It seems from the original question and several conflicting comments that the images were shot in the following way:

• No flash
• In fairly bright daylight
• Av exposure mode with a fairly wide aperture
• Drive mode set to 'High Speed Continuous', often referred to as "burst" mode.

If that is the case, the issue is most likely one of the following:

• Inconsistency caused by shutter wear or malfunction. Problems with worn shutters usually start showing up at the shortest shutter speeds first. Environmental factors, such as temperature and humidity, could also play a part in the performance of the shutter mechanism.

• Inconsistencies in voltage supplied by the camera's battery, particularly when shooting in high speed continuous burst mode. If the battery is not at almost full capacity, voltage supplied by the battery can drop for each subsequent frame of a continuous burst. This is one reason the vast majority of cameras with electronically controlled shutters include a large capacitor in the shutter power supply relay. But capacitors take time to recharge. The lower the voltage, the longer it takes to recharge a capacitor. Cameras with very high frame rates in burst mode are designed to be optimal only with a battery at or near full voltage. This issue is why maximum burst rate will be lowered by many high end cameras as the battery is used up. It's also why some Nikon bodies are rated at a higher maximum frame rate when using a battery grip with two fully charged batteries than when using a single battery.

• Using Av mode and a very wide aperture with such a bright scene. Forcing the camera to select 1/8000 at ISO 100, both of which are at the extreme edge of the Tv and ISO ranges, could indicate that the scene brightness is out of range for the selected aperture.

How the camera attempts to deal with this last possibility is dependent upon a number of other user selectable settings including the following:

1. 'Safety Shift'. If it is enabled the camera will attempt to ensure proper exposure by changing a parameter manually selected by the photographer. Which parameter is changed first is controlled by whether [Tv/Av] or [ISO] is selected under the [Safety shift] setting in the camera's menu.
2. 'Highlight Tone Priority' can affect how the camera meters the scene. Very slight changes in composition (camera position) can affect the metering and subsequent processing of the raw data when converted to JPEG in-camera.
3. 'Auto Lighting Optimizer' can affect how the camera applies in-camera processing to produce a JPEG image from the raw data. Very slight changes in composition (camera position) can affect the processing of the raw data when converted to JPEG in-camera.
4. 'Metering mode'. What metering mode is selected will affect how the camera exposes the same scene. Particularly with 'Evaluative' metering mode, slight changes in composition (camera position) can affect metering and subsequent processing of the raw data when converting to JPEG in camera.
5. 'Auto ISO'. Will allow the camera to shift ISO based on the results of metering (see #2, 3, and 4 above). The way Canon cameras handle the +1/3 and -1/3 stop ISO settings can also affect the way the raw data is converted and thus affect the brightness of particular areas of the converted jpeg image. Changes to the response curves used for the jpeg conversion will affect areas with different brightness values in the raw data differently.

Based on the results of the brightness variation overlay you showed in the question, where the highlight in the center of the frame are also affected, the first place I would look would be at 'Highlight Tone Priority' and "Auto Lighting Optimizer'.

From a later comment by the OP to the original question:

1. not using flash
2. shooting in daytime in sunlight
3. no, live view is not on
4. exposure mode is Av
5. silent shooting isnt enabled
6. shutter speed is 1/8000, ISO100

1. If you are not using flash you are not shooting with 'High Speed Sync' (please see original answer below).
2. Fairly obvious if your Tv is 1/4000 or shorter.
3. That guess was based upon your statement that you were using HSS. For the bottom of the frame to be darker than the top due to flash energy falloff during the exposure, the shutter curtain must close in the opposite direction from normal. With many top tier Canon cameras this only occurs when using 'Silent Shutter Mode 1' in Live view.
4. Thank you.
5. Please see #3 above.
6. Thank You.

---

The following answer is based upon the use of a flash specific term, 'High Speed Sync', in this comment by the OP to a since deleted answer:

There is a clear pattern I see in a lot of pics. Top-half bright and bottom-half dark. This is shot in High Speed Sync mode in 1D X Mark II... Shutter speed around 1/4000.

You're using High Speed Sync in burst mode. It's not unexpected that the flash might not be able to fully cycle between frames. You're seeing inconsistency with the flash. By the end of the burst the flash doesn't have as much energy in the capacitors for each shot as it had in the beginning.

Since HSS mode uses multiple pulses from the flash to create a more or less constant light from the time the first curtain begins opening until the second curtain fully closes, the flash power can vary significantly as the the narrow slit between the shutter curtains at 1/4000 second transit the frame. When you use HSS in burst mode, the capacitors in the flash probably don't have time to fully recharge between shots.

Unless you are using some very high end studio grade lights you'll never see perfect consistency between each flash in HSS. And you'll only see it then when you allow time between frames for the flash to fully cycle and fully recharge the capacitors.