Method and system for calculating de-noising dynamic space-time window and storage medium

Abstract

The invention provides a method and system for calculating a de-noising dynamic space-time window and a storage medium. According to the method, space-time window parameters are dynamically adjusted according to the severity of noise of different gathers, and finally a denoising result is obtained. According to the invention, the calculation precision and efficiency of suppressing noise are improved. According to the method, space-time window parameters are dynamically adjusted according to the severity of different gather noise, complex data can be flexibly processed, a good denoising effect is obtained, the mass data processing efficiency is improved, and the calculation cost is saved.

Description

Technical Field

[0001] This invention belongs to the field of seismic exploration, specifically involving a method, system, and storage medium for calculating a denoised dynamic spatiotemporal window. It can be used not only by researchers and producers for learning and learning, but also in processing and interpreting computational systems, and even in engineering geological exploration fields such as coalfields and solid minerals. Background Technology

[0002] Denoising is a crucial step in seismic processing. When dealing with large datasets and complex algorithms, denoising is typically divided into noise identification and noise suppression. When suppressing noise, time-segmentation is often used to effectively improve the computational accuracy of denoising. However, for complex exploration area data with significant differences between gathers, using fixed time-window parameters has certain limitations. Summary of the Invention

[0003] The purpose of this invention is to solve the problems existing in the prior art and provide a method, system and storage medium for calculating a dynamic spatiotemporal window for denoising. The spatiotemporal window parameters are dynamically adjusted according to the severity of noise in different gathers, which can flexibly adapt to complex data processing, improve the efficiency of massive data processing, save computing resources and achieve cost reduction and efficiency improvement.

[0004] This invention is achieved through the following technical solution:

[0005] In a first aspect, the present invention provides a method for calculating a dynamic spatiotemporal window for denoising, wherein the method dynamically adjusts the spatiotemporal window parameters according to the severity of noise in different gathers, and finally obtains the denoising result.

[0006] A further improvement of the present invention is that:

[0007] The method includes:

[0008] Step 1: Input the raw seismic data;

[0009] Step 2, input the noise model;

[0010] Step 3: Process the dynamic spatiotemporal window;

[0011] Step 4: Noise suppression processing to obtain the noise reduction result.

[0012] A further improvement of the present invention is that:

[0013] The operations in step 1 include:

[0014] Assume the original seismic data contains m seismic gathers, and the key for each gather is OriGNO. j , j∈[0,m), each trace set data is D GNOj= (nt, nx), where D is the original seismic data, nx is the number of traces in the spatial direction, and nt is the number of sampling points in the time direction.

[0015] A further improvement of the present invention is that:

[0016] The operations in step 2 include:

[0017] Input noise model;

[0018] The noise model has a total of m seismic gathers, and the number of each gather is denoted as GNO. j , j∈[0,m), each gather noise data is M GNOj = (nt, nx), where nx is the number of channels in the spatial direction and nt is the number of sampling points in the temporal direction.

[0019] A further improvement of the present invention is that:

[0020] The operations in step 3 include:

[0021] (31) Windowing: Constrain the value of each spatiotemporal window from the time dimension, spatial dimension and frequency dimension;

[0022] (32) Dynamic spatiotemporal window parameter combination.

[0023] A further improvement of the present invention is that:

[0024] Step (31) includes the following operations:

[0025] If we divide the spacetime into n groups, the parameters of each group of spacetime windows are as follows:

[0026] Par i =(keyNo i filterWin i ,traceWin i TimWin i ), i∈[0,n)

[0027] Among them, keyNo i Each spatiotemporal window is assigned a number, filterWin is the length of the filter window, traceWin is the length of the spatial window, and TimWin is the length of the temporal window.

[0028] The sampling rate of the original seismic data is dt. The spatiotemporal window parameter is converted into the sampling point window length using the following formula:

[0029] fw i =filterWin i / dt+1,i∈[0,n)

[0030] trw i=traceWin i +1, i∈[0,n)

[0031] tw i =TimWin i / dt+1,i∈[0,n)

[0032] Among them, fw i trw represents the length of the sampling point filter window for the i-th spatiotemporal window. i tw represents the length of the spatial window for the sampling points of the i-th spatiotemporal window. i This represents the length of the time window for the sampling points of the i-th spatiotemporal window;

[0033] The time window movement length can be calculated using the following formula:

[0034] filterWinUse i = (2-overPer)*fw i / 2+1, i∈[0,n)

[0035] traceWinUse i = (2-overPer)*trw i / 2+1, i∈[0,n)

[0036] TimWinUse i = (2-overPer)*tw i / 2+1, i∈[0,n)

[0037] Where overPer represents the overlap rate, overPer∈(0,50%), filterWinUse i Indicates the shift length of the filter window, traceWinUse i Indicates the length of the space window that has been moved, TimWinUse i Indicates the length of the time window movement.

[0038] A further improvement of the present invention is that:

[0039] The operation of step (32) includes:

[0040] Calculate the spatiotemporal window parameters for each gather:

[0041] When there is only one window group, i.e., n=1, then set keyNo0=0;

[0042] Par i =(keyNo i filterWin i ,traceWin i TimWini ), i = 0

[0043] All gather sets are calculated using Par0;

[0044] When the number of window groups n > 1, then Par i is sorted in ascending order according to the keyword keyNo of each window group i to obtain the keyword array keyNo; the minimum value keyNo_min of the keyword array keyNo = keyNo0, and the maximum value of the keyword array keyNo is keyNo_max = keyNo n-1 , keyNo i > 0, i ∈ [0, n);

[0045] Input the gather sets in sequence. Suppose the keyword of the gather set is GNO j , and the spatio-temporal window parameters corresponding to the gather set are:

[0046] par j = (keyNo j , filterWin j , traceWin j , TimWin j )

[0047] Compare the keyNo in the spatio-temporal window parameters with the keyword GNO of the input gather set in sequence, and perform the following operations: i j j If GNO

[0048] < keyNo_min, then perform the following operations: j

[0049] j keyNo j = keyNo_min;

[0050] If GNO j > keyNo_max, then perform the following operations:

[0051] j keyNo j = keyNo_max;

[0052] j If GNO j == keyNo i , then perform the following operations:

[0053] filterWin j = filterWin i

[0054] traceWin j = traceWini

[0055] TimWin j =TimWin i ;

[0056] If GNO j <keyNo i Then perform the following operations:

[0057] filterWin j =filterwin i-1 +(filterwin i -filterwin i-1 )*(GNO j -

[0058] keyNo i-1 ) / (keyNo i -keyNo i-1 );

[0059] traceWin j =traceWin i-1 +(traceWin i -traceWin i-1 )*(GNO j -

[0060] keyNo i-1 ) / (keyNo i -keyNo i-1 );

[0061] TimWin j =TimWin i-1 +(TimWin i -TimWin i-1 )*(GNO j -

[0062] keyNo i-1 ) / (keyNo i -keyNo i-1 ); i∈[1,n), j∈[0,m).

[0063] A further improvement of the present invention is that:

[0064] The operations in step 4 include:

[0065] (41) Execute the two-dimensional spatiotemporal window partitioning function extend_2d to calculate the original new data and the noisy new data from time and space respectively;

[0066] (42) Perform least squares matched filtering on the original new data and the noisy new data to obtain the denoising result.

[0067] A second aspect of the present invention provides a system for calculating a denoised dynamic spatiotemporal window, the system comprising:

[0068] The input unit is used to input the raw seismic data and noise model;

[0069] The spatiotemporal window processing unit is used to process dynamic spatiotemporal windows;

[0070] The noise reduction unit is connected to the input unit and the time-space window processing unit, respectively, and is used to perform noise suppression processing to obtain the noise reduction result.

[0071] A third aspect of the present invention provides a computer-readable storage medium storing at least one computer-executable program, which, when executed by the computer, causes the computer to perform steps in a method for calculating a denoised dynamic spatiotemporal window according to the present invention.

[0072] Compared with existing technologies, the beneficial effects of this invention are: it improves the computational accuracy and efficiency of noise suppression. This invention dynamically adjusts the spatiotemporal window parameters according to the severity of noise in different gathers, enabling flexible processing of complex data, achieving excellent denoising results, improving the efficiency of massive data processing, and saving computational costs. Attached Figure Description

[0073] Figure 1 A flowchart illustrating the steps of the method of this invention;

[0074] Figure 2-1 Raw data in the embodiments

[0075] Figure 2-2 The noise model in the embodiment;

[0076] Figure 2-3 Denoising results;

[0077] Figure 2-4 The actual noise subtracted. Detailed Implementation

[0078] The present invention will now be described in further detail with reference to the accompanying drawings:

[0079] To improve the noise suppression and denoising effect and computational efficiency in complex structural exploration areas, this invention proposes a method for calculating dynamic spatiotemporal windows for denoising. The spatiotemporal window parameters are dynamically adjusted according to the noise severity of different gathers, which is applicable to various seismic data types, can flexibly process complex data, and achieve good denoising results.

[0080] like Figure 1As shown, the method includes the following steps:

[0081] Step 1, Input raw seismic data:

[0082] Assume the original seismic data contains m seismic gathers, and the key for each gather is OriGNO. j , j∈[0,m), each trace set data is D GNOj = (nt, nx), where D is the original seismic data, nx is the number of traces in the spatial direction, and nt is the number of sampling points in the time direction.

[0083] Step 2, Input the noise model

[0084] Input an externally prepared noise model. This noise model is consistent with the original seismic data and contains m seismic gathers, each numbered GNO. j , j∈[0,m), each gather noise data is M GNOj = (nt, nx), where nx is the number of channels in the spatial direction and nt is the number of sampling points in the temporal direction.

[0085] Step 3, Processing dynamic spatiotemporal windows

[0086] (31) Windowing: Based on the actual data of the noise model, multiple spatiotemporal windows can be divided. The value of each spatiotemporal window is constrained from three dimensions: time, space, and frequency. The details are as follows:

[0087] If we divide the spacetime into n groups, the parameters of each group of spacetime windows are as follows:

[0088] Par i =(keyNo i filterWin i ,traceWin i TimWin i ), i∈[0,n)

[0089] Among them, keyNo i This is the number for each spatiotemporal window, which is obtained from the gather number (the user sets this number according to the characteristics of the seismic data). filterWin is the length of the filter window, traceWin is the length of the spatial window, and TimWin is the length of the temporal window.

[0090] The sampling rate of the original seismic data is dt. The spatiotemporal window parameter is converted into the sampling point window length using the following formula:

[0091] fw i =filterWin i / dt+1;(i∈[0,n)),fw iThe length of the filtering window for the sampling points of the i-th spatiotemporal window;

[0092] trw i =traceWin i +1; (i∈[0,n)), trw i The length of the spatial window for the sampling points of the i-th spatiotemporal window;

[0093] tw i =TimWin i / dt+1;(i∈[0,n)),tw i This refers to the length of the time window for the sampling points of the i-th spatiotemporal window.

[0094] In the calculation, the adjacent windows overlap in both time and space, denoted by overPer, where overPer ∈ (0, 50%) (the value of overPer is set by the user). The keyNo is used as the basis for the calculation. i For example, the time window movement length can be calculated using the following formula:

[0095] filterWinUse i = (2-overPer)*fw i / 2+1,(i∈[0,n))filterWinUse i Indicates filter

[0096] The length of the window's movement;

[0097] traceWinUse i = (2-overPer)*trw i / 2+1,(i∈[0,n))traceWinUse i Representation space

[0098] The length of time the window moves;

[0099] TimWinUse i = (2-overPer)*tw i / 2+1,(i∈[0,n))TimWinUse i Indicates the length of the time window movement.

[0100] (32) Dynamic spatiotemporal window parameter combination

[0101] Based on the set windowing, the spatiotemporal window parameters corresponding to each gather are calculated:

[0102] When there is only one window group, i.e., n=1, set keyNo0=0.

[0103] Par i =(keyNoi , filterWin i , traceWin i , TimWin i ), (i = 0)

[0104] All trace gathers are calculated using Par0.

[0105] When the number of window groups n > 1, for each window group, the keyword keyNo i (keyNo i > 0, i ∈ [0, n)), sort Par i in ascending order according to the value of keyNo i . The minimum value keyNo_min of the keyword array keyNo is keyNo0, and the maximum value of the keyword array keyNo is keyNo_max = keyNo n-1 .

[0106] Input the trace gathers in sequence. If the keyword is GNO j , the corresponding space-time window parameters are:

[0107] par j = (keyNo j , filterWin j , traceWin j , TimWin j )

[0108] Compare the keyNo in the space-time window parameter array Par with the keyword GNO of the input trace gather in sequence, and perform the following operations: i j j

[0109] If GNO j < keyNo_min, perform the following operations:

[0110] <0000\(132\) keyNo j = keyNo_min;

[0111] If GNO j > keyNo_max, perform the following operations:

[0112] j keyNo = keyNo_max;

[0113] If GNO j == keyNo i , perform the following operations:

[0114] filterWin j = filterWini

[0115] traceWin j =traceWin i

[0116] TimWin j =TimWin i ;

[0117] If GNO j <keyNo i Then perform the following operations:

[0118] filterWin j =filterwin i-1 +(filterwin i -filterwin i-1 )*(GNO j -

[0119] keyNo i-1 ) / (keyNo i -keyNo i-1 );

[0120] traceWin j =traceWin i-1 +(traceWin i -traceWin i-1 )*(GNO j -

[0121] keyNo i-1 ) / (keyNo i -keyNo i-1 );

[0122] TimWin j =TimWin i-1 +(TimWin i -TimWin i-1 )*(GNO j -

[0123] keyNo i-1 ) / (keyNo i -keyNo i-1 ); i∈[1,n), j∈[0,m)

[0124] Step 4, Noise Suppression Processing:

[0125] The original gather and the noise model gather are calculated cyclically by gather, using the OriGNO of the original gather. jGNO and noise model j For example, based on the windowing parameter Par j The least-squares matched filtering denoising calculation is performed. The process is as follows:

[0126] (41) Execute the two-dimensional spatiotemporal window partitioning function extend_2d to calculate the original new data and the noisy new data from both time and space perspectives:

[0127] Number of time windows ntw = nt / TimWinUse i +1

[0128] Number of spatial windows nxw = nx / traceWinUse i +1

[0129] The total number of spatiotemporal windows is wn = ntw * nxw. The data within the spatiotemporal windows is retrieved and calculated by iterating through the collection.

[0130] Original new data: dati1 k =extend_2d(D GNOj ,traceWin j TimWin j , Others,...), (k∈[0,wn))

[0131] New noise data: dati2 k =extend_2d(M GNOj ,traceWin j TimWin j Others j ,……), (k∈[0,wn))

[0132] The `extend_2d` function mentioned above is an existing function. The other parameters can be set according to the function's rules, and will not be elaborated here.

[0133] (42) The denoising result is obtained by performing least-squares matched filtering on the original new data and the noisy new data:

[0134] P(nt,nx)=M GNOj -F(nt,nx)D GNOj

[0135] Where, filter F(nt,nx)=least_filter(dati1) k dati2 k Par j The minimum energy criterion constraint is:

[0136] After subtraction, under the constraint of minimizing the energy of P(nt,nx), the corresponding filter F(nt,nx) (the filter corresponding to the minimum energy) is selected to obtain the final denoising result P(nt,nx).

[0137] The embodiments of the present invention are as follows:

[0138] We selected a real seismic track set containing 121 shots, with the starting shot number being 35 and the ending shot number being 155, and a shot number interval of 1, totaling 14,641 seismic tracks, and performed noise suppression calculations.

[0139] Example 1:

[0140] The first step is to input the original, noisy seismic shot gather data D(t,x), with a sampling rate of 8000ms, 221 sampling points, and 121 channels per shot gather.

[0141] Example 2:

[0142] The second step is to input the noise model data M(t,x) for identification, with a sampling rate of 8s, a sampling point count of 221, and a set of 121 tracks per shot.

[0143] Example 3:

[0144] The third step is to process dynamic spatiotemporal windows.

[0145] (1) Windowing: Set the window size for the three dimensions: time, trace, and frequency. Adjacent windows will overlap in time and space, so set it to 50%. Set the windowing parameters to two groups. The first group has the following parameters: keyNo = 35 for the first key of the trace set, filterWin = 160 for the filter window, traceWin = 12 for the spatial window, and TimWin = 100 for the time window. The second group has par = (50, 80, 12, 50).

[0146] The actual window length of Daoji 35 is:

[0147] fm=160 / 8+1=21; trm=12; tm=100 / 8+1=13;

[0148] Filter window filterWin=21, spatial window length trm=12, temporal window length tm=13

[0149] The actual window length of Daoji 50 is:

[0150] fm=80 / 8+1=11; trm=12; tm=50 / 8+1=7;

[0151] (2) Dynamic spatiotemporal window parameter combination

[0152] There are two sets of defined spatiotemporal windows.

[0153] For the Dao set number 35, par = (35, 21, 12, 13).

[0154] Daoji No. 36, fm = 21 + (11-21)*(50-36) / (50-35) = 12;

[0155] trm=12;

[0156] tm=13+(7-13)*(50-36) / (50-35)=15;

[0157] And so on.

[0158] Example 4:

[0159] Step 4: Noise suppression processing

[0160] Taking Daoji No. 36 as an example,

[0161] filterWinUse=(2-0.5)*12 / 2+1=10

[0162] traceWinUse=(2-0.5)*12 / 2+1=10

[0163] TimWinUse=(2-0.5)*15 / 2+1=12

[0164] Number of time windows ntw = 221 / 10 + 1 = 23

[0165] Number of spatial windows nxw=121 / 10+1=13

[0166] Original new data: dati1 k =extend_2d(D 36 ,12,15,……),(k∈[0,299))

[0167] New noise data: dati2 k =extend_2d(M 36 ,12,15,……),(k∈[0,299))

[0168] F(221,121)=least_filter(dati1 k dati2 k Par j , ...)

[0169] Noise subtraction model: P(221,121)=M 36 -F(221,121)D 36

[0170] Minimum energy criterion constraint:

[0171] Example 5:

[0172] The present invention also provides a system for calculating a denoised dynamic spatiotemporal window, the system comprising:

[0173] The input unit is used to input the raw seismic data and noise model;

[0174] The spatiotemporal window processing unit is used to process dynamic spatiotemporal windows;

[0175] The noise reduction unit is connected to the input unit and the time-space window processing unit, respectively, and is used to perform noise suppression processing to obtain the noise reduction result.

[0176] Example 6:

[0177] The present invention also provides a computer-readable storage medium storing at least one computer-executable program, which, when executed by the computer, causes the computer to perform steps in a method for calculating a denoised dynamic spatiotemporal window according to the present invention.

[0178] The method of this invention dynamically adjusts the spatiotemporal window parameters according to different noise levels in different gathers, is applicable to various seismic data types, can flexibly process complex data, achieve good noise reduction effect, and can be applied to processing, interpretation and calculation systems to achieve cost reduction and efficiency improvement.

[0179] The above technical solution is only one embodiment of the present invention. For those skilled in the art, based on the principles disclosed in the present invention, it is easy to make various types of improvements or modifications, and not limited to the technical solutions described in the specific embodiments of the present invention. Therefore, the foregoing description is only a preferred option and is not restrictive.

Claims

1. A method for calculating a denoised dynamic spatiotemporal window, characterized in that: The method dynamically adjusts the spatiotemporal window parameters according to the severity of noise in different gathers, and finally obtains the denoising result.

2. The method for calculating a denoising dynamic spatiotemporal window according to claim 1, characterized in that: The method includes: Step 1: Input the raw seismic data; Step 2, input the noise model; Step 3: Process the dynamic spatiotemporal window; Step 4: Noise suppression processing to obtain the noise reduction result.

3. The method for calculating a denoising dynamic spatiotemporal window according to claim 2, characterized in that: The operations in step 1 include: Assume the original seismic data contains m seismic gathers, and the key for each gather is OriGNO. j , j∈[0,m), each trace set data is D GNOj = (nt, nx), where D is the original seismic data, nx is the number of traces in the spatial direction, and nt is the number of sampling points in the time direction.

4. The method for calculating a denoising dynamic spatiotemporal window according to claim 3, characterized in that: The operations in step 2 include: Input noise model; The noise model has a total of m seismic gathers, and the number of each gather is denoted as GNO. j , j∈[0,m), each gather noise data is M GNOj = (nt, nx), where nx is the number of channels in the spatial direction and nt is the number of sampling points in the temporal direction.

5. The method for calculating a denoising dynamic spatiotemporal window according to claim 4, characterized in that: The operations in step 3 include: (31) Windowing: Constrain the value of each spatiotemporal window from the time dimension, spatial dimension and frequency dimension; (32) Dynamic spatiotemporal window parameter combination.

6. The method for calculating a denoising dynamic spatiotemporal window according to claim 5, characterized in that: The operation of step (31) includes: If we divide the spacetime into n groups, the parameters of each group of spacetime windows are as follows: Par i =(keyNo i ,filterWin i ,traceWin i ,TimWin i ),i∈[0,n) Among them, keyNo i Each spatiotemporal window is assigned a number, filterWin is the length of the filter window, traceWin is the length of the spatial window, and TimWin is the length of the temporal window. The sampling rate of the original seismic data is dt. The spatiotemporal window parameter is converted into the sampling point window length using the following formula: fw i =filterWin i / dt+1,i∈[0,n) trw i =traceWin i +1,i∈[0,n) tw i =TimWin i / dt+1,i∈[0,n] Among them, fw i trw represents the length of the sampling point filter window for the i-th spatiotemporal window. i tw represents the length of the spatial window for the sampling points of the i-th spatiotemporal window. i This represents the length of the time window for the sampling points of the i-th spatiotemporal window; The time window movement length can be calculated using the following formula: filterWinUse i =(2-overPer)*fw i / 2+1,i∈[0,n) traceWinUse i =(2-overPer)*trw i / 2+1,i∈[0,n) TimWinUse i =(2-overPer)*tw i / 2+1,i∈[0,n) Where overPer represents the overlap rate, overPer∈(0,50%), filterWinUse i Indicates the shift length of the filter window, traceWinUse i Indicates the length of the space window that has been moved, TimWinUse i Indicates the length of the time window movement.

7. The method for calculating a denoising dynamic spatiotemporal window according to claim 6, characterized in that: Step (32) includes the following operations: Calculate the spatiotemporal window parameters for each gather: When there is only one window group, i.e., n=1, then set keyNo0=0; Par i =(keyNo i ,filterWin i ,traceWin i ,TimWin i ),i=0 All Dao sets are calculated using Par0; When the number of window groups n>1, then Par i According to the keyword keyNo for each group of windows i The values ​​are sorted in ascending order to obtain the key array keyNo; the minimum value of the key array keyNo is keyNo_min = keyNo0, and the maximum value of the key array keyNo is keyNo_max = keyNo0. n-1 keyNo i >0, i∈[0,n); Enter the Dao Collection sequentially, assuming the keyword of the Dao Collection is GNO. j The spatiotemporal window parameters corresponding to the Dao Collection are: par j =(keyNo j 、filterWin j ,traceWin j ,TimWin j ) Sequentially select keyNo from the spatiotemporal window parameters i The keyword GNO in the input set j Compare the results and perform the following operations: If GNO j <If keyNo_min, then perform the following operations: keyNo j =keyNo_min; If GNO j If keyNo_max is greater than 0, then the following operations are performed: keyNo j =keyNo_max; If GNO j ==keyNo i Then perform the following operations: filterWin j =filterWin i traceWin j =traceWin i TimWin j =TimWin i ; If GNO j <keyNo i Then perform the following operations: filterWin j =filterwin i-1 +(filterwin i -filterwin i-1 )*(GNO j - keyNo i-1 ) / (keyNo i -keyNo i-1 ); traceWin j =traceWin i-1 +(traceWin i -traceWin i-1 )*(GNO j - keyNo i-1 ) / (keyNo i -keyNo i-1 ); TimWin j =TimWin i-1 +(TimWin i -TimWin i-1 )*(GNO j - keyNo i-1 ) / (keyNo i -keyNo i-1 );i∈[1,n),j∈[0,m)。 8. The method for calculating a denoising dynamic spatiotemporal window according to claim 2, characterized in that: The operations in step 4 include: (41) Execute the two-dimensional spatiotemporal window partitioning function extend_2d to calculate the original new data and the noisy new data from time and space respectively; (42) Perform least squares matched filtering on the original new data and the noisy new data to obtain the denoising result.

9. A system for calculating a denoised dynamic spatiotemporal window, characterized in that: The system includes: The input unit is used to input the raw seismic data and noise model; The spatiotemporal window processing unit is used to process dynamic spatiotemporal windows; The noise reduction unit is connected to the input unit and the time-space window processing unit, respectively, and is used to perform noise suppression processing to obtain the noise reduction result.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores at least one computer-executable program, which, when executed by the computer, causes the computer to perform the steps of the method for calculating a denoised dynamic spatiotemporal window as described in any one of claims 1-8.

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