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Sparse Decon L1 performs model-based sparse deconvolution by recovering a sparse reflectivity series from a seismic trace using a supplied wavelet. The module inverts the convolution model — that is, it finds the reflectivity sequence that, when convolved with the input wavelet, best reproduces the observed seismic trace. The sparsity constraint penalises solutions with many non-zero values, producing a blocky, band-limited reflectivity estimate that is more geologically interpretable than conventional deconvolution output.
Three deconvolution algorithms are available. The L1 method minimises a cost function combining a least-squares data misfit term and an L1-norm sparsity penalty, solved via majorization-minimization with an iterative sparse matrix solver. The L2 method uses a standard Tikhonov (L2-norm) regularization and produces a single closed-form solution without iteration. The L1 sparse method uses Orthogonal Matching Pursuit (OMP) to iteratively identify the strongest reflectors in a greedy fashion, selecting the dictionary atom (wavelet-shifted column) that best correlates with the current residual at each step.
Use this module in post-stack or pre-stack workflows where conventional deconvolution produces an over-smoothed result, or when you want to sharpen thin-bed reflectivity estimates for quantitative interpretation. A well-estimated wavelet is essential: the quality of the deconvolution output depends directly on how accurately the input wavelet represents the seismic embedded wavelet.
The primary data connection carrying the seismic gather to be deconvolved. Connect this to the output of the preceding module in the processing flow. This item carries associated metadata such as the SEG-Y file handle, trace headers, and geometry information that are passed through unchanged to the output.
The seismic gather containing the traces to be deconvolved. Each trace is processed independently. The gather can be any type — shot, CMP, offset, or post-stack. The sample interval of the gather must match the sample interval of the input wavelet; the module will report an error if the two differ.
A single-trace gather containing the wavelet used to drive the deconvolution. This is the assumed embedded wavelet in the seismic data. The wavelet is normalised to unit peak amplitude internally before use, so its absolute scaling does not need to match the data amplitude level. The wavelet must have the same sample interval as the seismic gather, and it must be non-zero — the module will report an error if the wavelet trace contains only zeroes. Typically this wavelet is extracted from the data using a wavelet estimation module or constructed synthetically.
The regularisation (noise) parameter that controls the balance between data fit and sparsity. Default: 0.01 (1%). Internally the parameter is scaled by the RMS amplitude of the data before being applied as the lambda in the L1 or L2 cost function. A smaller value places more weight on fitting the data exactly, producing a denser reflectivity estimate with more spike-like features but greater sensitivity to noise. A larger value enforces stronger sparsity, suppressing weak reflectors but also attenuating genuine thin-bed responses. This parameter applies to the L1 and L2 deconvolution types; it has no direct effect in the L1 sparse (OMP) mode.
The number of iterations used by the iterative solver. Default: 100. Minimum: 1. This parameter is active for the L1 and L1 sparse deconvolution types; it is not applicable to the L2 method, which is solved exactly in a single pass. For the L1 method, more iterations generally improve convergence of the cost function, but the solution often stabilises within 50–100 iterations. For the L1 sparse (OMP) method, this parameter controls the maximum number of reflectors (dictionary atoms) selected; setting it too high can cause over-fitting to noise.
Selects the deconvolution algorithm. Default: L1. Three options are available:
L1 — Iterative sparse deconvolution minimising a combined L1/L2 cost function using a majorization-minimization strategy. Produces a sparse reflectivity series that suppresses gradual, smeared energy in favour of distinct reflectors. Controlled by both the Noise and Number of Iteration parameters.
L2 — Tikhonov-regularised least-squares deconvolution. Produces a single closed-form solution in one pass. Faster than L1 but results in a smoother (less sparse) reflectivity estimate. Controlled only by the Noise parameter; the Number of Iteration parameter is not used.
L1 sparse — Orthogonal Matching Pursuit (OMP) algorithm. Greedily selects the strongest reflector positions one at a time, up to the number specified by Number of Iteration. Produces the most focused, most interpretable result when the true reflectivity is genuinely sparse, but may fail if the number of reflectors is underestimated. The Noise parameter does not affect this mode.