论文标题
通过减少顺序建模的波形反演
Waveform inversion via reduced order modeling
论文作者
论文摘要
我们基于数据驱动的降低顺序模型(ROM),引入了一种新型的波形反演方法。演示是针对声波方程式的,但是该方法可以扩展到弹性或电磁波。数据是通过采集系统收集的压力波的时间解析测量值,该系统用脉冲探测未知培养基并测量产生的波。我们建议通过在速度的当前猜测下从记录的数据计算出的ROM与从建模数据计算的ROM之间的ROM之间的正方形失误来解决速度估计的反问题。我们对ROM进行逐步计算,该计算非线性地取决于数据,但可以使用线性代数的有效方法以非文字方式从它们中获得。我们还解释了如何使ROM对数据不准确。 ROM计算需要完整的阵列响应矩阵,该矩阵与共处的来源和接收器收集。但是,我们表明该计算可以处理该矩阵的近似值,该矩阵是使用插值和互惠在触发器数据中从牵引流数据中获得的。 尽管在没有低频信息的情况下,非线性最小二乘数据拟合的全波倒置方法是具有挑战性的,但由于数据拟合目标函数的多个最小值,我们表明ROM失误目标函数具有更好的行为,即使是初始猜测较差。我们还通过在简单的设置中对目标函数进行明确计算表明,ROM错误拟合目标函数具有凸度属性,而最小二乘数据拟合目标函数显示了多个局部最小值。
We introduce a novel approach to waveform inversion, based on a data driven reduced order model (ROM) of the wave operator. The presentation is for the acoustic wave equation, but the approach can be extended to elastic or electromagnetic waves. The data are time resolved measurements of the pressure wave gathered by an acquisition system which probes the unknown medium with pulses and measures the generated waves. We propose to solve the inverse problem of velocity estimation by minimizing the square misfit between the ROM computed from the recorded data and the ROM computed from the modeled data, at the current guess of the velocity. We give the step by step computation of the ROM, which depends nonlinearly on the data and yet can be obtained from them in a non-iterative fashion, using efficient methods from linear algebra. We also explain how to make the ROM robust to data inaccuracy. The ROM computation requires the full array response matrix gathered with collocated sources and receivers. However, we show that the computation can deal with an approximation of this matrix, obtained from towed-streamer data using interpolation and reciprocity on-the-fly. While the full-waveform inversion approach of nonlinear least-squares data fitting is challenging without low frequency information, due to multiple minima of the data fit objective function, we show that the ROM misfit objective function has a better behavior, even for a poor initial guess. We also show by an explicit computation of the objective functions in a simple setting that the ROM misfit objective function has convexity properties, whereas the least squares data fit objective function displays multiple local minima.