2-D Field Data Results  

In 1997, WesternGeco distributed a 2-D dataset, acquired in the Mississippi Canyon region of the Gulf of Mexico, for the testing of multiple suppression algorithms. As illustrated on the CMP-stacked section, Figure , the data contain a variety of strong surface-related multiples which hamper primary imaging, and enough geologic complexity to render one-dimensional multiple suppression methods ineffectual.

 

gulf.stackraw
Figure 1 Stacked Mississippi Canyon 2-D dataset (750 midpoints), annotated with important multiple-generating horizons and multiples, after application of t² gain. Four multiple generators were modeled in the LSJIMP inversion: WB - seabed; R1,R2 - strong shallow reflections; TS - top of salt. Bottom of salt - BS, is also shown. Naming convention for pure first-order multiples: (reflector)M, e.g., R1M. Naming convention for first-order pegleg multiples: (target)PL(multiple generator), e.g., BSPLWB.

In this chapter, I show the results of testing my particular implementation of the LSJIMP technique on 750 CMP locations of the Mississippi Canyon dataset, modeling four multiple generators-the seabed, two strong shallow reflectors, and the top of salt-as labeled by the picks on Figure . Only first order multiples are included in the inversion. Thus in equation (), $n_{\rm surf}=4$ and p=1.

Estimation of a multiple generator's reflection coefficient is a crucially important step in my implementation of LSJIMP. Figures - illustrate the result of applying the reflection coefficient methodology outlined in Section to each of the four multiple generators shown in Figure . Each Figure shows a stack of the local windows around the primary reflection and first pure multiple after alignment with cross-correlation, weighted by a user-defined residual weight which is set to zero where the data appear incoherent, and to one elsewhere. The seabed and R1 reflections (Figures and ) have the greatest coherency, with fairly consistent estimated reflection coefficients across all midpoints, although the R1 pure multiple partially overlaps the strong R2 seabed pegleg and tends to bias the estimated R1 reflection coefficient upward. The short wavelength of the multi-peaked R2 reflection (Figure ) cause offset-dependent tuning effects that somewhat degrades our ability to reliably estimate a reflection coefficient. Lastly, strong head waves and a rugose salt top degrade the coherency of the top-of-salt reflection and its multiple (Figure ), although we can get a fairly reliable estimate between midpoints of about 12000 and 18000 meters.

 

rc.1.gulf Figure 2 Top: Stack of window around seabed reflection (WB). Center: Stack of window around seabed pure multiple (WBM). Bottom: estimated WB reflection coefficient.

 

rc.2.gulf Figure 3 Top: Stack of window around R1 reflection. Center: Stack of window around R1 pure multiple (R1M). Bottom: estimated R1 reflection coefficient.

 

rc.3.gulf Figure 4 Top: Stack of window around R2 reflection. Center: Stack of window around R2 pure multiple (R2M). Bottom: estimated R2 reflection coefficient.

 

rc.4.gulf Figure 5 Top: Stack of window around top-of-salt reflection (TS). Center: Stack of window around top-of-salt pure multiple (TSM). Bottom: estimated TS reflection coefficient.

WesternGeco supplied a depth interval velocity model, so computation of stacking velocities was trivial. I ran LSJIMP with 20 conjugate gradient iterations on 28 CPUs (1.3 Ghz Pentium 3) of a Linux cluster, for a total run time of around 3 hours, including all I/O. Coincidentally, the run time is very similar to the prestack wave-equation depth migration run to generate the results in section .

Figure illustrates the stack of the LSJIMP primary image, $\bold m_0$, which should contain only primaries. From the difference panel (c), note that important above-salt peglegs are almost entirely removed. Primaries are not visibly damaged. Salt rugosity contributes negatively to the separation, by forming diffractions that are not modeled by HEMNO, and by violating HEMNO's small reflector dip assumption. Still, LSJIMP does a fairly good job of removing the specular components of strong salt-related multiples. Some deep multiple energy remains. While unmodeled multiple events, such as internal salt multiples, may explain the residual, another likely contributor is the complex subsalt wave propagation. Time imaging operators like HEMNO generally perform more poorly than depth migration below large velocity contrasts.

 

stackcomp.gulf
Figure 6 Mississippi Canyon stacked section before and after LSJIMP. All panels windowed in time from 3.5 to 5.5 seconds and gained with t². (a) Raw data stack. (b) Stack of estimated primary image, $\bold m_0$. (c) Stack of the subtracted multiples. Prominent multiples labeled as in Figure .

Figures and make the same comparison as Figure , but in small windows to emphasize local features. The geological context of Figure is a generally well-behaved sedimentary basin, with shallow dips and low velocity contrast. Notice that a variety of strong peglegs are largely removed without badly damaging the many updipping primary events in the section. Figure is taken from over the tabular salt body. The multiples visible in this window are effectively separated from the data, even those from the top and bottom of the salt. Weak subsalt primaries, like the anticlinal structure which peaks around CMP 16000 m are not visibly harmed by the separation.

 

stackcomp.zoom.1.gulf
Figure 7 Zoom of Mississippi Canyon stacked section before and after LSJIMP. All panels windowed in time from 3.7 to 4.9 seconds and in midpoint from 500 to 3200 meters and gained with t². (a) Raw data; (b) Estimated primaries ($\bold m_0$); (c) Stack of the subtracted multiples. Multiples labeled as in Figure .

 

stackcomp.zoom.3.gulf
Figure 8 Zoom of Mississippi Canyon stacked section before and after LSJIMP. All panels windowed in time from 3.4 to 4.8 seconds and in midpoint from 13850 to 17850 meters and gained with t². (a) Raw data; (b) Estimated primaries ($\bold m_0$); (c) Stack of the subtracted multiples. Multiples labeled as in Figure . Subsalt primary events labeled ``P''.

Figures - show the LSJIMP results at three midpoint locations. In each Figure, panels (c), (d), (g), and (h) illustrate the estimated total first order multiple from each of the four multiple generators. For instance, to generate the estimated seabed pegleg panel (c), we construct a model vector,  

$$\bold m_{\rm wb} = \left[ \begin{array} {ccccccccc} \bold ... ... \bold 0 & \bold 0 & \bold 0 & \bold 0 \end{array} \right]^T,$$ (29)

where vector $\bf 0$ has the same dimension as a CMP gather and vectors $\bold m_{1,0,1}$ and $\bold m_{1,1,1}$ are the images of the source and receiver peglegs from the seabed. To compute the estimated total first-order seabed pegleg, we simply apply the LSJIMP forward model:  

$$\bold d_{\rm wb} = \bold L \bold m_{\rm wb}.$$ (30)

An analogous process can be repeated for the first-order peglegs from the other three multiple generators modeled here. The modeled data (panel (e)) is simply the sum of the estimated primaries (panel (b)) and the first-order peglegs from the four modeled multiple generators. The residual error (panel (f)) is the difference between the input data and modeled data, with the residual weight applied to account for missing traces in the input.

Figure comes from the sedimentary basin portion of the data. The multiples on this gather have fairly simple moveout behavior. From the relatively small amount of correlated energy on the residual error panel (f), we see that most multiples present in the data are modeled well by LSJIMP. However, notice the introduction of a ``new'' event to the modeled data around $\tau=4.15s$. The R1M event overlaps with R2PLWB, which leads to crosstalk leakage and a poor estimate of R1's reflection coefficient. As we will see later, in section , the nonlinear updating scheme of section helps solve this problem.

 

comp1.4.lsrow.gulf.55
Figure 9 Mississippi Canyon CMP 55 (1440 m). Events labeled as in Figure . All panels NMO'ed with stacking velocity and windowed in time from 3.5 to 5.5 seconds and gained with t². (a) Raw data; (b) Estimated primaries ($\bold m_0$); (c) Estimated WB peglegs; (d) Estimated R1 peglegs; (e) Estimated data (sum of (b), (c), (d), (g), and (h)); (f) Data residual (difference of (a) and (e)); (g) Estimated R2 peglegs; (h) Estimated TS peglegs.

Figure is drawn from the left-hand side of the salt body. The separation results are quite good, both for the relatively simple shallow multiples and for the complex salt-related multiples, which visibly split. A flat event around 4.5 seconds, which appears to be a primary, is actually most likely a pegleg multiple from the base of salt, flattened because the stacking velocity decreases below the salt.

 

comp1.4.lsrow.gulf.344
Figure 10 Mississippi Canyon CMP 344 (9150 m). Events labeled as in Figure . All panels NMO'ed with stacking velocity and windowed in time from 3.5 to 5.5 seconds and gained with t². (a) Raw data; (b) Estimated primaries ($\bold m_0$); (c) Estimated WB peglegs; (d) Estimated R1 peglegs; (e) Estimated data (sum of (b), (c), (d), (g), and (h)); (f) Data residual (difference of (a) and (e)); (g) Estimated R2 peglegs; (h) Estimated TS peglegs.

Figure is drawn from the right-hand side of the salt body. As with Figure , some of the complex splitting behavior in the salt-related peglegs is effectively modeled by HEMNO. In this case, the reflector dips are such that the events split at medium offsets, but happen to coincide at far offsets. Signal events are quite difficult to spot under the multiples, but some shallow events are uncovered.

 

comp1.4.lsrow.gulf.540
Figure 11 Mississippi Canyon CMP 540 (14400.0 m). Events labeled as in Figure . All panels NMO'ed with stacking velocity and windowed in time from 3.5 to 5.5 seconds and gained with t². (a) Raw data; (b) Estimated primaries ($\bold m_0$); (c) Estimated WB peglegs; (d) Estimated R1 peglegs; (e) Estimated data (sum of (b), (c), (d), (g), and (h)); (f) Data residual (difference of (a) and (e)); (g) Estimated R2 peglegs; (h) Estimated TS peglegs.