How Do 4-D and 4-C Seismic Work?

I. Purpose and Value-Chain Fit

4-D (time-lapse) seismic and 4-C (four-component seabed) seismic are subsurface imaging and surveillance tools used to understand how reservoirs change during production, injection, or storage. They sit in the subsurface characterization and reservoir management segment of the upstream value chain and directly inform infill drilling, water/chemical/CO2 flood management, pressure maintenance, and well/workover prioritization.

• I.1 4-D seismic (3D + time): Repeats a 3D seismic survey over the same asset to detect time-lapse amplitude changes, time-shifts, and AVO/AVA differences caused by evolving fluid saturations and pressures.
• I.2 4-C seismic (vector seabed sensing): Uses seabed receivers that measure pressure (P) and three-component particle motion (3C) to capture both compressional (PP) and converted shear (PS) wavefields, improving imaging under complex overburden and enabling rock-physics discrimination of fluids and lithology.
• I.3 Combined value: 4-D shows where and how the reservoir is changing; 4-C improves how clearly and reliably we see it, especially beneath gas clouds, basalts, and rugose salt where towed-streamer PP alone struggles.

II. How They Work — Stage-by-Stage

II.A 4-D (Time-Lapse) Seismic Workflow

• II.A.1 Feasibility and planning
  • Screen reservoir for 4-D sensitivity: expected saturation/pressure changes, rock/fluid properties, net thickness, and noise sources (near-surface variability).
  • Model “4-D signal vs. noise” using rock physics and synthetic seismograms to confirm detectability.
  • Define repeatability strategy (same geometry, source, season, tide window).
• II.A.2 Baseline acquisition
  • Acquire high-quality 3D reference survey with documented source/receiver geometry, signatures, navigation, and environmental conditions.
• II.A.3 Monitor survey design
  • Replicate baseline geometry (shot/receiver positions, azimuth, offsets) to maximize repeatability; adjust for obstructions with controlled deviations.
  • Schedule during similar metocean conditions to minimize 4-D noise.
• II.A.4 Acquisition execution
  • Maintain stable source signatures and tow depths; enforce tight navigation tolerances.
  • Real-time 4-D QC: near-surface velocity, feathering, bubble tests, noise floors, positional misfit.
• II.A.5 4-D processing and cross-equalization
  • Geometry match, statics/tidal corrections, deghosting, multiple attenuation, true-amplitude processing.
  • Cross-equalization: design convolutional match filters and spectral balancing to minimize non-reservoir differences.
  • 4-D registration/warping to correct residual time misalignments caused by near-surface changes.
• II.A.6 4-D attribute extraction and interpretation
  • Compute amplitude differences, normalized differences, time-shifts, impedance changes, and AVA/AVO differences.
  • Calibrate with production history, pressure/saturation forecasts, and well logs; update dynamic models.
• II.A.7 Decision support
  • Identify bypassed pay, thief zones, flood front advance, pressure depletion, and caprock/containment anomalies; target infill wells and re-design injection.

II.B 4-C (Four-Component Seabed) Seismic Workflow

• II.B.1 Survey concept
  • Use seabed receivers (cables or nodes) with hydrophone (P) + 3C geophones/accelerometers (X, Y, Z).
  • Acquire with surface sources (typically airguns) in multiple azimuths/offsets to illuminate with PP and PS modes.
• II.B.2 Deployment and coupling
  • Lay cables or place nodes via ROV; ensure firm seabed coupling and known orientation.
  • Calibrate orientation and tilt; verify noise floors and coupling via tap tests or pilot shots.
• II.B.3 Acquisition
  • Record pressure and tri-axial particle motion; manage azimuthal coverage and long offsets for PS imaging.
  • Quality control vector fidelity and positioning; monitor currents, tides, and source repeatability.
• II.B.4 Processing
  • Receiver-side processing: orientation/tilt correction; rotation of X/Y to radial–transverse; polarization filters.
  • PZ summation for deghosting; separate PP and PS wavefields; water-layer multiple attenuation.
  • PS time-depth scaling and registration; anisotropy (VTI/HTI) and shear-wave splitting corrections.
  • Migrate PP and PS volumes (Kirchhoff or RTM); joint PP–PS inversion for elastic properties.
• II.B.5 Interpretation and integration
  • Leverage PS sensitivity to Vs and fractures for lithology and fluid discrimination.
  • Combine PP impedance and PS attributes with wells to refine facies, net-to-gross, and geomechanics.

III. Major Equipment and Components

• III.1 Sources
  • Marine: airgun arrays with tuned volumes for bandwidth and signature stability.
  • Land: vibroseis fleets (sweep control), dynamite in special cases.
• III.2 Receivers
  • Towed streamers (4-D with marine PP) for fast repeat surveys.
  • Ocean-bottom cables (4-C) with hydrophones + 3C sensors; continuous line coverage.
  • Ocean-bottom nodes (4-C, optionally 4-D) for flexible geometry and dense azimuths.
  • Permanent reservoir monitoring arrays (PRM) for high-repeatability time-lapse under producing fields.
• III.3 Deployment and navigation
  • Node handling systems, ROVs, cable-lay spreads, acoustic positioning, DGPS/INS navigation.
• III.4 Recording and QC
  • High-dynamic-range recorders, source controllers, environmental monitoring (tide, currents, metocean), real-time positioning/QC packages.
• III.5 Processing/inversion
  • Compute clusters for deghosting, multiple suppression, tomography/FWI, RTM, and PP–PS joint inversion; databases for baseline/monitor management.

IV. Key Performance Drivers

• IV.1 Repeatability (4-D)
  • Navigation misfit, source depth/signature stability, tow feather match, seasonal timing, and near-surface velocity control determine noise.
  • Target normalized RMS (NRMS) difference on non-reservoir horizons: = 20–30%. See formula in Section V.
• IV.2 Vector fidelity (4-C)
  • Correct sensor orientation and coupling; minimize tilt noise; accurate radial–transverse rotation.
  • Receiver orientation error target: = 5°; tilt = 2–3° (estimated).
• IV.3 Bandwidth and low-frequency content
  • Broader bandwidth improves inversion stability; low frequencies (2–5 Hz) benefit FWI and 4-D time-shift resolution.
• IV.4 Imaging and inversion quality
  • Accurate velocity models (including anisotropy) and consistent true-amplitude migration are critical, especially for 4-D amplitude differences and PS imaging.
• IV.5 HSE and emissions
  • Vessel days drive fuel burn and exposure hours; optimizing source/receiver density and survey efficiency reduces emissions and cost.

V. Challenges, Mitigations, and Core Equations

V.A Typical Challenges and Mitigation

• V.A.1 4-D noise from near-surface changes
  • Challenge: Tides, currents, temperature/salinity, and towing feather alter wavelet and moveout.
  • Mitigation: Seasonal matching, tight navigation, tide corrections, deghosting, adaptive spectral/equalization filters, and residual warping.
• V.A.2 Source/receiver mismatch
  • Challenge: Differences in tow depth, array makeup, or receiver depth/coupling degrade repeatability.
  • Mitigation: Replicate baselines; maintain source QC; use PRM or node redeployment templates; apply PZ summation and consistent processing flows.
• V.A.3 Multiples and wavelet variability
  • Challenge: Surface-related and interbed multiples obscure small time-lapse signals.
  • Mitigation: SRME, model-based demultiple, true-amplitude Q compensation, wavelet-consistent processing across vintages.
• V.A.4 4-C vector issues
  • Challenge: Orientation ambiguity, tilt, poor coupling, and shear-wave attenuation.
  • Mitigation: Orientation from asymptote or direct-arrival methods, tilt correction, coupling QC, polarization filtering, and shear-wave splitting correction.
• V.A.5 Complex overburden and anisotropy
  • Challenge: Gas clouds, rugose salt, and strong VTI/HTI distort amplitudes and kinematics.
  • Mitigation: 4-C PS imaging beneath gas, multi-azimuth acquisition, anisotropic FWI, RTM, and joint PP–PS inversion.

V.B Core Equations and What They Mean

• V.B.1 4-D repeatability metric (NRMS)

  For baseline B(t) and monitor M(t) traces on non-reservoir windows:

  $\displaystyle \mathrm{NRMS} = \frac{2\,\mathrm{rms}[B(t) - M(t)]}{\mathrm{rms}[B(t)] + \mathrm{rms}[M(t)]}\times 100\%$

  Target: = 20–30% for actionable 4-D (lower is better).

• V.B.2 Time-shift from velocity change

  Time-lapse time-shift for PP due to velocity change along depth z:

  $\displaystyle \Delta t \approx \int_{z_1}^{z_2}\left(\frac{1}{V_{p}^{\,\text{monitor}}(z)} - \frac{1}{V_{p}^{\,\text{baseline}}(z)}\right)\,dz$

  Small changes: $\displaystyle \frac{\Delta t}{t} \approx -\frac{\Delta V_p}{V_p}$ (estimated, for thin layers).

• V.B.3 Linearized PP reflectivity (Shuey form)

  Angle-dependent PP reflection coefficient:

  $\displaystyle R_{PP}(\theta) \approx R_0 + G\sin^2\theta + F\left(\tan^2\theta - \sin^2\theta\right)$

  where $R_0 \approx \tfrac{1}{2}\frac{\Delta Z}{Z}$ (Z is acoustic impedance), G relates primarily to $\Delta V_p/V_p$ and $\Delta V_s/V_s$, and F to $\Delta V_p/V_p$.

• V.B.4 Linearized PS reflectivity (concept)

  PS reflections are more sensitive to $\Delta V_s/V_s$ and density than PP. A simplified angle-dependent trend is:

  $\displaystyle R_{PS}(\theta) \propto \sin\theta\cos\theta\left(a\,\frac{\Delta V_p}{V_p} + b\,\frac{\Delta V_s}{V_s} + c\,\frac{\Delta \rho}{\rho}\right)$

  (Constants a, b, c depend on background properties; used qualitatively to emphasize Vs sensitivity.)

• V.B.5 Vector rotation for 4-C receivers

  Rotate horizontal components X, Y to radial R and transverse T using receiver azimuth f:

  $\displaystyle \begin{bmatrix}R\\T\end{bmatrix}=\begin{bmatrix}\cos\phi & \sin\phi\\ -\sin\phi & \cos\phi\end{bmatrix}\begin{bmatrix}X\\Y\end{bmatrix}$

• V.B.6 PP–PS registration (time-domain)

  PS two-way time differs from PP due to slower Vs; a scaling based on $V_p/V_s$ is applied before joint interpretation:

  $\displaystyle t_{PS}(z) \approx \int_{0}^{z}\frac{dz'}{V_s(z')}\quad\text{vs.}\quad t_{PP}(z) \approx \int_{0}^{z}\frac{dz'}{V_p(z')}$

VI. Why It Matters (Economics and Operations)

• VI.1 Recovery uplift and capex efficiency
  • 4-D typically enables +1–5% incremental recovery (estimated) by locating bypassed pay and optimizing injection patterns, often at lower cost than a development well.
  • Better well placement and fewer dry or marginal sidetracks reduce capex and cycle time.
• VI.2 Risk reduction and assurance
  • Tracks flood-front movement and pressure support; early detection of sweep imbalance or thief zones.
  • Monitors containment for CO2 storage and EOR pilots; supports regulatory reporting.
• VI.3 Imaging under complexity
  • 4-C delivers reliable images beneath gas chimneys and complex overburden where PP alone fails, unlocking reserves and improving development plans.
• VI.4 Cost and HSE
  • Permanent arrays and repeatable geometries reduce survey days, vessel fuel burn, and offshore exposure.
  • Efficient surveillance cadence (e.g., every 1–3 years, asset-specific) optimizes NPV vs. monitoring cost.