disclosure, it should be understood that the disclosed apparatus and methods can also be implemented in other ways. The apparatus embodiments described above are merely illustrative; for example, the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0197] It should be noted that, in this disclosure, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element limited by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0198] While the embodiments disclosed herein are as described above, the foregoing content is merely for the purpose of facilitating understanding of this disclosure and is not intended to limit this disclosure. Any person skilled in the art to which this disclosure pertains may make any modifications and changes in form and detail of the implementation without departing from the spirit and scope of this disclosure; however, the scope of patent protection of this disclosure shall still be determined by the scope defined in the appended claims.

Claims

1. An interpolation method based on prior data, characterized in that, include: Seismic data is acquired, and the seismic data is subjected to a τ-P positive transformation within a preset data processing domain to obtain transformed data. Select the non-aliased and preset numerical aliased data from the transformed data, and aggregate the selected non-aliased and preset numerical aliased data into data to be processed; Five-dimensional interpolation is performed on the data to be processed to obtain the interpolation result; The seismic data is subjected to five-dimensional regularization based on the interpolation results to obtain the processing result.

2. The interpolation method based on prior data according to claim 1, characterized in that, The step of performing a τ-P positive transformation on the seismic data within a preset data processing domain to obtain transformed data includes: Determine the processing domain of the seismic data; The seismic data are coplanarly stacked according to the processing domain to obtain the stacking result; The superposition result is subjected to a τ-P positive transformation to obtain the transformed data.

3. The interpolation method based on prior data according to claim 1, characterized in that, The step of selecting non-aliased and preset numerically aliased data from the transformed data, and aggregating the selected non-aliased and preset numerically aliased data into data to be processed, includes: Extract the frequency range and tilt range of the converted data; The conversion data is selected based on the frequency range and tilt angle range to obtain the selected data; The selected data is inversely transformed to obtain inversely transformed data; Based on the inverse transformation data, un-aliased and preset numerical aliased data are generated, and the un-aliased and preset numerical aliased data are aggregated into data to be processed.

4. The interpolation method based on prior data according to claim 1, characterized in that, The step of performing five-dimensional interpolation on the data to be processed to obtain the interpolation result includes: The data to be processed is subjected to interference removal to obtain undisturbed data; The undisturbed data is spatially interpolated using a spatial interpolation method to obtain the spatial interpolation result; Based on the spatial interpolation result, temporal interpolation is performed on the undisturbed data to obtain the temporal interpolation result; Extract the attribute values ​​of the undisturbed data; Based on the time interpolation result, attribute interpolation is performed on the attribute values ​​of the undisturbed data to obtain the attribute value interpolation result; The interpolation result is generated by combining the spatial interpolation result, the temporal interpolation result, and the attribute value interpolation result.

5. The interpolation method based on prior data according to claim 1, characterized in that, The step of performing five-dimensional regularization processing on the seismic data based on the interpolation results to obtain the processing results includes: The seismic data is divided into multiple groups of seismic units; The data within each seismic unit is corrected to obtain corrected data. The corrected data is then processed according to the interpolation results to obtain regularized data; The processing result is generated based on the rule-based data.

6. The interpolation method based on prior data according to claim 5, characterized in that, The step of performing rule-based processing on the corrected data to obtain rule-based data includes: The corrected data is divided into multiple groups of regional data according to a preset spatial region; Spatial regularization is performed on each of the aforementioned regional data to obtain spatial regularization results; Based on the spatial regularization result, the corrected data is subjected to temporal regularization to obtain the temporal regularization result; The corrected data is then subjected to attribute regularization to obtain the attribute regularization result; Regularized data is generated based on the spatial regularization results, temporal regularization results, and attribute regularization results.

7. An interpolation device based on prior data, characterized in that, The device includes: The acquisition module is used to acquire earthquake data; The forward transformation module is used to perform a τ-P forward transformation on the seismic data within a preset data processing domain to obtain transformed data; The selection module is used to select non-aliased and preset numerical aliased data from the converted data; The five-dimensional interpolation module is used to perform five-dimensional interpolation on the data to be processed to obtain the interpolation result; The processing module is used to perform five-dimensional regularization processing on the seismic data based on the interpolation results to obtain the processing results.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the interpolation method based on prior data as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the interpolation method based on prior data as described in any one of claims 1 to 6.

10. A computer program product comprising a computer program / instructions, characterized in that, When executed by a processor, the computer program implements the steps of the interpolation method based on prior data as described in any one of claims 1 to 6.

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