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How robust is Rayleigh-Marchenko imaging?

This paper evaluates the robustness of Rayleigh-Marchenko redatuming for generating multiple-free seismic images and angle gathers from band-limited data and smooth velocity models, demonstrating its effectiveness in handling mode-converted waves in elastic media and its particular suitability for ocean-bottom and borehole seismic applications despite its underlying acoustic assumptions.

Original authors: Abdul Rahim Md Ars, Abdul Halim Abdul Latiff

Published 2026-07-03

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CC BY 4.0

Original authors: Abdul Rahim Md Ars, Abdul Halim Abdul Latiff

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to take a clear photograph of a hidden object deep inside a foggy, echo-filled room. Every time you shout, the sound bounces off the walls, the ceiling, and the floor before hitting the object and coming back to you. By the time the sound returns, it's a messy jumble of the original shout mixed with hundreds of echoes (multiples). Traditional methods try to clean up this mess by carefully identifying and removing the echoes, but it's like trying to separate a blended smoothie back into individual fruits—it's difficult, often imperfect, and requires you to know exactly what the original fruit tasted like (the source wavelet) to do it right.

This paper introduces a smarter way to take that picture, called Rayleigh-Marchenko imaging. Think of this method not as a cleaner, but as a time-traveling spotlight.

The Core Idea: The Virtual Flashlight

Instead of trying to clean the noisy sound recording, this method uses math to create a "virtual flashlight" inside the ground.

The Setup: You have microphones (receivers) on the ocean floor and speakers (sources) on the surface.
The Magic Trick: The researchers use a smooth, rough map of the ground (a velocity model) and the messy sound recordings to calculate a special "focusing function."
The Result: This function acts like a laser pointer that can be aimed at any specific spot deep underground. It concentrates all the energy exactly where you want to look, effectively ignoring the messy echoes bouncing around elsewhere. It creates a "Green's function," which is essentially a perfect, echo-free record of what happens at that specific virtual spot.

The Big Question: What About the "Ghost" Waves?

The researchers wanted to know: How robust is this method if the ground isn't simple?

In the real world, the ground is "elastic," meaning when a sound wave hits a rock, it doesn't just bounce back as a sound wave (P-wave). It can also turn into a different kind of wave called a shear wave (S-wave), or "mode-converted" wave. It's like throwing a tennis ball at a wall, and instead of bouncing back, it turns into a rubber ball that bounces differently.

The Rayleigh-Marchenko method was originally designed for "acoustic" (simple) environments where this conversion doesn't happen. The paper asks: If we use this simple method on complex, elastic ground full of these "ghost" waves, will the picture still work?

The Experiment: Synthetic and Real Tests

The team tested this in two ways:

The Simulation (The Lab): They created a computer model of the ocean floor that included both simple sound waves and complex shear waves. They ran the "simple" acoustic method on this "complex" data.
The Real World (The North Sea): They applied the method to actual data collected from the North Sea using Ocean Bottom Cable (OBC) sensors.

The Findings: A Clear Picture with Minor Glitches

Here is what they discovered, using simple terms:

It Works Surprisingly Well: Even though the method assumes the ground is simple (acoustic), it managed to produce a clear image of the underground structures even when the data was full of complex, converted waves. It successfully removed the "echoes" (multiples) that usually ruin the picture.
The "Ghost" Artifacts: Because the method didn't fully account for the "ghost" shear waves, there were some faint, blurry spots (artifacts) in the final image. Imagine looking through a very clean window, but there are a few smudges on the glass. You can still see the house outside perfectly, but those smudges are noticeable if you look closely.
No Wavelet Needed: A huge advantage is that this method doesn't need to know the exact "voice" of the source (the wavelet). It figures it out on its own, saving a lot of time and effort.
Cost Savings: Because it handles the echoes so well, you don't need to do expensive, complex preprocessing to clean the data before imaging. You can take the raw data, run it through this "time-traveling spotlight," and get a usable image.

The Verdict

The paper concludes that Rayleigh-Marchenko imaging is robust enough for real-world use, even in complex environments where waves change type.

While the resulting image isn't 100% perfect (those "smudges" from shear waves remain), it is good enough for geoscientists to interpret the underground structure. It successfully maps out where the rock layers are, which is the primary goal. The method is particularly well-suited for ocean-bottom data, where you have sensors on the sea floor that can measure both pressure and particle movement, allowing this "virtual flashlight" to work its magic.

In short: It's a powerful tool that cuts through the noise and echoes to show us the underground, even if the ground is a bit more complicated than the math originally assumed.

Technical Summary: Robustness of Rayleigh-Marchenko Imaging on Elastic Data

Problem Statement
Traditional seismic imaging methods, such as Kirchhoff migration, reverse time migration (RTM), and least-squares migration, typically require input data consisting solely of primary reflections. Multiples (events with more than one reflection point) must be removed prior to imaging, a process that is often challenging, particularly for internal multiples. While methods exist to remove free-surface multiples for marine data, internal multiple removal frequently relies on accurate subsurface models or manual identification of primaries. Furthermore, many advanced imaging techniques that utilize multiples or data-driven approaches still demand detailed velocity models and accurate knowledge of the source wavelet.

Marchenko redatuming offers a data-driven alternative to obtain focused, multiple-free Green's functions from surface reflection data and a smooth velocity model, without requiring prior knowledge of the source wavelet. However, standard Marchenko redatuming assumes co-located sources and receivers and relies on an acoustic approximation. In elastic media, the presence of mode-converted waves (e.g., P-to-S conversions) and "fast multiples" creates a complex transmission coda that acoustic formulations cannot fully resolve. The central problem addressed in this study is the robustness of applying acoustic Rayleigh-Marchenko redatuming to elastic seismic data (specifically Ocean-Bottom Cable or OBC data) where mode-converted waves are present and expected to interfere with the imaging process.

Methodology
The authors assessed the robustness of Rayleigh-Marchenko redatuming and subsequent imaging using a combination of synthetic and field data:

Synthetic Data Generation:
- Models: A 2D synthetic model was constructed using P-wave velocity, S-wave velocity (derived empirically as roughly half the P-wave velocity), and density models.
- Acquisition: 376 shots were fired at 10 m depth with 8 m intervals. 376 receivers were placed on the seafloor at 50 m depth with 8 m intervals.
- Data Types: Two datasets were generated using a finite-difference modeling program (fdelmodc):
  - Acoustic Data: Serving as a reference where theoretical assumptions are met.
  - Elastic Data: Including both P-waves and S-waves to simulate realistic mode conversions and stronger multiples.
- Input Processing: The input data (surface pressure and vertical particle velocity) were separated into upgoing and downgoing components in the frequency-wavenumber domain. A smooth velocity model was used to estimate direct arrivals, simulating a realistic scenario where the true model is unknown.
Field Data Application:
- The method was applied to a 2D line of North Sea OBC field data.
- The imaging zone was defined within the red rectangle of the acquisition geometry (Fig. 7).
- Results were compared against a single-scattering imaging result derived from the up-going component of the particle velocity data.
Imaging Workflow:
- The Rayleigh-Marchenko approach was used to estimate focusing functions and Green's functions ( $G^{\pm}$ ) for virtual sources at various subsurface depths.
- These functions were used to generate target-oriented images and true-amplitude common-image gathers (CIGs).
- The study specifically tested the "acoustic" Rayleigh-Marchenko formulation against "elastic" input data to observe the impact of ignoring mode conversions.

Key Contributions and Results

Green's Function Estimation:
- In the acoustic case, the Rayleigh-Marchenko estimates of the Green's functions matched the true forward-modeled functions with high accuracy.
- In the elastic case, where the input data contained mode-converted waves but the redatuming algorithm remained acoustic, the estimated Green's functions still showed a "satisfactory match" to the true Green's functions, despite the theoretical mismatch.
Imaging Performance:
- Acoustic Data: The imaging of acoustic data resulted in a "perfect" cancellation of multiples and clear imaging of primary events.
- Elastic Data: When applied to elastic data, the acoustic Rayleigh-Marchenko method successfully imaged all primary reflectors. However, the presence of shear waves introduced specific artifacts:
  - Faint artifacts appeared at specific depths (approx. 1050 m, 1110 m, 1520 m, and 1590 m), attributed to remnants of shear multiples or strong shear wave events.
  - Common-Image Gathers (CIGs) showed visible effects from shear wave events, which could influence Amplitude Versus Offset (AVO) analysis.
- Field Data: The application to North Sea OBC data demonstrated that the Rayleigh-Marchenko image reduced artifacts related to improper handling of multiples compared to the single-scattering image.
Operational Advantages:
- The method requires no prior multiple removal preprocessing.
- It does not require knowledge of the source wavelet.
- It relies only on a smooth velocity model and band-limited dual-sensor data (pressure and vertical particle velocity).

Significance and Claims
The paper claims that acoustic Rayleigh-Marchenko redatuming is robust enough to provide interpretable subsurface seismic images even when applied to elastic data containing mode-converted waves.

While the authors acknowledge that significant shear wave events influence the resulting CIGs and amplitude analysis (potentially limiting quantitative interpretation of AVO), they conclude that the resulting seismic image is "adequate for a reasonable seismic interpretation." The study highlights that the method offers a significant cost saving in seismic processing by eliminating the need for complex multiple removal steps or precise source wavelet deconvolution. The approach is identified as particularly suitable for ocean-bottom, source-over-spread streamer, and horizontal borehole seismic data where dual-sensor measurements are available.