Synthetic Seismogram Generation under Specific Reflection Coefficients and Conditions

Synthetic seismograms serve as essential tools in seismic exploration, simulating formation reflection characteristics to aid in interpreting actual seismic data. In MATLAB implementation, generating synthetic records under specific reflection coefficient conditions typically involves three core computational steps: reflection coefficient sequence design, seismic wavelet generation, and convolution synthesis.

First, the reflection coefficient sequence must be manually defined according to the target geological model. Users can specify reflection coefficient values at different depth positions using arrays, where positive and negative values represent interfaces with increasing or decreasing acoustic impedance respectively. For instance, thin interbedded formations can be simulated by alternately setting positive and negative coefficients. Code implementation involves creating a time-depth vector and corresponding amplitude array, often using MATLAB's array indexing capabilities for precise layer positioning.

Second, selecting appropriate seismic wavelets (such as Ricker wavelets) and configuring their dominant frequency and phase parameters is crucial. The wavelet's dominant frequency determines the resolution of synthetic records, while zero-phase or minimum-phase selections impact waveform symmetry. MATLAB's signal processing toolbox provides built-in functions like rickerWavelet for wavelet generation. The convolution operation between wavelet and reflection coefficients, implemented using conv function, produces preliminary synthetic seismic traces.

Finally, waveform visualization of synthetic records is achieved through the wigb function. This specialized plotting function uses time as the vertical axis and amplitude as the horizontal axis, employing variable-area or variable-density displays to accentuate peak/trough characteristics. Users can adjust wigb's fill colors and scaling parameters through function arguments to make synthetic records resemble actual seismic section morphology more closely.

For complex conditions (such as noise contamination and absorption attenuation), random noise addition post-convolution or Q-filter application can simulate actual seismic wave propagation effects. MATLAB's awgn function adds controllable Gaussian noise, while frequency-domain filtering algorithms mimic attenuation. This parametric flexibility enables synthetic records to adapt to various geological scenario analysis requirements through systematic parameter modulation.