Adaptive Groundroll filtering David Le Meur (CGGVerita), Nigel Benjamin (CGGVerita), Rupert Cole (Petroleum Development Oman) and Mohammed Al Harthy (Petroleum Development Oman) SUMMARY The attenuation of Surface Wave while maintaining a friendly preervation of the Body Wave i a difficult goal to achieve in land data proceing. However, Groundroll (GR) characteritic can be extracted from the input data themelve to feed an adaptive filtering in order to remove the Surface and Guided Wave. Thi approach i baed on a cacaded Elatic Modeling of the ignal and noie in the FX domain that ue the GR characteritic of everal frequency band. The part of the model correponding to the noie i then ubtracted from the data uing a leat quare approach. Thi method ha everal advantage over technique uch a FK filtering becaue it better preerve the ignal and work even when the noie i aliaed, diperive and ha irregular patial ampling.
Introduction On land, the effect of the near urface variation i the major caue of poor eimic data quality. The attenuation of the Groundroll (GR) i one of the firt iue that hould be addreed during the data proceing flow. GR are Surface Wave recorded a peudo- Rayleigh wave on a vertical geophone. They are the reult of interfering P and SV wave that travel along/near the ground urface. A GR arrive directly from the ource, it i linear on the near offet for the inline cable (of 3-dimenional data) but appear hyperbolic on the broadide cable for near offet. They are characterized by their low velocity, low frequency and high amplitude. GR can be trongly diperive and aliaed and act a guided wave (ometime called higher mode) - thi mean that for each frequency there are different phae velocitie. Over the lat 30 year, many approache have been developed to try to attenuate the GR on 2D or 3D eimic data including FK approache, HR Radon method, Wavelet Tranform and Elatic Modeling. All of thee method are currently ued ometime individually and ometime in cacaded application. However, thee method motly have fixed parameterization and regular grid pacing when ued over large urface area and hence have a very poor repone to the changing characteritic of the near urface. Thi often reult in leaving coherent artifact and give poor preervation of primary amplitude caued by over-aggreive or inadequate filtering. In thi paper we preent a data driven approach that perform an adaptive filtering of aliaed and diperive Surface Wave at their true patial coordinate (AGORA). Thi approach ue the GR characteritic contained in each hot (group and phae velocitie) to perform an Elatic Modeling of the ignal and noie (Surface Wave) in the FX domain for everal frequency band. Finally, a leat quare approach i ued to adapt the noie to the input data before ubtracting it. Technical background If we analyze everal hot from the ame urvey we oberve that the characteritic of the GR change from one hot location to another with repect to their diperion propertie (ee figure b-e). Map of the main mode of the GR for non-aliaed frequencie can eaily be made to highlight ignificant patial variation of the GR velocity reaching up to a factor of 4 at hort ditance (ee figure a). Obervation and meaurement on record indicate a real change in the GR characteritic (frequency content, phae velocity, amplitude and degree of aliaing) (figure a-e). Thi i the reaon why the GR characteritic hould be taken into account and the group and phae velocitie extracted from each record to feed the anti-noie filtering. Our anti-noie filtering i baed on an Elatic Modeling in the FX domain uing the true ditance between the ource and the receiver (irregular patial ampling). The principle i that the input data i a mixture of ignal plu coherent and incoherent noie (ee Perkin and Zwaan, 2000). The ignal (S) i modeled a hyperbolic event whoe trajectorie are decribed by tacking velocity (Vrm) (ee formula ). The coherent noie (GR) i modeled a a erie of diperive linear event, each ditinguihed by group and phae velocitie (ee formula 2). j,k S 2 x 2 vrm j = exp if t + k ( ) j,k GR = exp i + x ( 2) 2 j f 0 vp j f f 0 k vg j For a j th event: t o i the zero offet travel time, x k i the true hot to receiver ditance, f 0 i the central frequency of the wave and vp j and vg j are the phae and group velocitie extracted from the input data. Thee event form the component of the matrix A with column and row indice j and k.
In the frequency domain, the input data i repreented by a matrix D which can be decribed by a matrix A that contain the diperive linear and hyperbolic event multiplied by a vector W containing an unknown wavelet correponding to the ignal and GR plu a percentage of random noie N (ee formula 3). D = AW. + N (3) Rewriting formula 3 in appropriate term, a leat quare iterative inverion approach i ued to extract the GR from the input data. Notice that thi cheme i efficient if the current frequency i reaonably cloe to the defined central frequency. However in mot cae the GR may have a bandwidth of more than 30 Hz! Thi dilemma, however, i reolved by plitting the data into everal frequency band that allow the ue of everal different central frequencie in order to optimize the modeling of the coherent noie. Data example Thi adaptive anti-noie attenuation method i now applied to two data et to demontrate it effectivene. The firt example contain two receiver cable, a central and a broadide cable, extracted from a 3D hot record (figure 2). The top row of figure 2 how the central cable and the bottom row the broadide cable. From left to right, we have ucceively the raw receiver cable, the receiver cable after the adaptive filtering and the difference of both. On both raw receiver high-amplitude diperive GR energy i clearly viible with weaker primary reflection event croing the GR cone (Figure 2a-2c). After the adaptive filtering the GR energy ha been removed, but the weaker reflection event remain the ame (Figure 2b- 2e). Black arrow highlight the fact that no ignal leakage appear on the difference panel (Figure 2c-2f) but that only linear or diperive GR have been uppreed. The econd example how the efficiency of the filtering proce on 2D data. From top to bottom are diplayed the raw tack, the tack after the adaptive filtering (on the raw input hot) and the tack of the noie that ha been removed (difference tack). On the raw tack high amplitude dipping event cro and partially cover the hallow ection and the main primary event (Figure 3a). After the GR filtering on the raw hot the high amplitude low frequency GR ha been completely removed allowing u to ee the continuity of the hallower weak primarie at around TWT (Figure 3b). There i no ignal leakage on the tack of the noie although ome peudo-coherent event appear due to a contructive tack of the GR. Concluion We have decribed a data-driven filtering approach performing a hot by hot adaptive GR attenuation, even with irregular offet ditribution, in order to preerve the ignal amplitude. The GR characteritic are extracted from the data and ued during the Elatic Modeling. Moreover for improved efficiency a cacaded approach on narrow frequency band give the opportunity to ue everal central frequencie. Acknowledgement The author would like to thank Petroleum Development Oman and CGGVerita for their permiion to publih thi paper. Reference Perkin, C. and Zwaan, M. Ground roll attenuation. 62 nd EAGE, Expanded abtract, eion L002.
a b c d e 2 3 4 200 m/ 800 m/ = 300m/ 2 = 500m/ 3 = 600m/ 4 = 700m/ Figure : a) GR velocity map with record location, b-e) the correponding hot record. Figure 2: a) raw input central cable, b) filtered central cable, c) difference between a) and b) d) raw input broadide cable, e) filtered broadide cable, f) difference between d) and e)
2 km Figure 3a: tack of the input data 2 km Figure 3b: tack after an adaptive filtering of the GR on raw hot 2 km Figure 3c: tack of the noie removed during the adaptive filtering