Description

Post RTM 3D builds a 3D depth-domain result from an already-stacked (post-stack) seismic volume using acoustic reverse time migration (RTM). Depending on the Modelling type you select, the module can forward-model a synthetic post-stack response from a depth velocity volume (Exploding reflector), migrate a real post-stack time volume into depth (Post-stack RTM), or automatically refine the input depth velocity volume by iteratively comparing modeled and real data (FWI - full-waveform inversion). Use it when you need a fast, GPU-accelerated depth image directly from stacked data, want to QC a velocity model by generating a synthetic response from it, or want to sharpen a velocity model before running a full pre-stack depth migration.

Input data

Depth velocity

A 3D depth-domain interval velocity volume (in m/s) that describes the subsurface velocity field used to propagate and image the wavefield. The module reads the grid geometry - inline/crossline spacing, depth sample interval, elevation datum and velocity range - directly from this volume and uses it to build the modeling grid for all three Modelling type options. All traces in the volume must share the same elevation datum, and that datum must lie above the shallowest topography point, or you will get a validation error when the input is connected.

Time stack

The input post-stack, time-domain seismic volume to be migrated (used by Post-stack RTM) or compared against modeled data at every iteration (used by FWI). Its sample interval and trace count are read automatically once you connect it, and are shown in the Input data detected parameters group below.

Wavelet

The source wavelet used to forward-model the synthetic response in Exploding reflector mode, and to model and correlate synthetic data against the real Time stack during FWI. It should match the frequency content and, ideally, the phase of the real data as closely as possible. Not required when Modelling type is set to Post-stack RTM.

Output filename

The path and name of the .gsd file that will store the module's result. Unlike the other items in this section, this is not data you supply - it is where g-Platform writes the output. Depending on the Modelling type selected, the file will contain the synthetic time-domain stack (Exploding reflector), the depth-migrated image (Post-stack RTM), or the updated depth velocity model (FWI).

Input data detected parameters

These read-only fields are filled in automatically once you connect a Depth velocity and Time stack input. They report the geometry g-Platform detected so you can confirm the volumes are what you expect before running the module. You cannot edit them directly - if a value looks wrong, check the source data or its geometry rather than trying to change it here.

Velocity count X

Number of crossline positions found in the connected Depth velocity volume.

Velocity count Y

Number of inline positions found in the connected Depth velocity volume.

Velocity count Z

Number of depth samples in the connected Depth velocity volume.

Velocity DX

Average crossline (X) trace spacing of the Depth velocity volume, in meters.

Velocity DY

Average inline (Y) trace spacing of the Depth velocity volume, in meters.

Velocity DZ

Depth sample interval of the Depth velocity volume, in meters.

Velocity min

Minimum velocity value found in the connected Depth velocity volume, in m/s.

Velocity max

Maximum velocity value found in the connected Depth velocity volume, in m/s. Together with the grid interval (DX) and time step (DT) in Run parameters, this value governs whether the finite-difference modeling is numerically stable - use the Calculate optimum parameters action described under Run parameters to pick consistent values automatically.

Stack DT

Sample interval of the connected Time stack, in ms.

Stack NT

Number of time samples in the connected Time stack.

Parameters

Modelling type

Selects what the module produces. Exploding reflector forward-models a synthetic post-stack response from the Depth velocity volume using the supplied Wavelet - useful for QC-ing a velocity model or generating synthetic test data. Post-stack RTM migrates the real Time stack into the depth domain with acoustic reverse time migration, producing a depth image. FWI (full-waveform inversion) iteratively updates the Depth velocity volume so that an Exploding-reflector-modeled response increasingly matches the real Time stack, effectively refining the velocity model. Choose this first: Run parameters apply to every mode, while FWI parameters, FWI decon params, Bandpass params and most of the standalone parameters below Gradian Type only take effect when Modelling type is set to FWI.

Default: Exploding reflector.

Datum

The elevation of the modeling reference datum, read automatically from the source/receiver datum recorded in the Depth velocity volume. This field is read-only and shown only so you can verify the datum is what you expect - all traces in the Depth velocity volume must share the same datum, and it must lie above the shallowest topography point, otherwise the input is rejected.

Default: 0 m (auto-detected, read-only).

Run parameters

These parameters define the finite-difference modeling/migration grid used by all three Modelling type options. Because the grid interval (DX), the time step (DT) and the maximum velocity in your data must jointly satisfy a numerical stability condition, the toolbar action Calculate optimum parameters lets you pick consistent values automatically: it can either derive a stable DX from your chosen DT, or derive a stable DT (and re-estimate NT) from your chosen DX, using the maximum velocity detected in the Depth velocity volume and, for the DT option, the length of the connected Time stack.

DX

The spatial grid interval of the finite-difference modeling grid, applied equally in the inline, crossline and depth directions, in meters. When this differs from the spacing of the connected Depth velocity volume, g-Platform automatically resamples the velocity model onto a uniform DX x DX x DX grid before modeling. A smaller DX gives a more accurate result at higher computation cost; a DX that is too large for the velocities and frequencies present will produce dispersion artifacts or fail the stability check.

Default: 0 m (auto-filled with the smallest of the detected inline, crossline and depth spacing once a Depth velocity volume is connected). Use Calculate optimum parameters to derive a value consistent with DT and the model's maximum velocity.

DT

The time step used to numerically extrapolate the wavefield during modeling and migration, in ms. It must be small enough, together with DX and the maximum velocity in the Depth velocity volume, to satisfy the numerical stability condition - a run started with an unstable combination is rejected before any computation begins.

Default: 0.5 ms. Use Calculate optimum parameters to compute a stable DT for a given DX, or a stable DX for a given DT.

NT

The number of wavefield-extrapolation time steps computed during modeling/migration. Together with DT this sets the total modeling time (NT x DT), which should be long enough to cover the two-way travel time to the deepest target of interest. When you connect a Time stack, g-Platform re-estimates NT automatically from the stack's recorded length and the current DT - increase it manually if your target is deeper than the current modeling time reaches.

Default: 8000 steps.

Frequency

The dominant frequency the finite-difference modeling grid is designed for, in Hz. Set it close to the peak frequency content of your seismic data - too high a value for the chosen DX risks numerical dispersion artifacts, while too low a value reduces achievable resolution.

Default: 20 Hz, minimum 0.001 Hz.

FWI parameters

These parameters take effect only when Modelling type is set to FWI. They control how the RTM gradient (migration image) is converted at each iteration into a reflectivity estimate that is compared with the real data before being turned into a velocity update.

Smooth window

Length of the time window used to locally average and remove background bias from the reflectivity estimate at each depth point, before it is turned into a velocity update. Applies when Gradian Type is Spike deconvalution or Integration. Increase it to suppress noisy, high-frequency swings in the gradient; decrease it to preserve thin-bed detail.

Default: 0.1 ms, minimum 0.0001 ms.

Reflectivity threshold

A normalized threshold applied to the computed reflectivity/gradient volume (Spike deconvalution and Integration gradient types) to suppress low-amplitude noise before it is used to update the velocity model. Raise it if the FWI update looks noisy; lower it if you appear to be losing real, low-amplitude reflectors.

Default: 0.1 (10%), valid range 0 to 1.

Gradient smooth X

Horizontal (lateral) smoothing applied to the migration gradient before it is used to update the velocity model, expressed as a number of grid points. Larger values produce broader, more geologically plausible velocity updates; smaller values preserve more lateral detail but are more prone to noise.

Default: 20 grid points.

Gradient smooth Z

Vertical (depth) smoothing applied to the migration gradient, in grid points. Keep this small relative to Gradient smooth X, since velocity generally varies more smoothly laterally than with depth.

Default: 2 grid points.

Number of global iterations

The number of FWI update iterations (gradient computation, step-size search, and model update) performed before the final velocity model is written to Output filename. Each iteration is relatively expensive - a full RTM run, plus, when Update type is Dynamic, several additional trial migrations - so start with a small number and check the Misfit chart before committing to a long run.

Default: 10 iterations, minimum 1.

Rho power

Exponent controlling how strongly the frequency-dependent phase-correction ("rho") filter's effect grows with frequency, applied when Do rho is enabled. Higher values apply a stronger correction at high frequencies; leave at the default unless you have a specific reason to change it.

Default: 1.

RHO max freq

Upper frequency limit, in Hz, applied by the rho filter when Do rho is enabled - frequencies above this value are not further boosted. Set it close to the highest useful frequency present in your data.

Default: 120 Hz.

Do rho

When enabled, applies a 90 degree phase-rotation ("rho") filter to the real Time stack before it is compared against modeled data in FWI, which helps align the phase of a zero-phase wavelet response with the recorded data. Turn it off only if you are confident the data and wavelet phase are already consistent.

Default: On.

Do cross corel

When enabled, cross-correlates the real Time stack with the Wavelet before FWI starts, converting the input data into a form directly comparable with the exploding-reflector-modeled response used inside the inversion loop. Leave this on for normal FWI use; disable it only if your Wavelet is already a zero-phase spike, so the raw stack can be used directly.

Default: On.

FWI decon params

Controls for the sparse spike deconvolution used to sharpen the modeled reflectivity when Gradian Type is set to Spike deconvalution.

Lambda

Regularization weight used by the sparse deconvolution that sharpens the modeled reflectivity series during FWI gradient computation. Higher values produce a sparser, more spike-like result; lower values keep more of the original waveform shape.

Default: 0.2 (20%).

Number of iterations

Number of iterations the sparse deconvolution solver runs for at every depth point. Increase it if the deconvolution has not converged; reduce it to speed up each FWI iteration at the cost of a less sharply focused reflectivity estimate.

Default: 100 iterations, minimum 1.

Gradian Type

Selects how the raw RTM gradient (migration image) is converted into the reflectivity signal that FWI compares against the data at each iteration. Classic uses the raw migration image directly. Spike deconvalution additionally runs the sparse spike deconvolution described in FWI decon params to sharpen the reflectivity before comparison. Integration further integrates and normalizes the sharpened reflectivity, and is usually the most stable choice.

Default: Integration.

FWA param

A scaling factor that converts the raw gradient into a physically-scaled slowness (1/velocity) update, by matching the overall size of the gradient to the overall size of the current model's slowness field. Larger values produce bigger velocity updates per iteration - faster convergence, but a higher risk of instability; smaller values are more conservative.

Default: 0.05, minimum 0.00001.

Update type

Chooses how the step size - how far to move the velocity model along the update direction at each FWI iteration - is determined. Static applies a fixed multiplier given by Static update step. Dynamic instead runs an automatic line search (see Start model step, Find model step and Minimum find model step) that tries several step sizes and keeps the one that reduces the misfit the most, at the cost of extra trial RTM runs per iteration.

Default: Static.

Static update step

The fixed multiplier applied to the velocity update at each FWI iteration when Update type is set to Static. Increase it for faster (larger) velocity updates per iteration; decrease it, or switch Update type to Dynamic, if the model appears to overshoot or oscillate between iterations.

Default: 0.1, adjustable from -100 to 100. Only used when Update type is Static.

Min V

Hard lower bound, in m/s, on velocity values during FWI model updates - any updated velocity is clamped so it never falls below this value. Set it close to your expected minimum true velocity (for example, water or very shallow, unconsolidated sediment) to prevent the inversion from producing unphysical low-velocity artifacts.

Default: 1400 m/s, minimum 0.00001.

Max V

Hard upper bound, in m/s, on velocity values during FWI model updates. Set it close to your expected maximum true velocity (for example, hard carbonates or basement) to keep the inversion physically constrained.

Default: 5500 m/s, minimum 0.00001.

Max V deviaton

Maximum relative change allowed in any single grid point's velocity during one FWI iteration, expressed as a fraction of its current value. Lower values make the inversion more conservative and stable between iterations; higher values allow faster changes but increase the risk of instability or geologically implausible jumps.

Default: 0.1 (10%).

Start model step

The initial trial step-size fraction used to start the automatic line search when Update type is Dynamic. This is only the starting point - Find model step controls how it is refined from there. Not used when Update type is Static.

Default: 0.5 (50%), minimum 0.001.

Find model step

The multiplier used to grow or shrink the trial step size at each pass of the Dynamic line search, until the misfit stops improving. Values closer to 1 search more finely but require more trial migrations; values further from 1 search faster but more coarsely. Not used when Update type is Static.

Default: 0.5, minimum 0.001.

Minimum find model step

The smallest trial step-size fraction the Dynamic line search will try before it stops searching and accepts the best value found so far. Lowering it lets the search refine further at the cost of more trial migrations and longer run time. Not used when Update type is Static.

Default: 0.05 (5%), minimum 0.001.

Create sub models

When enabled, writes the intermediate depth velocity model produced at each FWI iteration to disk, in addition to the final result written to Output filename. Turn this on when you want to QC how the velocity model evolves iteration by iteration, or to keep intermediate snapshots from a long FWI run. Requires Path for depth models to be set.

Default: Off.

Path for depth models

Folder where the per-iteration velocity models are saved when Create sub models is enabled. The folder is created automatically if it does not already exist. Only required when Create sub models is on.

Bandpass params

Optional frequency filtering applied to the data used inside the FWI gradient computation, to focus the inversion on a specific bandwidth and suppress noise outside it.

Apply bandpass

Chooses whether, and with what filter shape, a bandpass filter is applied during FWI gradient computation. None applies no filtering. BP applies a trapezoidal (ramped) bandpass defined by Frequency 1-4. BP Butterworth applies a Butterworth bandpass instead. Enable filtering if your data or wavelet contain strong noise or energy outside the useful signal band that could bias the inversion.

Default: None.

Frequency 1

Low end of the filter's rejection band, in Hz - frequencies at and below this value are fully attenuated.

Default: 1 Hz, minimum 0.000001.

Frequency 2

Low end of the filter's pass band, in Hz - frequencies at and above this value pass through at full amplitude (frequencies between Frequency 1 and Frequency 2 are ramped up).

Default: 5 Hz, minimum 0.000001.

Frequency 3

High end of the filter's pass band, in Hz - frequencies up to this value pass through at full amplitude.

Default: 70 Hz, minimum 0.000001.

Frequency 4

High end of the filter's rejection band, in Hz - frequencies at and above this value are fully attenuated (frequencies between Frequency 3 and Frequency 4 are ramped down). Together, Frequency 1-4 should bracket the useful signal bandwidth of your data and wavelet.

Default: 80 Hz, minimum 0.000001.

Epsilon

Taper/ripple control parameter for the bandpass filter. Leave at the default unless you observe filter-related ringing artifacts in the modeled data.

Default: 1 (100%), minimum 0.

Output data

Result volume

The final result of the run, written to the file specified in Output filename (.gsd format), which can be reloaded into g-Platform as a seismic or velocity volume. Its content depends on Modelling type: for Exploding reflector it is a synthetic post-stack time volume; for Post-stack RTM it is the depth-migrated image; for FWI it is the updated depth velocity model after all Number of global iterations have completed.

Intermediate models

During FWI runs, live-updating preview panels (one section along the inline direction, one along the crossline direction, through the middle of the volume) showing the depth velocity model as it evolves after each global iteration, letting you watch the inversion converge without waiting for the final output file.

Exploding reflector models

During FWI runs, preview panels showing the synthetic post-stack response modeled from the current trial velocity model at each iteration and step-size trial, so you can visually compare it against the real data preview below.

Migs

During FWI runs, preview panels showing the raw RTM migration/gradient image computed at each global iteration - the signal that is smoothed and scaled into the next velocity update.

Input stack preview

A preview of the real Time stack after the Do cross corel and Do rho preprocessing steps described under FWI parameters, shown along the inline and crossline directions through the middle of the volume, for visual comparison against the Exploding reflector models preview.

Misfit chart

A chart plotting the data misfit (mismatch between modeled and real data) against the FWI global iteration number, so you can judge whether the inversion is converging and decide how many iterations you actually need for the Number of global iterations parameter.

References

Loewenthal, D., Lu, L., Roberson, R. and Sherwood, J. W. C., 1976, The wave equation applied to migration: Geophysical Prospecting, 24, 380-399.

Baysal, E., Kosloff, D. D. and Sherwood, J. W. C., 1983, Reverse time migration: Geophysics, 48, 1514-1524.