Improving Resolution of Finite Fault Inversions with Increasing Bandwidth

由于地震的过程不能直接观察到，我们必须通过确定描述断层两侧相对运动的源参数来推断地震过程，即破裂的运动学。在断层的每个点上，源参数是：1)滑动率时间函数，以函数形式表征，通常用几个参数指定；2)破裂时间？相对于地震的起源时间，滑动率函数开始的时间；3)最终滑动，一个分量沿走向而另一个向上倾斜（即垂直于走向分量）的矢量，它给出了断层一侧相对于另一侧的相对位移。研究人员预先假定了断层所处介质的速度和衰减结构，以及断层和震源的几何形状。有了这些信息，我们就可以计算空间中任何一点的地面运动，特别是记录地震的地震和大地测量仪器所在的位置。为了找到源参数，他们将解决一个不断调整源参数的反演问题。每次调整后，他们将计算记录地点的地面运动时间历史（合成时间），并将合成时间历史与记录的时间历史进行比较。同时，他们计算静态位移，以便与大地测量、GPS或InSAR进行比较。使用预定的成本函数来测量数据和合成物之间的不匹配，我们继续调整源参数的过程，直到我们有一个可接受的不匹配水平。直到最近，重点一直放在减少数据和合成之间的不匹配上。然而，现在人们认识到这不是问题，因为任何数量的不同的运动学描述都可以拟合数据。自由参数（即源参数）的数量通常远远大于独立数据的数量，这使得在合成和数据之间找到几乎完美的一致性成为可能。这就提出了两个需要在提案中解决的问题：1)是否有尚未使用的额外数据来约束源参数？2)我们如何确定模型之间的差异，而不是衡量合成与数据之间的不匹配？也就是说，我们如何确定一个源描述是否比另一个源描述更好？地震是自然界最基本的现象之一。两个巨大的土块是如何在几秒钟、几十秒，甚至几百秒的时间内相互移动的（例如，2004年苏门答腊地震；2010年智利Maule地震；2011年日本东北地震），释放积累了数百年或数千年的应变能，这是一个基本的科学问题。这也是一个与社会相关的问题。地震造成的震动和附带效应（如海啸、滑坡）严重影响建筑环境。为了对未来的地震做好准备，了解地震破裂的过程是必要的。通过使用地震的数据，我们可以推断出地震的一些行为。通过研究许多不同的地震，我们可以了解地震的共同特征。我们还可以了解地震的哪些特征对最强震动和辅助效应贡献最大。由于我们无法直接观测到地震，所以我们将地震产生的地震、大地测量和地质数据进行反演，以推断两块地球之间的相对运动。运动学源参数描述了破裂在时间和空间上的演变，即断层上某一点开始滑动的时间（由破裂速度控制）和断层上每一点滑动的增长（由介质的应力松弛控制）。从概念上讲，反演数据类似于找到一组点的最佳拟合线的参数（斜率和截距）。反演震源参数的困难之处在于所寻求的参数数量超过了独立数据的数量。这样就可以找到多个最适合的地震模型。问题是评估一个模型相对于其他同样适合数据的模型有多大的不同，以及不同模型有什么共同的特征。在这两个方面，这些信息可以指导地震模拟，以估计未来地震的地面运动范围。

Because the process of an earthquake cannot be directly observed, we must infer the process by determining source parameters that describe the relative motion between the two sides of the fault, i.e., the kinematics of the rupture. At each point on the fault the source parameters are: 1) the slip-rate time function, characterized by a functional form and generally specified with a few parameters, 2) the rupture time?a time relative to the origin time of the earthquake at which the slip rate function starts and 3) the final slip, a vector with one component along strike and the other up-dip (i.e., perpendicular to the strike component), that gives the relative displacement of one side of the fault with respect to the other. The investigators assume a priori the velocity and attenuation structure of the medium in which the fault is embedded as well as the geometry of the fault and the hypocenter of the earthquake. With this information we can compute the ground motion at any point in space, in particular, at the locations of the seismic and geodetic instruments that recorded the earthquake. To find the source parameters they will solve an inversion problem in which they continuously adjust the source parameters. With each adjustment they will compute ground motion time histories (synthetics) at the recording sites and compare the synthetic time histories with the recorded time histories. At the same time they compute the static displacements for comparison with the geodetic measurements, GPS or InSAR. Using a predetermined cost function that measures the misfit between data and synthetics, we continue the procedure of adjusting the source parameters until we have an acceptable level of misfit. Until relatively recently the emphasis has been on reducing the misfit between the data and the synthetics. However, that is now being recognized as not the issue because any number of different kinematic descriptions can fit the data. The number of free parameters (i.e., source parameters) is often far greater than the number of independent data making it possible to find nearly perfect agreement between synthetics and data. This raises two questions to be addressed in the proposal: 1) Is there additional data, not yet used, to constrain the source parameters? 2) Rather than measure the misfit between synthetics and data, how can we determine the difference between models? That is, how can we decide if one source description is better than another? An earthquake is one of the most fundamental phenomena in the natural world. How two massive blocks of earth move past one another in a matter of seconds, tens of seconds, perhaps a few hundred seconds for the very largest earthquakes (e.g., 2004 Sumatra; 2010 Maule, Chile; 2011 Tohoku, Japan) releasing strain energy accumulated over hundreds or thousands of years is a basic scientific question. It is also a societally relevant question. The shaking and subsidiary effects (e.g., tsunamis, landslides) created by an earthquake critically affect the built environment. In order to prepare for future earthquakes it is essential to understand the process of earthquake ruptures. By using the data from an earthquake we can infer some of its behavior. By studying many different earthquakes we can understand what features are common among earthquakes. We can also understand what features of an earthquake contribute most to the strongest shaking and to the subsidiary effects. Because we cannot directly observe an earthquake, we invert the seismic, geodetic and geologic data created by the earthquake to infer the relative motion between the two blocks of earth. The kinematic source parameters describe how the rupture evolves in time and space, i.e., the time when a point on the fault starts to slip (controlled by the rupture velocity) and the growth of the slip at each point on the fault (controlled by the stress relaxation of the medium). Conceptually the inverting the data is similar to finding the parameters (slope and intercept) of the best fitting line to a group of points. The difficulty with inverting for the source parameters of an earthquake is that the number of parameters being sought exceeds the number of independent data. Thus multiple, best-fitting earthquake models may be found. The problem is assessing how different one model is with respect to other models that fit the data equally well and what features different models have in common. In both respects the information can guide simulations of earthquakes for estimating the range of ground motions from future earthquakes.