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IrregularInterp

By Donald Berry,2014-05-27 14:58
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IrregularInterp

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     Irregular Interpolate (IRREGULAR_INTERP)

     Abstract

     Input traces are interpolated to output locations using Compact Regularization Operators (CROs). The CRO technique derives weights for the input traces via a least-square inverse sinc technique based only on the locations of the input traces. The word ??location?? in this SFM should be taken in a general sense and does not necessarily refer to spatial values such as X,Y coordinates or 3D Grid primary/secondary or inline/crossline numbers. The output locations can be specified on the parameter sets or can be read from the second input port.

     NOTICE Copyright protection as an unpublished work is claimed by WesternGeco. The work was created in 2008. Should publication of the work occur, the following notice shall apply. " 2008 Westerngeco". This work contains valuable tradesecrets; disclosure without written authorization is prohibited.

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     Contents

     1.0 Technical Discussion 1.1 1.2 1.3 1.4 2.0 Weight Computation Scanning Trace Handling Mechanics Output X,Y Shifts, Offset and Azimuth Changes and 3D Grid

     Inputs and Outputs 2.1 2.2 Inputs Outputs

     3.0

     Literal Summary 3.1 3.2 Inputs 3.1.1 STANDARD_INPUT Port Outputs 3.2.1 STANDARD_OUTPUT Port

     4.0 5.0

     Parameter Set Summary Setup Parameters 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 General Parameters When Using Specified Output Point Locations General Parameters When Using Desired Locations Port Gather Axis Interpolation and Point Locations Gather Axis Interpolation Primary Axis Interpolation and Point Locations Primary Axis Interpolation Secondary Axis Interpolation and Point Locations Secondary Axis Interpolation QC Measure

     5.10 Spatial Frequency Scanning 5.11 Change Output Coordinates, Offset, and Azimuth

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     1.0 Technical Discussion

     1.0 Technical Discussion

     1.1 Weight Computation

     Weights are computed via a multi-dimensional least-squares inverse sinc technique (sinc(x) is sin(x) divided by x). You specify an interpolation literal for each dimension. You specify the extent of the operator along each dimension (number of bins and their size). You specify the locations where you want output (via parameters, or via the second input port). In the most simple situation you specify 2 dimensions (primary and secondary) which construct output traces using traces only from within each input gather. You can also use a third dimension (called the gather dimension) which allows traces from a range of input gathers to be used to construct output traces (some printout for the gather dimension occurs even when not used). Each dimension is independent in the mathematical sense.

     The least-squares inverse sinc technique is an interpolation technique. Do not think of it as a smoothing technique. Increasing the size of the model does not mean the results will be smoother. You should specify the size of the model so that a reasonable number of input traces ??surround?? the output locations. Note that each dimension is independent in the mathematical sense. A consequence of this can be understood using the following example: Assume a typical marine shot with 500 traces per cable and 12 cables. Assume that some traces are missing and you decide to regularize so that each cable has the 500 traces that it was intended to have. You also decide to use a 5 by 5 model (5 traces by 5 cables). If trace number 6 is missing on cable 4 but all other traces near it exist (within the model extent), then trace 6 will be created using equal contribution from trace numbers 5 and 7 of cable 4 as well as trace number 6 from cables 3 and 5. Those 4 traces will get equal weight despite the fact that the cables are separated by more distance than the detectors on the cables (other input traces would also contribute weight in a similar fashion). But even if you use X and Y coordinate literals rather than trace and cable number literals, the input traces will contribute approximately the same weights to the output trace because each dimension is independent. Similarly, scaling a dimension literal before input will not change the weight contributions for a corresponding correct setup. Since the dimensions are independent you probably do not want to use a 5 by 5 model in this example situation. But you may want to use a 5 by 1 model (5 traces by 1 cable). This would create output traces just

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     1.0 Technical Discussion

     using traces along the same cable. Whether this is a good idea geophysically is beyond the scope of this document. With due consideration to the previous example it should be understood that the best results will be obtained when output traces can be created using a good sampling of input traces in all directions around the output location. For the MODEL_BASED option, input traces near the model edges are down-weighted to 0.1 before least-squares analysis (other traces are given an input weight of 1 as long as they have a STACK_WORD greater than 0). When the number of cells in a model direction is less than 5, no down-weighting is done. For 5 cells, only traces in the outer cell are down-weighted. For 7 cells, the down-weighting occurs for traces in the zone 1.5 cells inward from the edge. For 9 cells, the down-weighting zone is 2 cells inward from the edge. For 11 cells, the zone is 2.5 cells inward. For 13 or more cells, the zone is 3 cells inward. The down-weighting factors are multiplied together when a trace is near more than one edge of the model. Caution Even when the number of cells is set to 1 for a dimension the values of the interpolation literal can still affect the computed weights. To completely ??turn off?? the effects of a dimension you must use a literal which is constant, and set the number of cells to 1, the cell size to 1, and the maximum frequency to recover to 100.

     1.2 Scanning

     The scanning is over the maximum spatial frequency that the CRO is designed to interpolate. The operator size is fixed, as is the Nyquist. A spatial frequency of 80% means 80% of the spatial Nyquist. The Nyquist frequency depends on the increment for the literal being interpolated - e.g. if you are using an interpolation literal of 3DT_PRIM_ORD_MIDPT (primary ordinal) and the increment is 1, then the Nyquist is 0.5 cycles per ordinal. Similarly, if you are using XCORD_MIDPT (midpoint X coordinate) and the increment is 25 meters, then the Nyquist is 0.02 cycles/meter. Note that this is a spatial Nyquist - this has nothing to do with the (temporal) frequency content or time sampling of the data. The scanning is done for each output location. Scanning is from the highest frequency downward, so if the range (for a 1 dimensional scan) is from 20% to 80% in 5% increments, 80% will be attempted first, and if that is ??not good?? then 75% will be attempted next, and so on. ??Not good" means either the mean or maximum errors are above 0.1 or 0.3 respectively (assuming these parameters are defaulted). The scanning stops once this test is passed. Note that the scanning is based on the geometry alone - it does not depend on the data. Once the scanning stops, it means there is sufficient sampling to interpolate data at that percent of the spatial Nyquist, even though these spatial

    frequencies may not exist in your seismic data. For 2 dimensional scanning, the scanning still proceeds by decreasing frequency, but now in a 2 dimensional sense. A list of all possible frequency pair combinations is created and sorted into decreasing combined order (for instance: (80,80), (80,75), (75,80), ????, (20,20)). Again, the scanning stops as soon as a good operator is found.

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     1.0 Technical Discussion

     1.3 Trace Handling Mechanics

     Traces are input from the SEISMIC_INPUT port and stored on a temporary scratch disk file. Traces are input on a gather basis and input does not pause until end-of-gather is reached (end-of-gather is determined by the Omega system using the IDheader SORT_LITERALs and so on). Once input pauses, output traces are created by interpolation, then input resumes until next end-of-gather or end-of-file. The interpolation literals do not have to be in the list of SORT_LITERALs. When the output locations are specified via the parameter sets, the traces within output gathers are created in the order in which you specify the interpolation literals and the signs of their increments. When the DESIRED_LOCATIONS port is connected, the traces within output gathers are created in the order of traces from the DESIRED_LOCATIONS port. For multi-gather options, a small range of gathers are kept in the temporary scratch disk file. Your specified gather dimension interpolation literal must be a value that increases or decreases gather-by-gather. The SFM checks this as traces are input and will error-halt when this condition is violated (that is, your specified gather interpolation literal does not have to be in the list of SORT_LITERALs, but it does have to actually be ordered). Traces within the gathers on the SEISMIC_INPUT port do not have to ordered to match the output order. If no input trace exists within the model extent of an output location, no output trace is created. ?C The output trace headers are created initially by copying the nearest SEISMIC_INPUT trace header (nearest in terms of your specified interpolation literals, not necessarily the spatially nearest). When the DESIRED_LOCATIONS port is connected, its trace header literal values are used to replace values from the nearest seismic trace (creating missing literals if needed). Any literals that do not exist in the DESIRED_LOCATIONS port continue to have their values from the nearest seismic trace. By default the following literals are not copied from the DESIRED_LOCATIONS port (they involve values directly related to the time and amplitude of the seismic samples, which are being interpolated from the SEISMIC_INPUT port):

CMP_DATCOR CMP_DATCOR_APP CMP_DATCOR_SEC MUTE_TIME

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     Irregular Interpolate MUTE_TIME_INSIDE NOISE_LEVEL NORM_SCALAR POLARITY_CODE RESID_STATCOR_DETECT RESID_STATCOR_MIDPT

    RESID_STATCOR_SOURCE START_TIME STATCOR_DETECT STATCOR_DETECT_APP STATCOR_HI_DETECT STATCOR_HI_SOURCE STATCOR_LO_DETECT

    STATCOR_LO_SOURCE STATCOR_SOURCE STATCOR_SOURCE_APP

    STATIC_SHIFT_APPLIED TRACE_BALANCE_FACTOR TRACE_SCALE_FACTOR TRC_STATUS TRIM_STATCOR WNDW_MIDPT_MULT WNDW_MIDPT_TIME WNDW_START_TIME WNDW_STOP_TIME WNDW_S_N_RATIO

     1.0 Technical Discussion

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     1.0 Technical Discussion

     That is, by default the output trace literals containing geometry and similar values come from the DESIRED_LOCATIONS port (if connected) and the output literals containing time and amplitude values come from the SEISMIC_INPUT port. For explicit control of which literal values are copied to output, delete the literals before input to the DESIRED_LOCATIONS or SEISMIC_INPUT ports. The output IDheader is created initially by copying the IDheader from the SEISMIC_INPUT port. If connected, the DESIRED_LOCATIONS port IDheader values are not used in general, only the SORT_LITERAL and related literals and MAX_GATH_MULT are copied to the output IDheader (therefore traces input on the DESIRED_LOCATIONS port can have reduced length). Those values are copied because the output trace order is the same as the traces on the DESIRED_LOCATIONS port. Even if you specify different interpolation literals, the traces are output in the same order as they are input on the DESIRED_LOCATIONS port (so if the SORT_LITERALs are telling the truth in the DESIRED_LOCATIONS IDheader, they will be just as correct in the output IDheader). If the DESIRED_LOCATIONS port is not connected the SORT_LITERAL and related literals are deleted and reset in the output IDheader to the following three names: TD.IRR_LOC_GATH is the output gather axis location (corresponds to values of the gather interpolation literal). TD.IRR_LOC_PRIM is the output primary axis location (corresponds to values of the primary interpolation literal). TD.IRR_LOC_SEC is the output secondary axis location (corresponds to values of the secondary interpolation literal).

     The three previous literals are always created in the output trace

    headers and contain the output location values (note that these are double precision, which is needed in case the output locations are decimal fractions). The next four literals are created in the output trace headers if the four source and detector coordinate literals are found in the traces from the SEISMIC_INPUT port . These are computed from the four X,Y literals of the traces in the SEISMIC_INPUT port: TD.IRR_SD_DIST_NR is the source-detector distance of the SEISMIC_INPUT trace nearest the center of the model. TD.IRR_SD_DIST_WA is the restricted weighted-average source-detector distance of all SEISMIC_INPUT traces within the model extent. TD.IRR_SD_AZIM_NR is the azimuth of the SEISMIC_INPUT trace nearest the center of the model. TD.IRR_SD_AZIM_WA is the restricted weighted-average azimuth of all SEISMIC_INPUT traces within the model extent.

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     1.0 Technical Discussion

     The two ??restricted weighted-average literals?? are computed using the same sinc interpolation weights determined for the trace samples. These weights are always normalized to 1 for use with literals (regardless of the normalization option for trace samples). By default their values are restricted to a range close to the value of the trace nearest the center of the model (via a parameter on the General parameter sets). The following QC literals are created by default for all output locations: TR.IRR_FOLD_FOUND is the number of traces within the model extent. TR.IRR_NEAR_DIST is the distance between the model center and the nearest input trace (distance in terms of the interpolation literal values). TR.IRR_NEAR_WEIGHT is the weight of the nearest input trace (Note: weights are not constrained to be greater than 0 and less than 1). TR.IRR_MAX_WEIGHT is the maximum (negative or positive) weight of any input trace. TR.IRR_TOT_WEIGHT is the sum of the weights of the input traces. TR.IRR_MEAN_ERROR is the mean error. TR.IRR_MAX_ERROR is the maximum error. TR.IRR_SMAX_GATH is maximum spatial Nyquist percent for gather axis (possibly determined by scanning). TR.IRR_SMAX_PRIM is maximum spatial Nyquist percent for primary axis (possibly determined by scanning). TR.IRR_SMAX_SEC is maximum spatial Nyquist percent for secondary axis (possibly determined by scanning). TR.IRR_FOLD_CENTER is the number of input traces within center cell of model. TR.IRR_NEAR_DIST_XY is the distance between model center and nearest input trace (distance in terms of coordinates, but only computed when interpolation literals are 3D ordinals and 3D Grid is available). The output STACK_WORD is set to 1 unless the interpolation cannot be performed because the least-squares inversion is singular (or other

    similar problems), in which case the output STACK_WORD is 0 and some print occurs. Traces on the SEISMIC_INPUT port with STACK_WORD less than or equal to 0 are not used in the interpolation. The STACK_WORD on the DESIRED_LOCATIONS port is ignored; output traces are created at the locations of all traces on the DESIRED_LOCATIONS port (provided at least one live input seismic trace exists within the model extent at that location).

     Note

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     1.0 Technical Discussion

     1.4 Output X,Y Shifts, Offset and Azimuth Changes and 3D Grid

     Purpose of the shift options: The output trace seismic samples are interpolated to the output location values. For some setups these output locations are spatial locations. In a limited set of setups these output locations are 3D Grid ordinals . For some downstream SFMs/processes it is beneficial to produce an output trace header where the source and detector coordinates and related values have been shifted so their midpoint corresponds to the spatial location of the output seismic samples. Details: To understand how the output trace header shift is computed, first, remember that the output trace header is initially constructed from the nearest SEISMIC_INPUT trace (nearest in terms of the interpolation literal values, which is not necessarily nearest in terms of coordinates) and then some literal values are replaced from the DESIRED_LOCATIONS port (if connected). Second, remember that any trace that has coordinates can be shifted from its midpoint coordinates to its 3D Grid cell center. That is, obviously any midpoint can be shifted to the center of its own cell. For most interpolation literals, that shift is the best that can be computed (for instance, interpolation literals FIELD_CHANNEL_NUM and SOURCE_DETECT_DIST have no known relationship to coordinates or 3D Grid literals). However, if the output locations are 3D Grid ordinals they can be used to compute the shift between themselves and the trace midpoint. The reason that it is important to compute the shift between the output ordinal locations and the midpoint is that the nearest trace's midpoint is not necessarily in the same 3D cell as the output location because most seismic surveys have irregular trace distributions ( gaps and holes ). Despite these gaps and holes, the sinc interpolation in this SFM has produced seismic samples that represent the output location. The following diagram illustrates:

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     1.0 Technical Discussion

     In the diagram, shifts can always be computed from the midpoint nearest the output location (??m??) to the 3D Grid cell center (??C??) in the primary grid direction or the secondary grid direction or in both grid directions (resulting in a shift to the cell center). But to compute a shift to the output location, you have to understand the relationship between IRREGULAR_INTERP output literals and the standard CHANGE_XY parameter set. Standard CHANGE_XY Parameter Set, and the GRID_DEFINE SFM: The CHANGE_XY parameter set also exists in the GRID_DEFINE SFM (version 6). Correct use of this parameter set in both SFMs requires knowledge of one fundamental fact: The trace literal values output by IRREGULAR_INTERP usually come from the nearest trace on the SEISMIC_INPUT port, but you usually want to use the actual output locations which exist in other output literals.

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     1.0 Technical Discussion

     This means, for example, that even if you use a 3D Grid ordinal literal 3DT_PRIM_ORD_MIDPT as the primary interpolation literal, the output value of that literal is not usually the location value that you want to shift to . You usually want to shift to the value of output literal TD.IRR_LOC_PRIM. That is, you want to compute the shift between the nearest trace and the output location, not between the nearest trace and itself.

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     2.0 Inputs and Outputs

     2.0 Inputs and Outputs

     2.1 Inputs

     Seismic Input (Required) Desired Locations (Optional) SEISMIC_INPUT DESIRED_LOCATIONS

     2.2 Outputs

     Seismic Output (Required) SEISMIC_OUTPUT

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     3.0 Literal Summary

     3.0 Literal Summary

     3.1 Inputs

     3.1.1 STANDARD_INPUT Port

     Identification Header

     LITERAL DATA_DESC EARLIEST_TIME MAX_REFLECT_TIME SAMP_INT SORT_LITERAL DESCRIPTION Data Set Description Earliest Time Maximum Reflection Time Sample Interval Sort Literal

     Trace Header

     LITERAL LTRSAM STACK_WORD DESCRIPTION Length of Trace in Samples Stack Word

     3.2 Outputs

     3.2.1 STANDARD_OUTPUT Port

     Identification Header

     LITERAL MAX_GATHER_MULT SORT_LITERAL DESCRIPTION Maximum Gather Multiplicity Sort Literal

     Trace Header

     LITERAL STACK_WORD DESCRIPTION Stack Word

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     4.0 Parameter Set Summary

     4.0 Parameter Set Summary

     Parameter Set Name Geophysical Language GENERAL_SPECIFIED MAX_IN_GATHER_MULT MAX_OUT_GATHER_MULT MAX_TRC_MODEL_RATIO CRO_METHOD WHITE_NOISE_PCT NORMALIZE_WEIGHTS NORMALIZE_SINC_OP FILTER_OUTPUT TOLR_DIST_INFILL WA_LIT_CLIP_PCT OUTPUT_QC_LITS PRINT_INC GENERAL_DESIRED MAX_IN_GATHER_MULT MAX_OUT_GATHER_MULT MAX_TRC_MODEL_RATIO CRO_METHOD WHITE_NOISE_PCT NORMALIZE_WEIGHTS NORMALIZE_SINC_OP FILTER_OUTPUT TOLR_DIST_INFILL WA_LIT_CLIP_PCT OUTPUT_QC_LITS PRINT_INC SAMP_LITS_PORT GATHER_AXIS_POINTS INTERPOL_LIT INTERPOL_LIT_ABS MODEL_CELL_SIZE MODEL_NUM_CELLS MODEL_MAX_FREQ_PCT NUM_GATHERS November 2008 - WesternGeco Parameter Set Title Parameter Title Status

     General Parameters When Using Required Specified Output Point Locations Maximum Traces Per Input Gather Maximum Traces Per Output Gather Maximum Input Traces Within Model Extent Ratio Operator Design Method White Noise Percent Normalize Weights Normalize Sinc Operators Filter Output Tolerance Distance When Infilling Weighted Average Output Literals Clip Percent Output QC Literals Print Increment General Parameters When Using Required Desired Locations Port Maximum Traces Per Input Gather Maximum Traces Per Output Gather Maximum Input Traces Within Model Extent Ratio Operator Design Method White Noise Percent Normalize Weights Normalize Sinc Operators Filter Output Tolerance

    Distance When Infilling Weighted Average Output Literals Clip Percent Output QC Literals Print Increment Seismic Sample Related Literals Port Gather Axis Interpolation and Point Required Locations Interpolation Literal Interpolation Literal Absolute Value Model Cell Size Model Extent in Number of Cells Maximum Spatial Nyquist Frequency Percent To Try To Recover Number of Gathers In Range of Interpolation IRREGULAR_INTERP 14

     Irregular Interpolate Parameter Set Name Geophysical Language FIRST_OUTPUT_LOC LOC_INC GATHER_AXIS INTERPOL_LIT INTERPOL_LIT_ABS MODEL_CELL_SIZE MODEL_NUM_CELLS MODEL_MAX_FREQ_PCT NUM_GATHERS LOC_DIR PRIM_AXIS_POINTS INTERPOL_LIT INTERPOL_LIT_ABS

    MODEL_CELL_SIZE MODEL_NUM_CELLS MODEL_MAX_FREQ_PCT FIRST_OUTPUT_LOC LAST_OUTPUT_LOC LOC_INC PRIM_AXIS INTERPOL_LIT INTERPOL_LIT_ABS MODEL_CELL_SIZE MODEL_NUM_CELLS MODEL_MAX_FREQ_PCT SECN_AXIS_POINTS INTERPOL_LIT INTERPOL_LIT_ABS MODEL_CELL_SIZE MODEL_NUM_CELLS MODEL_MAX_FREQ_PCT FIRST_OUTPUT_LOC LAST_OUTPUT_LOC LOC_INC November 2008 - WesternGeco

     4.0 Parameter Set Summary Parameter Set Title Parameter Title First Output Location Increment Between Locations Status

     Gather Axis Interpolation Required Interpolation Literal Interpolation Literal Absolute Value Model Cell Size Model Extent in Number of Cells Maximum Spatial Nyquist Frequency Percent To Try To Recover Number of Gathers In Range of Interpolation Gather Location Direction Primary Axis Interpolation and Point Required Locations Interpolation Literal Interpolation Literal Absolute Value Model Cell Size Model Extent in Number of Cells Maximum Spatial Nyquist Frequency Percent To Try To Recover First Output Location Last Output Location Increment Between Output Locations Primary Axis Interpolation Required Interpolation Literal Interpolation Literal Absolute Value Model Cell Size Model Extent in Number of Cells Maximum Spatial Nyquist Frequency Percent To Try To Recover Secondary Axis Interpolation and Required Point Locations Interpolation Literal Interpolation Literal Absolute Value Model Cell Size Model Extent in Number of Cells Maximum Spatial Nyquist Frequency Percent To Try To Recover First Output Location Last Output Location Increment Between Output Locations IRREGULAR_INTERP 15

     Irregular Interpolate Parameter Set Name Geophysical Language SECN_AXIS INTERPOL_LIT INTERPOL_LIT_ABS MODEL_CELL_SIZE MODEL_NUM_CELLS MODEL_MAX_FREQ_PCT QC_MEASURE QC_TYPE NUM_QC_TRC FREQ_INC_QC PRINT_QC FREQ_SCAN MAX_MEAN_ERROR MAX_MAX_ERROR PREFER_EQ_FAC PRINT_SCAN MIN_FREQ_GATH MIN_FREQ_PRIM MIN_FREQ_SECN CHANGE_XY SHIFT_PRIM_LIT SHIFT_SEC_LIT BASIC_SD_AZIMUTH OFFSET_SD_XY ROTATE_SD_XY APPLY_GRID Parameter Set Title Parameter Title

     4.0 Parameter Set Summary Status

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