Synthetic CMP gather with primaries and interbed multiples

Theory

Interbed multiple modeling builds a synthetic CMP gather for a horizontally layered (1D) earth model. It produces the primary reflections, the interbed multiples generated between two chosen interfaces, the total field (primaries + multiples + optional noise) and the matching RMS velocity field.

The module needs no input data. Its main purpose is to create a controlled, reproducible test set for IMP (Interbed multiple prediction): the Total field and Vrms velocity outputs can be fed to IMP, and the Interbed multiples output is the exact answer to compare the prediction with.

Model. Each layer is defined by an interval velocity, a thickness and the reflection coefficient of the interface at its base. Interface i is the base of layer i. The module computes the zero-offset two-way time t0 of every interface and the time-weighted RMS velocity down to it.

Primaries are Ricker wavelets placed on the hyperbolic moveout t = √(t0² + x²/Vrms²) of each interface, scaled by its reflection coefficient.

Interbed multiples are generated between the Generator interface (time T1) and the Deep reflector interface (time T2). Order n arrives at t0(n) = T2 + n·(T2 − T1) and moves out with its own RMS velocity Vrms(n)² = (Vrms2²·T2 + n·v12²·(T2 − T1)) / t0(n), where v12 is the Dix interval velocity between the two interfaces. Its amplitude is R_deep · Multiple gain · (−|R_gen·R_deep|)ⁿ, so orders alternate in polarity.

The layer model and the exact multiple times, velocities and amplitudes ("ground truth") are printed to the log, so the T1, T2 and R1·R2 values to enter in IMP can be read from there.

Input data

None. The gather is generated entirely from the parameters.

Parameters

Interval velocities (m/s, comma separated)

Interval velocity of every layer, from top to bottom, in m/s, separated by commas, semicolons or spaces. Default: 2000,2300,2600,3000,3500,4000. At least two layers are required, and all values must be positive.

Layer thicknesses (m, comma separated)

Thickness of every layer in metres, in the same order. Default: 400,350,500,600,400,450. Must have the same number of entries as the velocities.

Reflection coefficients (comma separated)

Reflection coefficient of the interface at the base of each layer, in the same order. Default: 0.2,0.3,-0.25,0.4,0.2,0.5. Must have the same number of entries as the velocities.

Number of samples

Number of time samples per trace (minimum 16). Default: 2000. Record length = Number of samples × Sample rate.

Sample rate

Time sample interval in seconds. Default: 0.002 s (2 ms).

Number of offsets

Number of traces in the gather. Default: 40. Offsets are spaced evenly from 0 to Maximum offset.

Maximum offset

Offset of the last trace, in metres. Default: 2500 m.

Ricker peak frequency

Peak frequency of the Ricker wavelet used for all events, in Hz. Default: 30 Hz.

Wavelet half length

Half length of the wavelet in seconds; the wavelet spans ± this value around each event. Default: 0.05 s. Increase it for low peak frequencies so the wavelet is not truncated.

Generator interface (1-based)

Number of the interface that acts as the generator (the downward reflector of the reverberation), counted from the top starting at 1. Default: 3.

Deep reflector interface (1-based)

Number of the deep interface whose reflection reverberates. Default: 4. Must be deeper than the generator interface and within the model.

Max reverberation order

Number of multiple orders to generate. Range 1-20, default 3. Orders arriving after the end of the record are marked [PAST END OF RECORD] in the log.

Multiple gain (1 = physical)

Scale factor applied to the multiples. Default: 1, which gives physically correct amplitudes. Increase it to make weak multiples easier to see when testing; set 0 to generate primaries only.

Noise level (fraction of peak primary)

Amplitude of random noise added to the Total field, as a fraction of the largest primary amplitude. Range 0-1, default 0 (no noise). The noise uses a fixed random seed, so repeated runs give identical results.

Output data

Total field

Synthetic CMP gather containing primaries + interbed multiples (+ noise). Use it as the Input gather of IMP.

Primaries

The primary reflections only. This is the ideal result of multiple attenuation.

Interbed multiples

The interbed multiples only. Compare it with the Predicted multiples output of IMP.

Vrms velocity

RMS velocity function of the model, on the same time sampling as the gathers and repeated on every trace. Use it as the Vrms velocity input of IMP.

All output gathers are a single CMP (CDP 1) with offset and symmetric source/receiver coordinates filled in the trace headers.

Examples

With the default parameters the interfaces lie at t0 = 0.400, 0.704, 1.089, 1.489, 1.718 and 1.943 s. The generator (interface 3) is at T1 ≈ 1.089 s and the deep reflector (interface 4) at T2 ≈ 1.489 s, so ΔT = 0.4 s and R1·R2 = |−0.25 × 0.4| = 0.1. The multiples arrive at t0 ≈ 1.889, 2.289 and 2.689 s with amplitudes −0.04, +0.004 and −0.0004.

To test IMP on this model, connect Total field and Vrms velocity to IMP and set Generator horizon time = 1.089 s, Deep reflector time = 1.489 s and R1*R2 = 0.1 (or enable Estimate R1*R2 from data). Use Multiple gain > 1 to make the higher orders visible.

Related articles

• IMP (Interbed multiple prediction)
• Adaptive subtraction

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