  We present a sequential data assimilation algorithm based on the ensemble
Kalman inversion to estimate the near-surface shear wave velocity profile and
damping when heterogeneous data and a priori information that can be
represented in forms of (physical) equality and inequality constraints in the
inverse problem are available. Although non-invasive methods, such as surface
wave testing, are efficient and cost effective methods for inferring Vs
profile, one should acknowledge that site characterization using inverse
analyses can yield erroneous results associated with the inverse problem
non-uniqueness. One viable solution to alleviate the inverse problem
ill-posedness is to enrich the prior knowledge and/or the data space with
complementary observations. In the case of non-invasive methods, the pertinent
data are the dispersion curve of surface waves, typically resolved by means of
active source methods at high frequencies and passive methods at low
frequencies. To improve the inverse problem well-posedness, horizontal to
vertical spectral ratio (HVSR) data are commonly used jointly with the
dispersion data in the inversion. In this paper, we show that the joint
inversion of dispersion and strong motion downhole array data can also reduce
the margins of uncertainty in the Vs profile estimation. This is because
acceleration time-series recorded at downhole arrays include both body and
surface waves and therefore can enrich the observational data space in the
inverse problem setting. We also show how the proposed algorithm can be
modified to systematically incorporate physical constraints that further
enhance its well-posedness. We use both synthetic and real data to examine the
performance of the proposed framework in estimation of Vs profile and damping
at the Garner Valley downhole array, and compare them against the Vs
estimations in previous studies.
