## 2 Data-Driven Strategies for Stacking Parameter Estimation
### Simultaneous Search Strategy  
The pragmatic search strategy resulted from the need to employ computing resources in the most efficient way, necessitating a bulky and highly complex code. Later, with increasing processing power, it became more and more possible to shift the goal from an efficient to an effective implementation. The authors of [33] presented a global 1 \(\times\) 3 parameter search applied to a small synthetic data set, using a simulated annealing strategy to find the optimum parameter triple. The same approach was later applied to real data by [34; 35; 36] carried out, for a synthetic dataset with a single dipping reflector, a systematic comparison between the pragmatic search strategy and a global 1 \(\times\) 3 parameter search with a very fine grid. Ref. [37] applied a global 1 \(\times\) 3 parameter grid-search with local optimization to very shallow SH-wave data from an urban environment with pronounced lateral velocity variations and low signal-to-noise ratio. Similarly, ref. [38] successfully employed a differential evolution global optimization algorithm without any velocity guide on challenging data sets with low-fold and low signal-to-noise ratio; in addition, ref. [39] used differential evolution for global CRS parameter optimization demonstrating that it provides significantly better parameters and improved stack results for complex salt bodies. The concept of utilizing local slopes instead of coherence as an alternative strategy for stacking parameter estimation was first proposed by [40] and used in a global 3 \(\times\) 1 parameter search scheme. Five years later, ref. [41] applied multi-dimensional local slopes for a global 1 \(\times\) 3 parameter search in a real data study. Estimating the effort of a global three-parameter simultaneous search in pre-stack data compared to a sequence of three line-searches in specific gathers involves consideration of two factors: firstly, the total number of coherency calculations required to create a stacked sample, and secondly, the number of traces included in each coherence calculation. For the simultaneous search, a 3D coherence matrix is computed where each value corresponds to a specific parameter combination, whereas, for the pragmatic search, three 1D coherence vectors are computed successively. In the simultaneous approach, all pre-stack traces within a spatial search aperture contribute to a single coherence calculation while, in the line searches, the search aperture is limited to either an offset range in a CMP gather or a midpoint range in the preliminary stacked section. Assuming a grid search with ten parameter values per dimension and neglecting iterative refinement steps, the simultaneous search requires 1000 coherence calculations, while the three subsequent line searches require only 30. Additionally, a single coherence calculation for a spatial operator in the pre-stack data covers approximately five CMP gathers on average, whereas each line search involves a number of traces comparable to one CMP gather. Based on these calculations, aiming at giving the reader a rough quantitative understanding of the relative numerical effort, the pragmatic search is estimated to be around 166 times faster than the simultaneous search. [PERSON]'s law can be used as a rough measure for how much computing power has increased since the first implementation of CRS stacking. It states that the number of transistors in a dense integrated circuit doubles about every two years (see: [[https://en.wikipedia.org/wiki/[PERSON]](https://en.wikipedia.org/wiki/[PERSON])]([https://en.wikipedia.org/wiki/[PERSON]](https://en.wikipedia.org/wiki/[PERSON]))'s_law, accessed on 29 May 2024). Since transistors are also getting faster, computing power can roughly be assumed to double every 18 months. Consequently, computing power has grown at least by a factor of 1000, between the year 2000 and 2024.