receiver deghosting workflow to mitigate fk-transform artifiacts: a non-windowed approach
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RECEIVER DE-GHOSTING WORKFLOW TO MITIGATE FK-TRANSFORM
ARTIFACTS:A non-windowed Approach
Vikram Jayaram, Dylan Copeland, Charles Sicking*, Carola Ellinger, Stu Nelan and Joshua Gilberg
Global Geophysical Services
Receiver De-Ghosting Without Artifacts
OVERVIEWDEEPLY TOWED MARINE CABLES
• Provides broader band signal in the low frequencies
• Have ghost notches which must be removed for data quality• Ghost is sufficiently delayed in two-way time to allow high fidelity removal
• The ghost delay varies with offset along the cable and with two-way time. This is true for both the flat and the slant cable systems
• Windowing the de-ghost operation in offset and time creates numerical artifacts at the edges of the windows
• We present a method for de-ghosting that does not have the edge effects of windowed processing
Receiver De-Ghosting Without Artifacts
THEORY – OPERATOR IN F-K
• In F-K, the complex operator is given by:
• Where f = frequency, Kx = wave-number, and z = depth
• The location of the notch in frequency is controlled by z and is given by:
• In this expression, z is constant and represents the delay time of the ghost. The ghost delay changes with offset and two-way time.
Receiver De-Ghosting Without Artifacts
ILLUSTRATION OF GHOST VARIATION WITH OFFSET
• Ghost arrival time becomes shorter with longer offset• For the near offset, the ghost has a delay = 2z/Vel, where z is the depth of receiver• For the far offset, the ghost has a delay time that is less than 2z/Vel• The arcs show the wave front at the near and far offset:
• At Near offset, the wave front is moving vertical• At Far offset, the wave front is moving at a high angle to surface
Receiver De-Ghosting Without Artifacts
SYNTHETIC DATA WITH GHOSTTHE GHOST NOTCH VARIES IN TIME-OFFSET AND IN F-K
Tim
e
Fre
qu
en
cy
Offset K
Receiver De-Ghosting Without Artifacts
CONTINUOUS DELAY TIME FOR GHOST OFFSET AND 2-WAY TIME FOR SLANT CABLE
• Black lines are the moveout with offset for reflections
• Color is the delay time of the ghost for the cable depth and offset
• The ghost delay is shorter at long offsets
Note that the delay changes more quickly versus offset for early arrival time events than for later arrival time events
Offset
Tim
e
Receiver De-Ghosting Without Artifacts
AMPLITUDE SPECTRARECORDED DATA, DE-GHOSTED DATA, AND GHOST
For the deeper towed cable, the ghost can be removed with high fidelity
Recorded Data Primary without Ghost Ghost Only Data
Receiver De-Ghosting Without Artifacts
COMPUTE THE DE-GHOST OUTPUT FOR A RANGE OF GHOST DELAYSSTEPS OF ~0.666 MILLISECONDS (0.5 METERS)
WORKFLOW FOR EACH CABLE:• Forward Transform to F-K space
• Select a delta T (Min -> Max)• Apply the de-ghost operator • Inverse Transform to X-T• Output traces for current delta T• Repeat for each delta T
• Result is a 3D volume (time, offset, delta T)• A second application extracts the best de-ghost trace for
each offset in the cable • delta T varies as a function of offset and two-way
time• Trace interpolation is used to construct each de-
ghosted trace in the cable• The optimum de-ghosted traces for the cable is output
from the second application
REPEAT FOR EACH CABLE
Receiver De-Ghosting Without Artifacts
ARTIFACTSWINDOWED DE-GHOST VERSUS CONTINUOUS DE-GHOST
Windowing de-ghost DifferenceContinuous de-ghost
Receiver De-Ghosting Without Artifacts
STACKED SECTION AT WATER BOTTOMBEFORE AND AFTER DE-GHOSTING
Before After
Receiver De-Ghosting Without Artifacts
SUMMARYDE-GHOSTING WITHOUT ARTIFACTS
• The ghost delay varies with offset along the cable and with two-way time. This is true for both the flat and the slant cable systems
• Windowing the de-ghost operation in offset and time creates numerical artifacts at the edges of the windows
• We have presented a method for de-ghosting that provides high quality results that have continuous ghost removal variation in offset and time
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