Seismic reflectivity inversion problem can be formulated using a basis-pursuit method, aiming to generate a sparse reflectivity series of the subsurface media. In the basis-pursuit method, the reflectivity series is composed by large amounts of even and odd dipoles, thus the size of the seismic response matrix is huge and the matrix operations involved in seismic inversion are very time-consuming. In order to accelerate the matrix computation, a basis-pursuit method-based seismic inversion algorithm is implemented on Graphics Processing Unit (GPU). In the basis-persuit inversion algorithm, the problem is imposed with a L1-norm model constraint for sparsity, and this L1-norm basis-pursuit inversion problem is reformulated using a linear programming method. The core problems in the inversion are large-scale linear systems, which are resolved by a parallelised conjugate gradient method. The performance of this fully parallelised implementation is evaluated and compared to the conventional serial coding. Specifically, the investigation using several field seismic data sets with different sizes indicates that GPU-based parallelisation can significantly reduce the computational time with an overall factor up to 145. This efficiency improvement demonstrates a great potential of the basis-pursuit inversion method in practical application to large-scale seismic reflectivity inversion problems.

中文翻译：

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使用L1-norm基追踪法和GPU并行化进行地震反射率反演

地震反射率反演问题可以采用基本追踪法来拟定，目的是生成地下介质的稀疏反射率序列。在基本追踪法中，反射率序列由大量偶数和奇数偶极子组成，因此地震响应矩阵的大小巨大，并且涉及地震反演的矩阵运算非常耗时。为了加速矩阵计算，在图形处理单元（GPU）上实现了基于基追踪的地震反演算法。在基本追踪求逆算法中，问题具有稀疏性的L1范数模型约束，并且使用线性规划方法对L1范数的基本追踪求逆问题进行了重构。反演的核心问题是大型线性系统，通过平行共轭梯度法求解。评估了这种完全并行化实现的性能，并将其与常规串行编码进行了比较。具体来说，使用几个具有不同大小的现场地震数据集进行的调查表明，基于GPU的并行化可以显着减少计算时间，总因子最高为145。这种效率的提高证明了基本追踪反演方法在实际应用中的巨大潜力大型地震反射率反演问题。