Questions: Synthetic Seismogram Generation and Forward Modeling

Question 1

A geophysicist constructs a reflectivity series from a 1D earth model but finds it does not resemble the actual seismic trace at the well location. What step is most likely missing?

• A. The reflectivity series needs to be transformed to the frequency domain before comparison
• B. The reflectivity series must be convolved with a source wavelet to produce the synthetic seismogram
• C. The velocities must be converted from km/s to m/s to match the seismic trace units
• D. The reflection coefficients must be summed to produce a single composite amplitude

Answer: (B)

The reflectivity series is a spike train showing reflection strengths at each interface — it is not yet a seismogram. A real seismic source emits a wavelet (a short oscillating pulse), not an infinitely sharp spike. The recorded seismogram is the convolution of the reflectivity series with this wavelet: each spike is replaced by a scaled, time-shifted copy of the wavelet, and all copies are summed. Without this convolution, there is no physically meaningful comparison to recorded data. The convolution step is the core of synthetic seismogram generation.

Question 2

Two geological layers are separated by 20 meters of depth. The dominant seismic wavelength is 80 meters. What does synthetic seismogram theory predict about resolving these layers as separate reflections?

• A. The layers will be clearly resolved because any interface produces a reflection regardless of spacing
• B. The layers will appear as a single composite reflection because their spacing is at or below the tuning thickness of one-quarter wavelength
• C. The layers will produce identical synthetic traces regardless of the wavelet used
• D. Resolution depends only on acquisition geometry and source energy, not on wavelength

Answer: (B)

The vertical resolution limit for conventional seismic reflection is approximately one-quarter of the dominant wavelength — the tuning thickness. With a dominant wavelength of 80 m, the tuning thickness is ~20 m. Two interfaces separated by 20 m or less produce reflected wavelets that overlap in time, interfering constructively or destructively into a single composite waveform rather than two distinct reflections. This is a fundamental physical limit imposed by wave physics, not an equipment limitation. Synthetic seismograms explicitly model this blending through the convolution operation.

Question 3

A synthetic seismogram is computed by convolving the reflection coefficient series with a source wavelet, where reflection coefficients at each interface depend on the acoustic impedance contrast across that boundary.

• T. True
• F. False

Answer: True

This is the complete, correct definition of the synthetic seismogram workflow. Acoustic impedance Z = ρV (density × velocity). Reflection coefficient at each interface R = (Z₂ − Z₁)/(Z₂ + Z₁). The sequence of these R values plotted against two-way travel time is the reflectivity series. Convolving this with the source wavelet produces the synthetic seismogram. Every element in this chain is directly grounded in the physics of elastic wave propagation and the mathematics of linear convolution.

Question 4

Synthetic seismograms generated from well-log data are primarily used to predict seismic responses in undrilled areas, because they reveal the geology where no wells exist.

• T. True
• F. False

Answer: False

Synthetic seismograms are generated FROM well data and are used to calibrate the seismic interpretation AT the well location — this is the 'well tie.' By matching the synthetic trace to the actual recorded seismic trace at the known well, interpreters verify which seismic wiggles correspond to which geological boundaries. This verified calibration then allows extending the interpretation AWAY from the well into areas covered by seismic but without wells. Synthetics illuminate geology at a known location, not in unknown undrilled areas.

Question 5

Explain why convolution of the reflectivity series with the source wavelet is the central operation in synthetic seismogram generation, and what physical process this convolution represents.

Model answer: A real seismic source emits a wavelet — a short oscillating pulse — not an infinitely sharp spike. When this wavelet reaches each subsurface interface, a reflected copy of the wavelet is generated, scaled by the reflection coefficient at that interface. The total seismogram at the surface is the sum of all these scaled, time-shifted wavelet copies. Convolution is precisely the mathematical operation that replaces each spike in the reflectivity series with a scaled wavelet copy and sums them all — representing the physical superposition of reflected waveforms.

Understanding convolution as a physical process rather than a mathematical trick is key. The source emits one pulse; it arrives at many interfaces at different travel times; each interface sends back a reflected copy of that pulse, scaled by the local impedance contrast. The seismometer records the sum of all these reflections arriving over time. When interfaces are closely spaced, their reflected wavelets overlap in time and interfere — this is why thin beds below tuning thickness appear as one composite wiggle. The wavelet's duration sets the temporal resolution limit, and convolution makes this blurring explicit. Sensitivity analysis — changing layer properties and observing how the synthetic changes — directly exploits this relationship to determine what geology is detectable.