receiver deghosting workflow to mitigate fk-transform artifiacts: a non-windowed approach

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


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.


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


SYNTHETIC DATA WITH GHOSTTHE GHOST NOTCH VARIES IN TIME-OFFSET AND IN F-K

Tim

e

Fre

qu

en

cy

Offset K


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


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


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


ARTIFACTSWINDOWED DE-GHOST VERSUS CONTINUOUS DE-GHOST

Windowing de-ghost DifferenceContinuous de-ghost


STACKED SECTION AT WATER BOTTOMBEFORE AND AFTER DE-GHOSTING

Before After


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

RECEIVER DE-GHOSTING WITHOUT ARTIFACTS

Thank You to:

Co-authors for their contributions

Global Geophysical for supporting this paper

Contact information:

[email protected]

receiver deghosting workflow to mitigate fk-transform artifiacts: a non-windowed approach

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